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A simulated annealing method for target-oriented forest landscape blocking and scheduling Liu, Guoliang 2000

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A SIMULATED ANNEALING METHOD FOR TARGET-ORIENTED FOREST LANDSCAPE BLOCKING AND SCHEDULING By GUOLIANG LIU B. Sc. Mechanical Engineering Northeast Forestry University of China, 1985 Master of Forestry The University of British Columbia, Canada, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF FOREST RESOURCES MANAGEMENT We accept this thesis as confirming to the requiredjfStandard T H E UNIVERSITY OF BRITISH COLUMBIA June 2000 © Guoliang Liu, 2000 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Forest Resources Management Faculty of Forestry The University of British Columbia Vancouver, Canada Date: Abstract The objective of this research was to conceptualize and develop a Target-oriented Forest landscape Blocking and Scheduling (TFBS) approach that can assist in solving complex forest landscape transformation problems. T F B S blocks and schedules forest treatments according to the requirements of transforming forest landscapes to desired states and projected forest stand dynamics. Timber flows are the results of the landscape transformations. The forest treatment schedules produced by T F B S not only sustain a wide range of non-timber resources but also maximize and maintain timber flows. T F B S can facilitate the forest management transition from timber harvesting regulation-based planning to desired state-oriented forest planning. A desired state of a forest landscape is a state where all the resource layers on the landscape are in their desired states. The polygons created from overlaying multiple resource layers form the basic units for building the cutblocks. These dynamic cut blocks are combined overtime to create patches and desired landscape structures. Age structures and patch size distributions are used as common indicators for all non-timber resources. Each resource layer is assigned one or more age structures and patch size distributions according to the management objectives. To achieve the objectives of this research, a tool, Forest Simulation Optimization System (FSOS) was developed and tested on a simplified 400-polygon (10 ha per polygon) grid data set as well as a complicated 80,000 ha (18,000 polygons) Tree Farm in the Slocan Valley. The results spatially and temporally demonstrated the processes required in building blocks and patches, transforming forest landscapes to desired states and sustaining the desired states. F S O S is also compared to a time-step simulation model, ATLAS. The results show that TFBS can produce strategies to transform forest landscapes to the same desired states with different initial states and different natural disturbance rates and patterns. TFBS simultaneously blocks and schedules the whole landscape for the entire planning horizon and the impacts of treatments on future landscape states are considered. Adaptive strategies are modified accordingly. It was found that Simulated Annealing (SA) was an efficient algorithm for TFBS problems. No guarantee of optimality can be assured; however, S A can find good solutions within a reasonable time for complex problems. This is difficult or even impossible with directed search methods such as mixed integer programming. Key words: Simulated annealing, target-oriented, landscape modeling, harvest scheduling. ii TABLE OF C O N T E N T S Abstract ii Table of Contents iii List of Tables vi List of Figures vii Acknowledgements xi Chapter 1. Introduction 1 1.1 Problem Background 1 1.2 Objectives 6 Chapter 2. Literature Review 9 2.1 Mixed Integer Programming 10 2.2 Heuristic Approaches 10 2.2.1 Interchange 12 2.2.2 Simulated Annealing 12 2.2.3 Tabu Search Algorithm 13 2.2.3 Evolution Programs 14 Chapter 3. Simulated Annealing Algorithm Applied to Target-oriented Forest Blocking and Scheduling 16 3.1 Forest Landscape Non-timber Resources 17 3.1.1 Wildlife Habitat and Biodiversity 17 3.1.2 Visual Quality 18 3.1.3 Watershed Protection 19 3.1.4 Two Common Indicators for Non-timber Resources 19 3.2 Target-oriented Forest Blocking and Scheduling (TFBS) 21 3.3 Simulated Annealing Applied to T F B S 28 3.3.1 Solution Representation 28 3.3.2 Solution Evaluation 29 3.2.2.1 Patch Size Distribution 29 3.2.2.2 Age Class Structures 31 3.3.2.3 Volume Flow 33 iii 3.3.2.4 Cut block Size 34 3.3.2.5 Profit, Road Construction, Logging and Transportation Costs 36 3.3.2.6 Objective Function 37 3.3.3 Solution Transformation 38 3.3.4 Procedures of simulated annealing for T F B S 41 Chapter 4, Model Testing 44 4.1 Basic Scenario (Scenario S4.1) 46 4.2 Testing Cost Objectives 53 4.2.1. The Effects of Road Construction Costs on Blocking and Scheduling 53 4.2.2. The Effects of Transportation Costs on Blocking and Scheduling 56 4.3, Age Structures and Patch Size Testing Using Different Initial States 59 4.4 Sensitivities of Timber Flows to Natural Disturbances 77 4.5 Comparison with ATLAS 86 4.5.1 ATLAS Runs 86 4.5.2 F S O S Runs 95 Chapter 5. Case Study 104 5.1 Management Layers and Their Objectives 107 5.1.1 Visual Quality Objectives (VQOs) 109 5.1.2 Caribou Connectivity Corridors 110 5.1.3 Wildlife Trees (Stand-level Biodiversity) 111 5.1.4 Landscape Level Biodiversity 111 5.1.5 Riparian Zones 113 5.1.6 Watersheds 114 5.2 Harvest Criteria 115 5.3 Objective Weightings 116 5.4 Results and Discussions 117 5.4.1 Timber Flows 120 5.4.2 Watersheds 122 5.4.3 Visuals 123 5.4.4 Natural Disturbance Type and Biodiversity 123 5.4.5 Wildlife Connectivity Corridor 127 5.4.6 General Observations 128 Chapter 6 Conclusions and Recommendations 129 Literature Cited 132 V List of Tables 3.1 Sample age structure (% of area of a specific layer) 18 3.2 Sample patch size distribution 18 3.3 Example of harvest schedule represented by a 2-dimensional array 29 3.4 A sample solution before transformation 39 3.5 Sample solution after transformation 40 4.1 Testing scenarios 45 4.2 Summary of ten runs with different cooling control parameter (S4.1) 51 4.3 Temporal Performance of SA with cooling rate C=0.01 for scenario S4.1 52 4.4 Parameters for scenarios S4.2.1.1, S4.2.1.2, and S4.3.1.3 53 4.5 Summary of scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3 55 4.6 Parameters for scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3 56 4.7 Summary of scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3 58 4.8 Initial states for scenarios S4.3.1, S4.3.2, S4.3.3, and S4.3.4 60 4.9 Timber flows with different natural disturbances 78 4.10 Descriptions of ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3 87 4.11 Age structure weights for scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3 95 4.12 Summary of ATLAS runs (S4.5.1.1, S4.5.1.2, S4.5.1.3) and F S O S runs (S4.5.2.1, S4.5.2.2, S4.5.2.3) 102 5.1 Summary of TFL #3 Area 107 5.2 Resource Emphasis Layers -< 108 5.3 Visual quality objectives (VQO) 109 5.4 Wildlife trees reserve percentages 111 5.5 Biodiversity age class structure targets and current states 113 5.6 Patch size distribution targets for yang and old stands 113 5.7 Watershed young stand targets and current states 115 5.8 Weighting parameters 117 5.9 Solution times 117 5.10 Timber volume flows of TFL #3 121 VI List of Figures 3.1 Representation of non-timber values at the landscape level by age structure and patch size distributions 20 3.2 Target age structure and patch size distributions 22 3.3 Forest landscape transformations 23 3.4 Combined short- and long-term forest planning 24 3.5 The process that generates resultant polygons 25 3.6 Resultant polygons and attributes 26 3.7 Building cutblocks and patches with resultant polygons 27 3.8 Patch size distribution penalty curve 30 3.9 Age structure penalty curve 32 3.10 Timber volume flow penalty curve 33 3.11 Cut block size penalty curve 35 3.12 Sample acceptance probabilities based on equation 3.14 39 3.13 Procedure for solution initialisation 42 3.14 General procedure for the simulated annealing algorithm 43 4.1 Two-layer block size targets for scenario S4.1 47 4.2 Cut blocks built during the first four periods for scenario S4.1 48 4.3 S A objective function values for each run (scenario S4.1) 49 4.4 Timber flows of the four runs for scenario S4.1 50 4.5 Timber volume per year for 7 different cooling control parameters (10 runs each) for scenario S4.1 51 4.6 Cut blocks for first ten years with different road construction cost ($/Km) for scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3 54 4.7 Timber flows for scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3 56 4.8, Cut blocks build during first ten years with different transportation costs ($/m3/Km) for scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3 57 4.9 Timber flows for scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3 59 4.10 Age sand patch targets for scenario S4.3.1, S4.3.2, S4.3.3, and S4.3.4 60 4.11 Old (>100 year) stands in layer 1 for scenario S4.3.1 62 4.12 Old (>100 year) patches in layer 1 for scenario S4.3.1 62 4.13 Old (>100 year) stands in layer 2 for scenario S4.3.1 63 4.14 Old (>100 year) patches in layer 2 for scenario S4.3.1 63 4.15 Four snapshots of old (>100 year) stands (patches) for scenario S4.3.1 64 4.16 Old (>100 year) stands in layer 1 for scenario S4.3.2 66 4.17 Old (>100 year) patches in layer 1 for scenario S4.3.2 66 4.18 Old (>100 year) stands in layer 2 for scenario S4.3.2 67 4.19 Old (>100 year) patches in layer 2 for scenario S4.3.2 67 4.20 Four snapshots of old (>100 year) stands for scenario S4.3.2 68 4.21 Old (>100 year) stands in layer 1 for scenario S4.3.3 70 4.22 Old (>100 year) patches in layer 1 for scenario S4.3.3 70 4.23 Old (>100 year) stands in layer 2 for scenario S4.3.3 71 4.24 Old (>100 year) patches in layer 2 for scenario S4.3.3 71 4.25 Four snapshots of old (>100 year) stands for scenario S4.3.3 72 4.26 Old (>100 year) stands for scenario S4.3.4 74 4.27 Old (>100 year) stands in layer 1 for scenario S4.3.4 74 4.28 Old (>100 year) patches in layer 1 for scenario S4.3.4 75 4.29 Old (>100 year) stands in layer 2 for scenario S4.3.4 75 4.30 Four snapshots of old (>100 year) stands for scenario S4.3.4 76 4.31 Timber flows with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3 78 4.32 Young (<=20 year) stands with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3 79 4.33 Old (>100 year) stands with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3 79 4.34 Old (>100 year) patches with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3 80 4.35 Natural disturbance pattern for scenario S4.4.2 (0.125% / year random) 81 4.36 Natural disturbance pattern for scenario S4.4.3 (0.25% / year random) 81 4.37 Snapshots of old patches without natural disturbance (S4.4.1) 83 4.38 Snapshots of old patches with 0.125%/year natural disturbance (S4.4.2) 84 4.39 Snapshots of old patches with 0.25%/year natural disturbance (S4.4.3) 85 4.40 Timber flows for ATLAS scenario S4.5.1.1, S4.5.1.2, and S4.5.1.3 88 4.41 Young (<20 year) stands for ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3 90 4.42 Old (>100 year) stands for ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3 90 4.43 Old (>100 year) patches of ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3 91 4.44 Four snapshots of old patches for ATLAS scenario S4.5.1.1 92 4.45 Four snapshots of old patches for ATLAS scenario S4.5.1.2 93 4.46 Four snapshots of old patches for ATLAS scenario S4.5.1.3 94 4.47 Timber flows for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3 96 4.48 Young (<20 year) stands for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3 97 4.49 Old (>=100 year) stands for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3 97 4.50 Old (>=100 year) patches for F S O S scenarios S4.5.2.1, 2, and 3 98 4.51 Four snapshots of old patches for F S O S scenario S4.5.2.1 99 4.52 Four snapshots of old patches for F S O S scenario S4.5.2.2 100 4.53 Four snapshots of old patches for F S O S scenario S4.5.2.3 101 5.1 TFL 3 tenure map 105 5.2 Resultant polygons in TFL #3 106 5.3 Visual Quality Objective areas in TFL #3 109 5.4 Caribou Connectivity Corridors 110 5.5 Biogeoclimatic zones in TFL #3 112 5.6 Watersheds in TFL #3 114 5.7 Objective function values for Scenario S5.2 over 1 million iterations 118 5.8 Harvest blocks for 20 years (4 periods) 119 5.9 Average cut block size over all periods 120 5.10 Timber volume flows over all periods 121 5.11 Young (<35 years) stands of Airy 31.3D watershed 122 5.12 Young (<20 year) stands of V Q O retention area 123 5.13 Old stands (>250 year) of NDT1, Landscape Unit 16 124 5.14 Patch size distribution for NDT1, Landscape Unit 16 126 5.15 Old (>250 year) patches of NDT1, Landscape Unit 16 127 5.16 Young (<40 year) patches of NDT1, Landscape Unit 16 127 5.17 Caribou connectivity corridor mature stands over time 128 X A C K N O W L E D G E M E N T S First and foremost, I would like to extend my gratitude to Dr. John Nelson, who, over the last six years, has provided tremendous support to my studies at UBC. It is his expertise, guidance and financial assistance that made this thesis possible. I would also like to thank Dr. Hamish Kimmins and Dr. Shelby Brumellee for their inputs and advice. Dr. Carl Waters' suggestions certainly helped me improve the study. In addition, I want to thank my friend and colleague, Chad Wardman, for his great time reviewing my thesis. The case study data is provided by Chris Niziolomski and Don Thibodeau from Hugh Hamilton Limited and Alex Ferguson from Slocan Forest Products. And a big "thank you" to Tim Shannon for endless help during my studies at the University of British Columbia since I began my Master's program. XI Chapter 1 Introduction 1.1 Problem Background Forest resource management is shifting from a timber harvesting regulation-oriented approach to a target-oriented1 approach. Although the origins of forest management have been rooted in the desire to sustain forests by supplying of one or more forest values, forest management has frequently failed to achieve its goals (Kimmins, 1995). One of the reasons for this failure is that forest management is usually based on harvesting regulations. For example, maximum opening size and adjacency constraints are typical rules used to prevent large clear-cut areas. Following these harvesting rules can lead, however, to an "undesirable" forest. In British Columbia, today's forests have been created primarily by following adjacency constraints during the last decade, and as a result, are not desirable in terms of wildlife habitat, visual quality, biodiversity2 and natural disturbance regimes. This is because the adjacency regulations have led to fragmentation, and the fragmented forest may take a long time to revert back to a more natural forest. 1 The target-oriented approach is a method of forest management that schedules forest treatments that transform forests into desired states. 2 Biodiversity - Biodiversity (biological diversity) is the diversity of plants, animals and other living organisms in all their forms and levels of organization, and includes the diversity of genes, species and ecosystems, as well as the evolutionary and functional processes that link them (MOF, 1995). 1 Forest ecosystem 3 landscape 4 patterns on Canadian forests have evolved in an unplanned way, through a sequence of individual activities, even though many individual projects were normally well planned and executed. In current practice, forest management involves a "linear" decision-making process. Typically, a number of harvest and silviculture interventions that provide a sustainable wood supply for the working forest are first identified. Next, the interventions are gradually implemented, subject to a host of operating regulations, such as maximum opening size. In the linear approach, forest feedback control does not exist, since there is no stated forest objective as a basis for evaluating forest response to intervention. The harvest level objective may be achieved and the regulations will be followed. The forest that emerges, however, will not be measurable against a target. Management has not focused on achieving a forest condition, and in this case, according to Wardoyo and Jordan (1996), forest management does not exist. Simulation models were developed and used to analyze the impacts of landscape patterns on different resources such as wildlife habitat, water and visual quality. These models follow a rule-based planning philosophy: "we do not know where we are going, but the roads will take us there". Often, this is not true. Numerous regulations may take us nowhere, and numerous roads may take us 3 An ecosystem is any system composed of physical, chemical and biological process active with any space-time unit (Lindeman 1942). More definitions about ecosystem can be found in Kimmins' book "Forest Ecology" (Kimmins, 1987). 4 A landscape is defined as a homogeneous area consisting of repeated interactive and interconnected ecosystems (Forman and Godron 1986). 2 places we might not want to go. Unfortunately, we may not realize it until we have arrived at the wrong place. Nature cannot always create a sustainable forest landscape over the temporal and spatial scales desired by humans or required by wildlife, because of the variation in the occurrence and scale of natural disturbances such as wildfire, insects, disease and windthrow. The life spans of humans and animals are shorter than the rotation of most forests. Within a region, there could be 100% old growth and no young stands for the current generation of humans or wildlife. There could be 100% young and no old growth for the next generation of humans or wildlife in the same region following a large forest fire. Management intervention is, therefore, extremely important in achieving a sustainable forest over the spatial and temporal scales that humans and wildlife desire. Simply protecting the forest from harvesting will not necessarily retain current resource values because forests are not static. All stands are going through a series of developmental stages from regeneration to old stands and back to regeneration. New trees will grow up to replace their parents. Natural disturbances from fires, insects, disease and windthrow will probably consume the old forest sooner or later. Today's old growth will be tomorrow's young growth; today's young growth will be tomorrow's old growth; today's connection will be tomorrow's isolation; and today's isolation will be tomorrow's connection. With proper harvest scheduling, the loss to fire, insects, disease and windthrow can be greatly reduced. In Canada, between 1979 and 1993, fire, insects and disease affected more area in the commercial forest than harvesting 3 (Natural Resources Canada, 1996). On average, natural disturbances affected 0.6% of the forest annually, while only 0.4% of the forest was harvested (Natural Resources Canada, 1996). Ideally, stands should be harvested before fire, insects, windthrow or disease destroy them. Proper scheduling of harvest units may help to reduce timber production costs. Integrated resource management regulations are expensive. A conservative estimate of the annual cost to the people of British Columbia of implementing the B.C. Forest Practices Code is $2.1 billion, equal to $570 per B.C. resident (Haley, 1996). These costs include planning, administration, legal expenses and increased operational costs associated with building and maintaining more roads, road deactivation, logging practices, and modified silvicultural systems (Haley, 1996). Current forest management is complex. Many different interest groups express their concerns about forest management. For example, wildlife experts want some areas to be maintained for habitat and local communities want some areas to be maintained for aesthetic values. Environmentalists may require that a specific ecosystem be protected. Different groups have different indicators for measuring forest conditions. These different values greatly increase the complexity of managing forests. Further complexity is added by dynamic growth of the forest through time. Many forest management problems are caused by conflicts between historical forest management practices and new regulations. The current forest states may be far from the desired state, and we cannot immediately transform 4 the forest to the desired state. Moreover, the desired forest states may change over time. However, by properly scheduling harvest units, we can moderate the conflict, reduce the impacts of new regulations and gradually transform the forest landscape to the desired state. Nelson (1993) viewed the integrated resource management problem as a puzzle, where various non-timber and timber interests represent the pieces. The question is how all these different pieces fit together in timber supply? If these different values fit together properly, all values can be achieved and maintained; if these values do not fit together properly, at a minimum, some outputs will decrease, and at the worst, a feasible solution may not be achievable. Scheduling harvest units is like solving the puzzle. If the harvest units are scheduled properly, there is a better opportunity to maintain all values. If a harvest unit is not treated at the proper time, it will not produce its maximum value and it may adversely affect the scheduling of adjacent stands. Harvest scheduling problems are difficult to solve because of the size of the problem and the constraint structure. The number of possible treatments can grow very large, and finding a good solution becomes computationally difficult. These large-size, non-linear combinatorial optimization problems have been impossible to solve using direct search methods. The current spatial constraints in British Columbia make complicated scheduling problems (i.e. multiple-layer stand age structures and patch size distribution requirements). Regulation-based, time-step simulation models can only generate a number of scenarios and assess the consequences of alternative strategies 5 (Gustafson and Crow, 1996). In other words, the simulation models in themselves do not produce strategies - they only quantify consequences of defined strategies. Considerable effort has been directed towards heuristic search techniques. The heuristic search approach is able to produce near optimal or high quality solutions with acceptable computing time and resources. There are numerous references on regulation-oriented forest harvest scheduling methods. However, there is little' reference available for target-oriented approaches. Forest ecosystem management has to change because of new knowledge and new non-timber values. A target-oriented approach is urgently needed for the new management of forest ecosystems and landscapes. 1.2 Object ives The objectives of this thesis are: • To develop common indicators for non-timber resources at the landscape level; • to develop a target-oriented Forest harvest Blocking and Scheduling (TFBS) method that is capable of transforming forest landscapes to desired states (as measured by the indicators) and sustaining the desired states while maximizing timber flows; and • to apply T F B S and explore tradeoffs between production of timber and non-timber objectives in case studies. The design of T F B S is governed by the following principles: 6 1) T F B S will simultaneously block and schedule treatments to meet timber and non-timber objectives instead of following strict harvest regulations. 2) It will include age-structure and patch-size distribution targets, which are two common indicators used to measure resource values on the landscape. 3) Polygons created from overlaying multiple resource layers will be the basic units to build harvest blocks, and the blocks can be combined over time to form patches. 4) T F B S must be able to create flexible strategies that can adapt to natural disturbance and other uncertainties (Walters, 1986). 5) T F B S must include objective weights that can be altered to control how quickly and strictly targets are achieved. 6) T F B S must include multiple treatments over time so that multiple rotations can be modeled. 7) Treatments will be scheduled by year, so that any reporting period can be selected (1-year, 5-year, 10-year, etc.). The remainder of this thesis is organized by the following chapters: 1. Chapter 2 reviews the literature on forest harvest scheduling methods, models and algorithms used in forest resource planning. 7 2. Chapter 3 describes the simulated annealing algorithm used in the model. It describes how objectives are formulated for timber, age structures, and patches. 3. Chapter 4 contains sensitivity analysis of T F B S using a 400-polygon sample data set, including cooling schemes, road costs, objective weights, and natural disturbance. 4. Chapter 5 is a case study based on a tree farm (18,000 polygons and 80,000 hectares) in the Slocan Valley. This case study has 46 resource layers (such as watersheds, wildlife, visuals) and has many conflicting objectives. Several scenarios are run under different objective weighting schemes. Results are also compared to a time step simulation model. 5. Finally, conclusions and recommendations are in Chapter 6. 8 Chapter 2 Literature Review Most forest harvest scheduling methods share two common characteristics: 1) they follow harvest regulations to schedule harvest blocks, and 2) they block and schedule forest treatments by separate processes. The blocks are laid out for the whole area (and the entire planning horizon) according to current forest states and regulations. Regulation-based models are used to schedule the predetermined blocks. A common objective of forest planning has been to generate a long-term harvest schedule that maximizes the volume harvested (or the net profit), subject to numerous constraints. Typical constraints are: 1) the maximum clear-cut size, and 2) the minimum exclusion period between adjacent clear cuts. In addition, harvest flow and budget constraints are usually added to control resources in each time period. The need to deal with adjacency constraints has been presented in many papers (Synder and Revelle, 1995; Thompson et al., 1973; Jamnick and Walters, 1991; Jones et al., 1991; Torres et al., 1990; Barahona et al., 1992). There have been numerous publications during the last few years about regulation-based harvest scheduling methods based on different optimization techniques. Linear programming (LP) was one of the first methods introduced (Navon, 1971, Thompson et al., 1973). F O R P L A N (Johnson et al 1986, and Kent 1985) was designed to address the problem of optimal scheduling of harvests with linear programming. In addition to solution difficulties, infeasibility occurred 9 frequently. Infeasibility in F O R P L A N can arise from a number of causes, and these are often difficult to identify in tightly constrained problems (Kent, Kelly and Flowers 1985). Recently, dynamic programming was used for solving large-scale adjacency problems (Borges et al., 1999). 2.1 Mixed Integer Programming (MIP) MIP is a specific case of linear programming where some variables are restricted to integer values. There are a few of studies that applied MIP to harvest scheduling (Kirby, 1986, Nelson and Brodie, 1990, and Weintraub et al, 1995). MIP has had limited success because of restricted computing resources as well as difficulties in formulating the problem and interpreting the results (Boston and Bettinger, 1999, Hof et al 1994). In response to problem-size limitations, heuristic techniques have been designed for generating near-optimum solutions. 2.2 Heuristic Approaches An example of a simple heuristic technique is the sampling approach called Monte Carlo Integer Programming (MCIP) (Nelson and Brodie (1990), O'Hara et. al. (1989), Clements et. al. (1990)). This approach is a biased sampling scheme designed to generate feasible solutions. The success of Monte Carlo Integer Programming is directly related to the number of sample solutions generated. If the sample size is very large, MCIP is more likely to obtain near-10 optimal solutions. However, larger sample sizes require longer computing times. The advantage of Monte Carlo Integer Programming is its ability to generate feasible solutions in a short time. However, it is quite inefficient at finding near-optimal solutions. As more problem-specific information becomes available, more efficient algorithms can be designed to take advantage of specific structures. Prioritizing harvest units within simulation models has produced good results (O'Hara et al. 1989, Nelson and Finn, 1991). Prioritized simulation combined with random search methods has also been applied to tactical forest planning problems (Sessions and Sessions, 1991). Other heuristics including Interchange, Simulated Annealing, Tabu Search and Genetic Algorithms begin with a random solution (or a set of random solutions) and successively improve upon it (or them). These improvement methods lead to near-optimal solutions, without the need to generate a large sample, as is the case with the MCIP approach. The time needed to improve an initial solution is less than the time needed to generate a large number of MCIP solutions, so these improvement methods provide high quality solutions in a relatively short time. The differences lie in their strategies for moving towards better solutions and avoiding convergence on local optima. Comparisons of interchange, simulated annealing, and Tabu search were reviewed by Murray and Church (1993). Monte Carlo Integer Programming (MCIP), Simulated Annealing (SA) and Tabu Search (TS) were applied to solve four harvest-scheduling problems (Boston and Bettinger, 1999). The results showed that S A found the best solutions for three of the four problems while TS n found the best solution for one of the four problems. In the next few sections, I review these four common heuristic search algorithms in detail. 2.2.1 Interchange Interchange is a random search method, which is also called the hill-climbing algorithm (Murray and Church, 1993, and Liu, 1985) because only improvement transformations in the solution space are accepted. There have been many successful applications of interchange procedures for 0-1 integer-programming problems. The success of the interchange approach depends primarily on the starting point. The interchange process begins with a feasible solution and maintains feasibility throughout the solution transformations. If there is an adjacency constraint violation, then polygons that violate the rules are set to a non-harvest status. If the new solution maintains feasibility for all other constraints, then its objective function is evaluated. If the transformation results in an improvement, the new solution becomes the current solution. The process continues until no improved transformation can be found. Interchange is simple and works very well for harvest scheduling problems (Liu, 1995). The disadvantage of the interchange procedure is that it is likely to get trapped at local optima. 2.2.2 Simulated Annealing (SA) Simulated annealing is analogous to metal annealing. Metal annealing is the process of particle arrangement when moving from a high-energy state to 12 low-energy state. In a high-energy state, particles are active and able to move freely. As temperature gradually decreases, the particle position gradually freezes. Kirkpatrick et al (1983) first applied simulated annealing algorithms to combinatorial optimization problems based on the work of Metropolis et al. (1953). Since 1980, simulated annealing has been used in many fields such as the design of computer circuits, and transportation networks. The key issue in annealing is how to control the cooling process in order to bring the solid to a low energy state while maintaining the desired particle arrangement. S A differs from interchange in its moving strategy, which attempts to avoid converging on a local optimum. SA begins with a high probability of accepting inferior moves and this probability gradually decreases to zero after a number of iterations. S A has been successfully used for harvest scheduling problems (Lockwood and Moore, 1993, and G. Liu and Nelson 1994, Boston and Bettinger, 1999, Kong 1999). 2.2.3 Tabu Search Algori thm Tabu search has enjoyed numerous successful applications in a wide variety of problem areas (Glover, 1989, Hertz and de Werra, 1990). The tabu search algorithm has been used successfully for solving adjacency problems (Brumelle, et al., 1998, Murray and Church, 1993, Boston and Bettinger, 1999). Murphy (1999) also used Tabu search for allocating stands and cutting patterns to logging crews. 13 Tabu search differs from simulated annealing and interchange in its strategies to overcome local optimality (De Werra and Hertz, 1989). Rather than relying on a functional probability of accepting non-improvement solutions, Tabu search systematically forces the process into new regions of the solution space using short-term and long-term memory search strategies (Glover, 1989, 1990). Short-term memory keeps the process from cycling back into a locally optimal solution that has been identified, and long-term memory is used to boost the process into a solution region that has not been previously encountered. 2.2.4 Evolution Programs During the last 3 decades, there has been a growing interest in problem solving systems based on the principles of evolution and genetics. Such systems maintain a population of potential solutions; they have some selection process based on fitness of individuals, and some recombination operators (Michalewicz, 1991). The evolution program is a probabilistic algorithm that maintains a population of individuals where each individual represents a potential solution to the problem. Each solution is evaluated to give a measure of its "fitness". Then, a new population is formed by selecting the more fit individuals. Some members of the new population undergo transformations by means of "genetic" operators to form new solutions. After a number of generations the program converges -the best individual hopefully represents the optimum solution. The two common operators are: 1) mutation, which introduces new information into the population, and 2) crossover, which spreads the new information throughout the population. 14 Clearly, many evolution programs can be formulated for a given problem. Such programs may differ in many ways; they can use different data structures for encoding a single individual, different "genetic" operators for transforming individuals, different methods for creating an initial population, different methods for handling constraints of the problem, and different parameters (population size, probabilities of applying different operators, etc.). However, they share a common principle: a population of individuals undergoes transformations, and during this evolution the individuals strive for survival. The population undergoes a simulated evolution: at each generation the relatively "good" solutions reproduce, while the relatively "poor" solutions die. Evolution programs are based entirely on the idea of genetic algorithms; the difference is that evolution programs allow any data structure (i.e. chromosome representation) to be used together with any set of "genetic" operators. Classical genetic algorithms use a fixed-length binary string for the individuals and two genetic operators: binary mutation and binary crossover. For harvest scheduling problems, evolution programs are not as efficient as simulated annealing. Crossover operators with adjacency constraints damage the solutions, and it requires a lot of time to repair the damaged solutions. If repairs are not done, considerable time is wasted evaluating infeasible solutions (Liu, 1995). 15 Chapter 3 Simulated Annealing Algorithm Applied to Target-oriented Forest Blocking and Scheduling Applications of simulated annealing, hill climbing and evolution programs to forest harvest scheduling problems were explored in Liu (1995). These methods are random search techniques that start with an initial solution and improve it gradually. Evolution programs simultaneously work with a population of solutions (chromosomes) while simulated annealing works with only one solution. I have found that simulated annealing is relatively simple and provides good solutions within a reasonable time and computing resources. In order to apply the Target-oriented Forest landscape Blocking and Scheduling (TFBS) approach, I have developed a spatial Forest Simulation and Optimization System (FSOS) model. This model is a spatial landscape level model. The spatial data are stored in original GIS formats such as IDRSI, M O S S and ArcView GIS shape files. The remaining data are stored in MS A C C E S S database tables. A spatial data set that includes the proposed harvest units and the road network information is a prerequisite for this model. F S O S uses simulated annealing to schedule harvest units and design forest landscapes according to a wide range of spatial and temporal targets. The fundamental difference between F S O S and rule-based, time step simulation models is that F S O S focuses on creating a desired forest landscape according to a set of objectives, whereas rule-based models generate a harvest schedule and a forest landscape subject to a series of rules. 16 In this chapter, I will identify two common indicators for all the non-timber resources, present the blocking and scheduling process, and describe the simulated annealing algorithm. 3.1 Forest Landscape Non-timber Resources Non-timber values include biodiversity, wildlife habitat, visual quality, and water quality. It is difficult for forest managers to find a common indicator for these resource values. Before developing the target-oriented forest landscape blocking and scheduling approach, I will analyze and summarize the non-timber resources and identify some common indicators. 3.1.1 Wildlife Habitat and Biodiversity The Forest Practices Code (MOF, 1995) acknowledges the importance of landscape ecology concepts by enabling district managers to designate planning areas called landscape units, each with specific landscape objectives. The Biodiversity Guidebook (MOF, 1995) recommends procedures to maintain biodiversity at both the landscape and stand levels. This approach, which uses the principles of ecosystem management, tempered by social considerations, recognizes that the habitat needs of most forest and range organisms are met if a broad range of age classes and landscape patterns are maintained across landscapes. Table 3.1 shows a sample desired age class structure and Table 17 3.2 shows a sample patch 5 size distribution as identified in the Biodiversity Guidebook (MOF, 1995). Table 3.1 - Sample age class structure (% area within a layer). Young (<40 years) Mature (>80 years) Old (>250 years) <23% >54% >13% Table 3.2 - Sample patch size distribution. Patch size (ha) % area within an age class of a layer <40 30-40 41-80 30-40 81-250 20-40 3.1.2 Visual Quality The Recreation Branch of the BC Ministry of Forests produced guidelines for recreation resources in timber supply analysis. To achieve visual landscape objectives, young stand and opening size constraints on harvesting are used when clear-cutting. The maximum percentage harvest permitted for each of the visual quality objectives is set to reflect current management strategies and the conditions of the particular forest with regard to landscape sensitivity and existing visual conditions. All forested areas of the land base, even those not available for harvest (inoperable) are factored into the calculation of cover constraints to reflect their impact on the visual landscape. The impact of these inoperable areas is dependent on their spatial arrangement. 5 A patch is a relatively homogeneous nonlinear area that differs from its surroundings (Forman and Godron 1981) 18 3.1.3 Watershed Protection Watershed protection is usually addressed by employing disturbance constraints with green-up heights based on hydrologic recovery, and maximum disturbance rates based on provincial or regional guidelines for watershed management. Watershed protection at a landscape level can also be represented by age class structure and patch size distribution. 3.1.4 Two Common Indicators for Non-timber Resources From the above description, non-timber resource values at the landscape level can be represented by the following indicators (Figure 3.1): 1) age class structure, and 2) patch size distribution. 19 Non-timber Forest Values Wildlife Habitat Visual Quality Biodiversity Water Quality Other Values Patch Size Distribution Agel Class Distribution Figure 3.1 - Representation of non-timber values at the landscape level by age class structure and patch size distributions. Age Class Structure 'Age class structure' is defined as the percentage of an area occupied by various age classes. In British Columbia, age class structure classifications are taken directly from the B C MOF Biodiversity Guidebook (1995) and are applied by Natural Disturbance Type (NDT 6) within Landscape Units. Patch Size Distribution 'Patch size distribution' is defined as the percentage of an area occupied by various patch sizes. The patch can be defined by age, cover type or the combination of age and cover type. 6 NDT (Natural Disturbance Type) is defined according to the occurring frequency of stand-initializing events. NDT1 = ecosystem with rare stand-initializing events, NDT2 = ecosystem with infrequent stand-initializing events, NDT3 = ecosystem with frequent stand-initializing events (MOF, 1995). 20 3.2 Target-oriented Forest Blocking and Scheduling (TFBS) The T F B S process begins with the selection of management objectives for resources such as visual quality, water, wildlife and biodiversity. Committees of experts in each of these resource areas define the states necessary to meet the specified objectives, and determine age structures and patch size distribution targets. The user ranks the relative importance of these two key parameters (age class structure and patch size distribution) relative to each other and to four other model output parameters listed below: 1) Total Volume Production - This is a measure of the total volume harvested in the planning horizon (i.e. 200 years), 2) Even Volume Flow - This is a measure of the variation in harvest volume between periods, 3) Cut Block Size - This value is constrained within a specified range to eliminate small inoperable cutblocks or excessively large ones, and 4) Timber Values and Production Costs - These values include timber market values and production costs (logging, transportation and road construction) that can be used in short-term planning. Each resource layer on the landscape can have a target age class structure and the stands of each age class can have a patch size distribution (Figure 3.2). 21 Patch Size Target Age Class Target^ 0-40 yrs -20% 1^-120 yrs -20% (121-250 yrs -40% >250 yrs -20% 0-40 ha -30% Wl-80 ha -30% >80 ha -40% 0-40 ha -30% Wl-80 ha -30% >80 ha -40% Figure 3.2 - An example of target age structures and patch size distributions. Figure 3.3 depicts two sample forest landscape states. State 1 represents the current forest landscape, while state 2 represents the desired forest landscape. State 1 is a dispersed small-patch landscape and state 2 is an aggregated large-patch landscape. The transition targets (i.e. wildlife habitat, water quality and visual quality) will be defined by experts according to desired states represented by age class structure and patch size distributions. The 22 transition process must also meet certain biological and economic requirements such as minimum harvest age, harvest priorities and timber flows. 1 - Current State • 2 - Desired State Figure 3.3- Forest landscape transformations. T F B S combines short-term and long-term planning into one process (Figure 3.4). Projections can be made for hundreds of years, and 20-year and 5-year plans can be extracted without further analysis because F S O S schedules all management periods simultaneously. Simultaneous blocking and scheduling for the entire planning horizon allows tradeoffs between the long-term and the short-term. 23 Long-term Management Strategies <—*—» 2 0 Y e a r P , a n "r Short-term Strategies 5 Year Dev't Plan J n — i 1 1 1 1 0" 50 100 150 200 Years Planning Horizon Figure 3.4 - Combined short- and long-term forest planning. Weighting Multiple Objectives Timber and non-timber values are included in the objective function. The objective is to maximize the difference between the timber value and the sum of the weighted deviations of non-timber values from their respective targets. Target values are set for the indicators that measure non-timber values. The model calculates a "penalty" based on the difference between the target for each parameter and the value actually attained in each period. The "penalties" are summed for all periods and weighted according to user preference. To minimize the total "penalty" over the planning horizon, the model attempts to achieve targets sooner for highly weighted values as opposed to lower weighted values. Harvest priorities can be applied to stands with a high probability of damage by fire, insects or windthrow. 24 Block and Patch Building Strategies To provide the flexibility in building blocks and patches, the forest partitioned into polygons through an overlay process (Figure 3.5). Resultant coverage -numerous polygons with unique attributes Figure 3.5 - The process that generates resultant polygons. Each polygon has attributes (e.g. current age, area, stand type, reserve status, etc.) that are essential for landscape level modeling (Figure 3.6). My ID UJ ST Corned Figure 3.6 - Resultant polygons and attributes. 26 The limitation of many models has been in how they define a patch. The term "patch" has been synonymous with "cut block". So to create large patches, these models have to create large cut blocks. Figure 3.7 - Building blocks and patches with resultant polygons. In the F S O S model, the terms "cut block" and "patch" are distinctly different. Patch is defined as a contiguous area of forest cover in a defined age 27 class and with common forest cover attributes, such as species composition (MOF, 1995). The resultant polygons are basic elements, which can be combined to form harvesting blocks, which can amalgamate to build patches over time. This gives great flexibility in harvest scheduling because adjacent polygons can be added or subtracted from the simulated cut block through successive iterations. Figure 3.7 is an example of a young patch that is the result of 9 cut blocks created over 4 harvest periods (1998-2024). 3.3 Simulated Annealing Applied to TFBS The three major elements of simulated annealing include: 1) solution representation, 2) solution evaluation, and 3) solution transformation. In the next sections, I will describe these elements. 3.3.1 Solution Representation The solution can be represented by placing the polygon numbers in a one-dimension array according to the cutting sequence (Liu, 1995). For multiple-rotation scheduling problems, one-dimension arrays will not work and the solution has to be represented by a 2-dimensional array (Table 3.3). The 2-dimensional array shows the cutting times of each polygon during the planning horizon. Additional data sets hold polygon attributes (age, area, adjacent polygons, road network access, etc.) necessary for interpreting the solution. 28 Table 3.3 - Example of harvest schedule represented by a 2-dimensional array. Polygon Id Cut Year 1 2000 2095 2212 2 2050 2165 2255 3 2070 2180 2275 4 2045 2135 2260 3.3.2 Solution Evaluation To evaluate the solution, additional polygon attributes are used to calculate the achieved values for each target over the entire planning horizon. There are six categories of targets: 1) patch size distributions, 2) age structures, 3) cut block sizes, 4) timber flows, 5) total timber volume, and 6) timber value and production costs. The mathematical formulations are described below. 3.3.2.1 Patch Size Distribution When the patch size distribution deviates from the desired patch size distribution, penalties are imposed (Figure 3.8 and equation 3.1). The patch size distribution penalty is: Pds Layers AgeGrp(j)Sizes(l,j) x=2] X £ I PatchF> - <3-1) p=i 1=1 ]=\ k=i Where, p is the period (p = 1,2,3 ... Pds); I is the layer (I = 1,2,3 ... Layers); j is the age class in layer 10 = 1.2,3 ... AgeGrps(l)); 29 k is the patch size group in age class j of layer I (k = 1,2,3 ... Size(l j)); X is the total patch size distribution penalty caused by the deviation of the actual area from the desired area (all patch sizes, all age classes and all layers during all periods); PatchPpyk is the penalty caused by the deviation of the actual area from the desired area of patch size k of age class j of layer I at period p (equation 3.2); Pds is the total number of planning periods; Layers is the total layer number; AgeGrps(l) is the number of age classes in layer I; and Sizes(l,j) is the total number of patch sizes in age class j of layer I. PatchP DPApi j k PApyk Figure 3.8 - Patch size distribution penalty curve. PatchPpi j k = (1 + Wi) (1 + W k ) |DPA p y k - PA p , j k | (3.2) where, PApyk is the actual area of patch size k in age class j of layer I at period p; DPApyk is the desired area of patch size k in age class j of layer I at period p; 30 W| is the weight of layer I (the range is from 0.0 to 1.0 and the default value is 0); and W k is the weight of patch size k (the range is from 0.0 to 1.0 and the default value is 0). Figure 3.8 shows that the penalty is 0 when the actual area PApijk (of patch size k in age class j of layer I at period p) equals the desired number DPApijk. The penalty rate increases when the actual area PApijk deviates from DPApijk. The slopes of these two lines can be changed according to importance of these targets. 3.3.2.2 Age C l a s s Structures To control age class structure, a penalty value is incorporated in the objective function when age class structure deviates from the target age class structure (Figure 3.9 and equation 3.3). The age class structure penalty for the whole solution is: Pds Layers AgeGrpsQ) Y = E E 2 AgeStP p l j (3.3) P=i 1=1 j=i where, Y is the total age class structure penalty caused by the deviation of actual area from the desired area (all age classes, and all layers during all periods); AgeStPpy is the penalty caused by the deviation of actual area from the desired area of age class j of layer I at period p (equation 3.4); Pds is the total number of planning periods; Layers is the total number of layers; and AgeGrps(l) is the total number of age groups in layer I; 31 AgeStPpy = (1 + Wi ) (1 + Wj )|DSA B - SA,j| (3.4) where, SAy is the actual area of age group j in layer I; DSAy is the desired area of the age group j in layer I; W| is the weight of layer I (the range is from 0 to 1 and the default value is 0); and Wj is the weight of age class j (the range is from 0 to 1 and the default value is 0). AgeStPpy 4 ^ • DSAy S A y Figure 3.9 - Age class structure penalty curve. Figure 3.9 shows that penalty is 0 when the actual area of age class j in layer I equals the desired area DSAy. The penalty increases when the actual area of age class j in layer I deviates from DSAy. 32 3.3.2.3 Volume Flow To control the volume flow, a penalty value is incorporated in the objective function (Figure 3.10 and equation 3.5). Total timber production over the entire planning horizon is: Polys Cuts(b) V = S £ Pbc b=l c=l The volume flow penalty is: Pds (3.5) Z = £ FlowPp P=\ where, Pbc is the volume from cut c of polygon b; Cuts(b) is the total number of cuts of polygon b during the planning horizon; Polys is the total number of polygons; V is the total timber production from all cuts (equation 3.5); p is the period (p = 1,2,3 ... Pds); FlowP, (3.6) Figure 3.10 - Timber volume flow penalty curve. Z is the total penalty caused by the deviation of the achieved volume from the desired volume in all periods (equation 3.6); 33 FlowPp is volume flow penalty caused by the deviation of the actual volume from the desired timber volume in each period p (equation 3.7); and Pds is total number of planning periods. FlowPp = ( 1 + W v p ) |DVp - V p | (3.7) where, DV P is the target volume in period p when the harvest volume flow target is applied, otherwise DV P is the average volume flow achieved by the model; V p is the volume harvested in period p; and Wvp is the weight of period p (the range is from 0.0 to 1.0 and the default value is 0). Figure 3.10 shows that penalty rate is 0 when the actual volume V p equals the desired volume DV P . The penalty rate increases when the actual volume V p deviates from the desired volume DV P . 3.3.2.4 Cut Block Size To control cut block size, a penalty value is incorporated in the objective (Figure 3.11 and equation 3.8). The cut block size penalty for the whole solution is: Pds S = £ CsizePp (3.8) P=\ where, S is the cut block size penalty caused by the deviation of actual size from desired size for all periods (equation 3.8); 34 CsizePp is cut block size penalty caused by the deviation of achieved size from desired size in period p (equation 3.9); and Pds is total number of planning periods. Layers BlkN(l) CsizePp = £ X (1+W,) |DS,-S b | (3 .9) /=1 6=1 where, Layers is the number of layers; BlkN(l) is the number of cutblocks layer I; DSi is the desired cut block size of layer I; Sb is the size of cut block b; and W| is the weight of layer I (the range is from 0.0 to 1.0 and the default value is 0). 35 Figure 3.11 shows that penalty is 0 when the actual cut block size Sb equals the desired size DS|. The penalty increases when the actual cut block size Sb deviates from DS|. 3.3.2.5 Profit, Road Construction, Logging and Transportation Costs The road construction and transportation costs per cubic metre are incorporated in the objective function. Costs are most important in the short-term, so the logging, road construction and transportation costs are only applied in the first rotation. Total value is calculated by equation 3.10; the road construction and transportation cost is calculated in equation 3.11; and the profit is calculated from equation 3.12. Periods Polys TValue= £ £ V o l p b * S P p b (3.10) p=\ A=l Periods Polys(p) Cost= E (RoadCpb + TranCpb + LogCpb + OtherCpb) (3.11) p=\ 6=1 P = TValue - Cost (3.12) where, Polys(p) is the number of polygons harvested at period p ; Periods is number of cost control periods (<one rotation). TValue is the timber value produced in the cost control periods, Volpb is the timber volume produced from polygon b in period p; Cost is the total road construction and transportation cost; RoadCpb is road construction cost of block b in period p; 36 TranCpb is transportation cost of block b in period p; LogCpb is the logging cost of block b in period p; OtherCpb is other timber production cost from polygon b in period p; P is the total profit (timber value - cost); and SPpb is the timber price of polygon b in period p ($/m3). 3.3.2.6 Objective Function The objective function (equation 3.13) is: Maximize F = V/Vo - (v^X /Xo+ w 2 Y/Yo + W3Z/Z0 + W4S/S0) + W 5 P / P 0 (3.13) Where, F is the total objective function value (equation 3.13); V is the total timber production; X is the total patch size distribution penalty (equation 3.1); Y is the total age class structure penalty (equation 3.3); Z is the total volume flow penalty (equation 3.6); S is the cut block size penalty (equation 3.8); P is the profit (equation 3.12); Vo, Xo, Yo, Zo, So and Po are initial values (at iteration 1) of V, X, Y, Z, S and P, respectively. V, X, Y, Z, S, and P are not directly comparable because they have different measuring units. To make them comparable, the objective function value at iteration N is the sum of the ratios between the values at iteration N and the initial values (at iteration 1), respectively, w-i, w 2 , w 3, w 4 and w 5 are weighted 3 7 factors for each objective, respectively. The default values of w-i, w 2 , w 3 , W4 and w 5 are 1. Penalties in the objective function are additive. An alternative would be more effective at detecting large deviations within individual planning periods. 3.3.3 Solution Transformation The transformation operation uses the following 3-step procedure: Step 1. Randomly select a polygon, Step 2. Randomly select a cut year for the polygon. This change may affect subsequent cuts of the polygon, which may require adjustments to maintain minimum harvest ages. Step 3. Evaluate the new solution and decide whether it is to be accepted or rejected. The acceptance probability equation used is: P = 1 f o r E a ^ E L (E2-EV)/El P = e ( ^ > f o r E 2 < E 1 (3.14) where, e = 2.71828 (constant); P is the acceptance probability; k is a constant (Boltzmann's constant); T is temperature; Ex is the objective function value of the old solution; and E2 is the objective function value of the new solution. 38 At the beginning iterations, k and T should make P large enough so that the process can escape the local optimum. Gradually the acceptance probability P is reduced to zero as the iterations increase in order to freeze the solution (Figure 3.12). (E1-E2)/E1=-1% (E1-E2)/E1=-0.5% (E1-E2)/E1=-0.1% (E1-E2)/E1=-0.01% Figure 3.12 - Sample acceptance probabilities based on equation 3.14. The solution transformation process is illustrated with the following example (Table 3.4 and Table 3.5): Table 3.4 - A sample solution before transformation. . Polygon Number of First Cut Second Cut Third Cut Fourth Cut Cut Times Year Year Year Year 1 2 2000 2200 2 3 2035 2155 2255 3 2 2055 2345 4 4 2010 2100 2190 2210 5 3 2060 2170 2295 39 Step 1. Randomly select a polygon A, for this example, let A = 2. Step 2. Randomly select a cut B of polygon A among {1, 2, 3}, let B = 2. Transform the solution. In this step, randomly change the cut year (2155) of B of polygon A, let the new cut year be 2175. The subsequent cut year has to be checked to be sure that the minimum harvest age is satisfied. If not, a new cut year has to be selected. All subsequent cut years are checked in the same way. If the last cut year of polygon A is changed, it is necessary to check if more cuts are possible during the planning horizon. In this example, the minimum harvest age is 70 and 2255-2175 = 80 > 70, so it is not necessary to change the third cut year 2255 (Table 3.5). Table 3.5 - Sample solution after transformation. Polygon No. Cut First Cut Second Third Cut Fourth Cut Times Year Cut Year Year Year 1 2 2000 2200 2 3 2035 2175 2255 3 2 2055 2345 4 4 2010 2100 2190 2210 5 3 2060 2170 2295 Step 3. Evaluate the new solution by calculating the timber flows, timber value, production costs, and penalties, and decide whether to accept or reject the transition. If the new solution is equal or better than the previous one, accept the new one immediately; otherwise base acceptance on equation 3.14. The poorer the solution is, the lower is the acceptance probability. The high iteration numbers also have a low acceptance probability (Figure 3.12). 40 The transformation process will be repeated (step 1 - 3) until a maximum iteration is reached, or no acceptable transitions occur in a specified number of tries. 3.3.4 Procedures of Simulated Annealing for TFBS Figure 3.13 shows the procedure for solution initialization. There are five steps in this procedure: Step 1. build a list of available polygons for harvesting according to "hard constraints" such as minimum harvest age; stop if no polygons are in the list. Step 2. randomly select a polygon "x" from the list; Step 3. identify next harvest year range "R" of the selected polygon (the harvest year range is defined according to biological minimum harvest age and maximum harvest age); Step 4. randomly identify a harvest year "y" in the range R of polygon "x"; and Step 5. if "y" is inside the planning horizon, accept the cut and go to step 3, else go to step 1. 41 Build the list of available polygons •4 . Available polygons =0 i f Available polygons >0 Randomly pick a polygon "x" 1 f 1 • Identify next cut year range 1 t Randomly identify next cut year "y" of polygon "x" "y" is inside the plan horizon "y" is outside of planning horizon Accept this cut Figure 3.13 - Procedure for solution initialization. The simulated annealing procedures used in this thesis are summarized in Figure 3.14. After the solution is initialized (Figure 3.13), randomly select and change the harvesting year. The new solution is evaluated. The probability of accepting the new solution is calculated by equation 3.14. 42 J Solution Initialization Iteration = 0 Evaluate Solution Obj 1 = Timber - Age Structure Penalty of all Layers at all periods - Patch Size Penalty of all Layers at all periods - Volume Flow Penalty at all periods - Cutblock Size Penalty at all periods T Iteration = Iteration + 1 Iteration <= Maximum Iteration Number Iteration > Maximum Iteration Number Propose a change T Evaluate Solution Obj2 = Timber - Age Structure Penalty of all Layers at all periods - Patch Size Penalty of all Layers at all periods - Volume Flow Penalty at all periods - Cutblock Size Penalty at all periods T Accept the transition let Obj 1 =Obj2and modify the average flow level i f no timber flow target is specified.. or reject the transition Figure 3.14- General procedure for the simulated annealing algorithm. 43 Chapter 4 Model Testing In this chapter, each function of the F S O S is tested on a simple data set. The sample data set has 400 square polygons and each polygon is 10 hectares in size. The following scenarios (Table 4.1) are tested: 1) The first scenario, S4.1, is used to test sensitivity of the solutions to different starting points and cooling rates. Scenario S4.1 includes block size control, total timber production, and periodic timber flow control. The best cooling scheme was identified according to the performances of all the runs in scenario S4.1, and this cooling scheme is used for all the following scenarios. 2) Scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3 test the sensitivity of road construction cost on block building and scheduling. 3) Scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3 test the sensitivity of transportation cost on block building and scheduling. 4) Scenarios S4.3.1, S4.3.2, S4.3.3 and S4.3.4 test the sensitivity of age structure and patch size distributions under different initial inventories (forest states). 5) Scenarios S4.4.1.1, S4.4.1.2, S4.4.1.3, S4.4.2.1, S4.4.2.2, and S4.4.2.3 are used to compare volume flows, age and patch size distribution results to those generated by a time step simulation model, ATLAS. 44 6) Scenarios S4.5.1, S4.5.2 and S4.5.3 test the sensitivity of natural disturbance on timber flows and patch patterns. Table 4.1 - Testing scenarios. Scenarios Objectives Block Size Total Timber Volume Timber Flow Timber Value Costs Age Structure Patch Size Distribution S4.1 Identify proper cooling schemes. Test block size controls. Yes Yes Yes No No No No S4.2.1.1 S4.2.1.2 S4.2.1.3 Test road cost Impacts on block locations. Yes Yes Yes Yes Yes No No S4.2.2.1 S4.2.2.2 S4.2.2.3 Test transportation cost impacts on block locations. Yes Yes Yes Yes Yes No No S4.3.1 S4.3.2 S4.3.3 S4.2.4 Test age structure, patch size distribution controls. Yes Yes Yes No Yes Yes Yes S4.4.1 S4.4.2 S4.4.3 Test natural disturbance impacts on timber flows and patches. Yes Yes Yes No No Yes Yes ATLAS Runs: S4.5.1.1 S4.5.1.2 S4.5.1.3 Compare time-step simulation model Atlas and FSOS. Yes Yes Yes No No Yes Yes FSOS Runs: S4.5.2.1 S4.5.2.2 S4.5.2.3 Plan horizon (Years) 200 200 200 10 10 200 200 Timber value and costs are applied for 10 years only, because: 1) timber value changes rapidly with market fluctuations and utilization levels, 2) 45 production costs change when technology and harvesting systems change, and 3) roads are rarely laid out beyond 10 years. The planning horizon for all other objectives is 200 years. 4.1 Basic Scenario (Scenario S4.1) The objectives of the basic scenario are to test if the model can build desired block sizes and to identify the best cooling schemes. To simplify the problem, only timber flow and block size controls are applied. Two layers are defined in Figure 4.1, and different target block sizes are applied to each layer. The following assumptions are made: 1) all polygons are 160 years old, 2) all polygons use the same volume-age curves, and 3) adjacent blocks are not allowed in the same period. Adjacent blocks are defined as blocks sharing a common point. To test if blocks are built properly and if different starting points (initial solutions) affect model performance, four runs were conducted with the same parameters but with different starting points. The target block size for layer 1 is greater than or equal to 10 ha and less than 40 ha, while for layer 2 it is greater than or equal to 20 ha and less than or equal to 60 ha. 46 Layer 2 Desired block size: 20 - 60 hectares Desired block size: 10-40 hectares Layer 1 Figure 4.1 - Two-layer block size targets for scenario S4.1. Figure 4.2 shows the blocks built during the first 4 periods of each run. The block patterns are different for each run, but almost all the blocks in the four runs meet the desired sizes. Only one block (circled in run 2, Figure 4.2) in layer 2 is 10 ha which is less than the minimum desired size of 20 ha. 47 Run 1 Run 2 m Run 3 Run 4 _J I 1 • Period 1, • Period 2, W% Period 3, 11 Period 4. — — • = Layer boundary. Figure 4.2 - Cut blocks built during the first four periods for scenario S4.1. Figure 4.3 plots the simulated annealing objective function values for each run. These values are similar for different starting points (all other parameters held constant). This is expected because there are numerous good solutions for this problem. 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Run 1 -^—Timber BlockSize VolFlow T - o a> co io M- co co CN T - o CO O) o Cooling Step 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 04 Run 2 ,l,,,,,,,,,,l,,..,,,,,,,„,-,,,,,,, r ~ - i r ) C 3 T - a > r - . i o c O T - a > r - -v - c N c o T r - M - m c D h - c o o o c j ) 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 i Run 3 .III [Hill iflllllllllf ..,.*•.,,.,.!.•!.II. T - 0 > ^ L O C 0 t - O ) ^ L O C O T - O > h ~ v . c N c o - r j - T r m c o t ^ o o o o o j 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 Run 4 i n 11 ufln 111 n u ii 11 ii 11 ii 11 n i m 11 rn 11 ill i n 11 ul I II 11II111 in nn in 11 II 11 II 11 IN T - C 5 r ~ m c 0 T - O ) r - c n c O - i - O ) h -T - c M c o ^ j - T i - m c D i - — o o c o a > Figure 4.3 - S A objective function values for each run (scenario S4.1). Figure 4.4 shows the timber flows for each run. The timber flows are almost identical for the different starting points, although the harvesting patterns are different (Figure 4.2). This result was expected because there are numerous 49 good solutions for this problem. The runs indicate that different starting points affect the harvest patterns but have little effect on volume flows and total solution value. Timber Flows Figure 4.4 - Timber flows of the four runs for scenario S4.1. Sensitivities of Timber Flows to Cooling Schemes The performance of SA for maximizing timber volume was tested using 7 different cooling rates in scenario S4.1. Hill climbing, which can be thought of as the fast cooling scheme, is the least effective while S A with C=0.01 consistently performs the best. Al l solutions found by SA are between 96% and 100% of the best solution found by S A (Figure 4.5 and Table 4.2). All runs met targets for block size and volume flows within a 5% tolerance. The runs are summarized in 50 Table 4.2. Table 4.3 shows the temporal performances of S A when the cooling rate is 0.01. Timber flow is sensitive to the cooling scheme, which suggests a number of runs are necessary to identify the best cooling scheme. Timber Volume with Different Cooling Parameters 40000 Run Figure 4.5 - Timber volume per year for 7 different cooling schemes (10 runs each). Table 4.2 - Summary of timber flows for 10 runs with 7 different cooling schemes for scenario S4.1. Cooling Control Parameters C=1 C=0.1 C=0.5 C=0.01 C=0.001 C=0.0001 Hill Climbing Average (m3/year) (% of Maximum) 37,041 (97.11%) 37,095 (97.27%) 37,335 (97.88%) 37,597 (98.57%) 37,427 (98.13%) 37,283 (97.75%) 32,869 (86.17%) Maximum (m3/year) (% of Maximum) 37,358 (97.94%) 37,370 (97.98%) 37,808 (99.12%) 38,142 (100%) 37,840 (99.21%) 37,838 (99.20%) 35,226 (92.35%) Minimum (m3/year) (% of Maximum) 36,620 (96.01%) 36,577 (95.90%) 36,772 (96.41%) 37,104 (97.28%) 37,026 (97.07%) 36,749 (96.35%) 30,768 (80.67%) 51 Table 4.3 - Temporal performance of S A with C=0.01 for scenario S4.1. Iterations Temperature With cooling control parameter c = 0.01 Time(Minutes) with Pentium 266 98 MB RAM Total Volume (percent of maximum SA solution found) Total Objective Function Value Timber Volume Divided by Initial Timber Volume Block Size Penalty Divided by Initial Block Penalty Volume Flow Penalty Divided by Initial Volume Flow Penalty 5,000 100 0.5 5,093,035 (67.6%) 0.003 1.001 0.698 0.3 10,000 70 0.93 6,507,719 (86.4%) 1.278 1.281 0.002 0 15,000 40 1.45 6,796,042 (90.2%) 1.336 1.333 0 0 20,000 20 1.91 7,027,543 (93.3%) 1.382 1.382 0 0 25,000 10 2.40 7,140,005 (94.8%) 1.404 1.402 0 0 30,000 9 2.90 7,145,801 (94.8%) 1.403 1.405 0.002 0 35,000 8 3.42 7,291,247 (96.8%) 1.431 1.432 0.002 0 40,000 7 3.89 7,281,231 (96.6%) 1.43 1.432 0.001 0 45,000 6 4.41 7,338,836 (97.4%) 1.441 1.441 0.001 0 50,000 5 4.93 7,434,878 (98.7%) 1.456 1.46 0.006 0 55,000 4 5.30 7,472,150 (99.2%) 1.457 1.468 0.012 0 60,000 3 5.89 7,501,771 (99.6%) 1.455 1.473 0.019 0 65,000 2 6.39 7,533,876 (100%) 1.477 1.479 0.004 0 70,000 1 6.86 7,500,991 (99.6%) 1.475 1.474 0 0 75,000 0.5 7.32 7,448,303 (98.9%) 1.452 1.465 0.013 0 80,000 0.1 7.80 7,471,136 (99.2%) 1.46 1.466 0.009 0 85,000 0.05 8.30 7,466,438 (99.1%) 1.463 1.466 0.005 0 90,000 0.01 8.78 7,472,592 (99.2%) 1.464 1.469 0.005 0 95,000 0.001 9.10 7,474,897 (99.2%) 1.47 1.468 0 0 100,000 0.0001 9.50 7,475,097 (99.2%) 1.47 1.468 0 0 52 4.2 Testing Cost Objectives In this section, cost control functions are used to test the sensitivity of block locations and schedules to costs. Costs include logging costs, transportation costs, road construction costs and other costs. Other costs ($/m3) include administration, stumpage, and supervision. To clearly demonstrate how the costs affect block locations, one layer is used. The same initial forest state as scenario S4.1 (all polygons are 160 years old) is used. Section 4.2.1 tests the sensitivity of block locations to road construction costs, and section 4.2.2 tests the sensitivity of block locations to transportation costs. The blocks must be 10 to 20 hectares in size, and the fluctuation of timber flows within 10%. The cost and profit flows are applied for the first 10 years only, while all other objectives are applied for 210 years. 4.2.1. The Effects of Road Construction Cost on Blocking and Scheduling In Table 4.4, the three scenarios differ only in the road construction cost ($/Km). The remaining parameters are the same as scenario S4.1. Table 4.4 - Parameters for scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3. Scenario S4.2.1.1 S4.2.1.2 S4.2.1.3 Timber value ($/mJ) 200 200 200 Road construction cost for all roads ($/km) 100,000 10,000 1,000 Transportation cost ($/mJ/km) 0.1 0.1 0.1 Logging cost ($/mJ) 18 18 18 Other cost ($/mJ) 39 39 39 53 S4.2.1.1 3.0 Km new road, rag »j $100,000/km M ^ O D D S i B888 I Hi B Bl m 1 » 8888 i88^  E M i l l < J • na S4.2.1.2 ^ |ggg m 7.2 Km new road, MM; Bl M M M •_, noon BBSS BBS 8 8 • B ^ M i l l < « _ B JOOC 1 H i S4.2.1.3 ggg 12.0 Km new road, ^ 1 i Sl,000/km ™ ™ 1 i BS 8888 Mtflfl Figure 4.6 - Cut blocks for first ten years with different road construction costs ($/km) for scenario S4.2.1.1, S4.2.1.2, and S4.2.1.3. (solid lines are existing roads, and dotted lines are proposed roads). 54 Figure 4.6 shows harvest blocks and road systems during the first 10 years. All blocks are in the target size range (10-20 hectares). In scenario 4.2.1.1, most of the blocks are allocated around existing roads, and three kilometers of new road are needed. In scenario 4.2.1.2, when the road construction cost per kilometer is reduced to $10,000/km, more blocks are allocated in areas without existing roads, and 7.2 kilometers of new roads are required. In scenario 4.2.1.3, the road construction cost per kilometer is reduced again to $1000/km, and more blocks are allocated in areas without roads (12 kilometers of new roads, Table 4.5). The total logging and transportation costs are about 23 million dollars, of which the road construction costs are less than 0.3 million dollars. In this example, the road construction cost is only about 1.5% of the total cost, so the results are not very sensitive to road construction costs. However, block patters do indicate the expected trends relative to road construction costs. Table 4.5 - Summary of scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3. Scenario S4.2.1.1 S4.2.1.2 S4.2.1.3 . , Timber volume flows (m ) 383,573 394,228 394,228 Timber value ($) 76,714,560 78,845,520 78,845,520 New road (km) 3.0 7.2 12.0 Road construction cost for all roads ($) 297,489 71,596 12,031 Transportation cost ($) 486,811 481,027 432,896 Logging cost ($) 6,904,313 7,096,099 7,096,099 Other cost ($) 14,959,335 15,374,872 15,374,872 Total cost ($) 22,6471947 23,023,594 22,915,898 Profit ($) 54,066,613 55,821,926 55,929,622 55 Figure 4.7 shows the timber flows for the three scenarios. The timber flows are similar even though the block patterns are different. There appears to be many good solutions for these problems. The total profit and cost for the three scenarios are similar because the road construction cost is only 1.5% of the total cost; as a result, road construction cost has little impact on the total cost and profit. Timber Flows (cubic meters / period) 450000 -, 1 3 5 7 9 1 1 1 3 15 17 P e r i o d (10 y e a r s / p e r i o d ) Figure 4.7 - Timber flows for scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3. 4.2.2. The Effect of Transportation Costs on Blocking and Scheduling The three scenarios in Table 4.6 differ only in transportation cost ($/m3/km). Table 4.6 - Parameters for scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3. Scenario S4.2.2.1 S4.2.2.2 S4.2.2.3 Timber value ($/m3) 200 200 200 Road construction cost for all roads ($/km) 100,000 100,000 100,000 Transportation cost ($/mJ/km) 0.1 1 10 Logging cost ($/m3) 18 18 18 Other cost ($/m3) 39 39 39 • S1 OS2 • S3 56 S4.2.2.1 Transportation Cost= raj raj $0.1/m3/km M m m 1 m a Hi 8888 B881^^ 1 M i l l <— ^ i i g 1 — BS S4.2.2.2 » Transportation Cost= SI /m3/km raj raj • • M i l l « • "J" ™^  B 1 B | | B S4.2.2.3 Transportation Cost= •Kin /m3/l™ ffi m ^ BOOB HOW H M BOOB 8889 |||| g ^ M i l l < J " m ma w 8888 jf^f ^§ Bflfiti re 4.8 - Cut blocks built during first ten years with different transportation costs ($/m3/km) for scenarios S4.2.1.1, S4.2.1.2, and S4.2.1.3. (solid lines are existing roads and dotted lines are proposed roads). Figure 4.8 shows the block patterns created during the first 10 years of each scenario. More blocks are allocated closer to the mill when the transportation cost ($/m3/km) increases. Table 4.7 summarizes the costs for each scenario. Table 4.7 - Summary of scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3. Scenario S4.2.2.1 S4.2.2.2 S4.2.2.3 Timber volume flows (rrrVyear) 383,573 383,573 394,228 Timber value ($/mJ) 76,714,560 76,714,560 78,845,520 New roads (km) 3.0 3.4 2.8 Road construction cost for all roads ($) 297,489 342,178 278,978 Transportation cost ($) 486,811 4,021,972 37,826,212 Logging cost for ($) 6,904,313 6,904,313 7,096,099 Other cost ($) 14,959,335 14,959,335 15,374,872 Total cost ($) 22,647,947 26,227,797 60,576,161 Profit ($) 54,066,613 50,486,763 18,269,359 Figure 4.9 shows that the timber flows for all three scenarios are similar suggesting that there are numerous spatial solutions which result in good values. Scenario S4.2.2.3 with the most expensive transportation cost ($/km/m3) has the lowest profit. 58 Timber Flows (cubic meters / period) 450000 - i 1 3 5 7 9 11 13 15 17 19 Period (10 years/period) Figure 4.9 - Timber flows for scenarios S4.2.2.1, S4.2.2.2, and S4.2.2.3. 4.3 Age Structures and Patch Size Testing Using Different Initial States To test if the model can build and maintain desired age structures and patch size distributions from different initial states, two layers (Figure 4.10) are used. The initial states (age and arrangements of stands) for the four scenarios are different (Table 4.8), but target age structures and patch size distributions for the four scenarios are the same (Figure 4.10). For both layers, the old (>100 years) stand age class target is a minimum target, the small (<40 ha) old patch target is a maximum target and the large (>=40 ha) old patch target is a minimum target for all scenarios. The tolerance for all age structure and patch targets is 10%. The layers differs only in the % area allocated to each patch target (30% v. 70%). • S1 • S2 • S3 59 Layer 2 I T Age Structure Target: Minimum 40% > 100 years Patch Targets: Minimum 70% >= 40 ha Maximum 30% < 40 ha Age Structure Target: Minimum 40% > 100 years Patch Targets: Minimum 30% >= 40 ha Maximum 70% < 40 ha Layer 1 Figure 4.10 - Age and patch targets for scenarios S4.3.1, S4.3.2, S4.3.3, S4.3.4. Table 4.8 - Initial states for scenarios S4.3.1, S4.3.2, S4.3.3, and S4.3.4. Scenario Initial ages for polygons S4.3.1 160 years S4.3.2 0 - 1 6 0 years (random) S4.3.3 50 years S4.3.4 0 - 50 years (random) Results of Scenario S4.3.1 (All polygons are 160 years old in the initial forest) Figure 4.11 and 4.12 show temporal changes in the age structures and patches in layer 1, respectively. The existing forest is already in the desired state, and the desired state is maintained within a 10% tolerance over the entire planning horizon. The current state of old stands in layer 1 is 100%, and this is gradually reduced to 38% over time. This desired state is maintained for the rest 60 of the planning horizon within the 10% tolerance. The current state of old patches in layer 1 is 100% in the larger size (>=40 hectares) category and is gradually divided into smaller (<40 hectares) patches as scheduling creates a transition towards the desired patch targets. Figure 4.13 and 4.14 show temporal changes in the age structures and patches in layer 2. The existing forest is already in the desired state, and the desired state is maintained within a 10% tolerance over the entire planning horizon. The old stands in layer 2 currently cover 100% of the layer and are gradually reduced to 40% (within a 10% tolerance). The old patches in layer 2 are currently 100% in the larger size (>=40 hectares) and are gradually divided into smaller sizes (<40 hectares) as scheduling creates a transformation toward the target. The desired age structure and patch targets for both layers are achieved and maintained even though they have different targets. 61 Figure 4.11 - Old (>100 years) stands in layer 1 for scenario S4.3.1 (All polygons are 160 years old at the start). Old (>100 years) patches overtime (%) Target (<40 ha) Achieved (<40 ha) Target (>=40 ha) Achieved (>=40 ha) 1 3 5 7 9 11 13 15 17 19 Period (10 years/period) Figure 4.12 - Old (>100 years) patches in layer 1 for scenario S4.3.1 (All polygons are 160 years old at the start). Figure 4.13 - Old (>100 years) stands in layer 2 for scenario S4.3.1 (All polygons are 160 years old at the start). Old (>100 years) patches overtime (%) Target (<40 ha) Achieved (<40 ha) Target (>=40 ha) Achieved (>=40 ha) Per iod (10 years /per iod) Figure 4.14 - Old (>100 years) patches in layer 2 scenario S4.3. 1 (All polygons are 160 years old at the start). Figure 4.15 shows four snapshots of the old (>100 years) patches at years 2000, 2100, 2150 and 2200 (or years 0, 100, 150 and 200) for scenario S4.3.1. The existing forest is a 160-year old even age forest. The old stand and patch targets are met at the beginning and maintained for the entire planning horizon. Period 0, Year 2000 PeriodlO, Year 2100 tm Period 15, Year 2150 Period 20, Year 2200 = Layer boundary. Figure 4.15 - Four snapshots of old (>100 years) stands for scenario S4.3.1 (All polygons are 160 years old at the start). 64 Results of Scenario S4.3.2 (Polygon ages are randomly 0-160 years in the initial forest) Figures 4.16 and 4.17 illustrate the temporal changes of the old (>100 years) stands and patches for layer 1. The existing forest is very close to the desired state. This desired state is maintained within a 10% tolerance during the planning horizon. Figures 4.18 and 4.19 show the temporal changes of the old stands and patches in layer 2. The existing forest is already in the desired state, and the desired state is maintained with a 10% tolerance throughout the planning horizon. Comparing Figures 4.17 and 4.19, the patch targets for both layer 1 and layer 2 are achieved even though the two layers have very different patch targets. The old large (>=40 hectares) patch target for layer 1 is 30% while the same target for layer 2 is 70%. The old small (<40 hectares) patch target for layer 1 is 70% while the equivalent target for layer 2 is 30% (Figure 4.10). 65 100 80 60 40 20 Old (>100 years) stands over time (%) Target •Achieved 1 3 5 7 9 11 13 15 17 19 Period (10 years/period) Figure 4.16 - Old (>100 years) stands in layer 1 for scenario S4.3.2 (Polygons are randomly 0-160 years at the start). Old (>100 years) patches over time (%) 5 7 9 11 13 15 17 19 Period (10 years/period) • Target (<40 ha) •Achieved (<40 ha) Target (>=40 ha) j •Achieved (>=40 ha) I Figure 4.17 - Old (>100 years) patches in layer 1 for scenario S4.3.2 (Polygons are randomly 0-160 years at the start). 100 80 60 40 20 0 Old (>100 years) stands over time (%) i—i—i—i—i—i—i—i—r ro LO N O) i Period (10 years/period) - - - Target Achieved i 1 1 1 1 1 1 r co io o) Figure 4.18 - Old (>100 years) stands in layer 2 for scenario S4.3.2 (Polygons are randomly 0-160 years at the start). Old (>100 years) patches over time (%) 5 7 9 11 13 15 Period (10 years/period) - - Target (<40 ha) —Achieved (<40 ha) - Target (>=40 ha) —Achieved (>=40 ha) Figure 4.19 - Old (>100 years) patches in layer 2 for scenario S4.3.2 (Polygons are randomly 0-160 years at the start). Figure 4.20 illustrates the four snapshots of the old (>100 years) patches at years 2000, 2100, 2150 and 2200 (or years 0, 100, 150, and 200 respectively) with scenario S4.3.2. The age structure and patch size distributions of existing forests are already in the desired states and are maintained for the entire planning horizon. Period 0, Y e a r 2 0 < ; . : p • 30 Period 10, Year 2100 M m m % b " B ™ • , m , n . n M L j ! i IH HH H| ESQ T Period 15, Year 21. 50 Period 20, Year 2200 . > . I I M I , _ 1 TW- ^ -— — - — — = Layer boundary. Figure 4.20 - Four snapshots of old (>100 years) stands for scenario S4.3.2 (Polygons are randomly 0-160 years at the start). 68 Results of Scenario S4.3.3 (All polygons are 50 years old in the initial forest) Figure 4.21 and 4.22 illustrate the temporal changes of old stands (>100 years) and patches in layer 1. Because the initial inventory is young (50 years), it requires 60 years to reach the old (>100 years) stand and patch targets. After 60 years, the desired states are maintained for the remainder of planning horizon within a 10% tolerance. By period 5, all stands in layer 1 reach 100 years old, and about 30% of the layer is harvested in periods 5 and 6. All old stands become one large patch that is gradually divided into small patches, however, the desired patch target is maintained for the remainder of the planning horizon. Figure 4.23 and 4.24 depict the temporal changes of old stands (>100 years) and patches in layer 2. Similar to layer 1, it takes 60 years to reach the old stand and patch targets, and the desired states are maintained for the rest of planning horizon. At period 6, all stands in layer 2 have reached 100 years, and about 40% of the layer has been harvested at periods 5 and 6. About 90% of the old stands are in sizes equal or greater than 40 hectares. The amount of old large patches is gradually reduced to 70% and maintained for the rest of the planning horizon. In comparing Figure 4.22 and 4.24, the patch targets for both layer 1 and layer 2 are achieved even though these two layers have very different patch targets. 69 Old (>100 years) stands over time (%) Target -Achieved 5 7 9 11 13 15 17 19 Per iod (10 years/per iod) Figure 4.21 - Old (>100 years) stands in layer 1 for scenario S4.3.3 (All polygons are 50 years old at the start). Old patches (>100 years) over time (%) 5 7 9 11 13 15 Period (10 years/period) Traget (<40 ha) Achieved (<40 ha) Target (>=40 ha) Achieved (>=40 ha) Figure 4.22 - Old (>100 years) patches in layer 1 for scenario S4.3.3 (All polygons are 50 years old at the start). Old (>100 years) stands overtime (%) - Target —Achieved 7 9 11 13 15 17 Period ( 1 0 years/period) 19 Figure 4.23 - Old (>100 years) stands in layer 2 for scenario S4.3.3 (All polygons are 50 years old at the start). Figure 4.24 - Old (>100 years) patches in layer 2 for scenario S4.3.3 (All polygons are 50 years old at the start). Figure 4.25 shows four snapshots of the old (>100 years) patches at years 2000, 2100, 2150 and 2200 (or years 0, 100, 150 and 200, respectively). The current forest does not have any old stands or patches. The desired states are met in period 7 and maintained for the rest of planning horizon. Period 0, Year 2000 No oldj)atches_ PeriodlO, Year 2100 Period 15, Year 2150 Period 20, Year 2200 j j [ | | | HBH||[HI|[!| l l ^ ' l ^ n I : r-Wi 1 1 — — — — = Layer boundary. Figure 4.25 - Four snapshots of old (>100 years) stands for scenario S4.3.3 (All polygons are 50 years old at the start). 72 Results of Scenario S4.3.4 (Polygon ages are randomly 0-50 years in the initial forest) Figure 4.26 and 4.27 illustrate the temporal changes of old stands (>100 years) and patches in layer 1. Since the initial inventory ages are random between 0 and 50, it takes 95 years to reach the old stand target. After 95 years, the desired states are maintained for the rest of planning horizon (10% tolerance). At period 7, there are only 210 hectares (about 10% of the layer) in old stands and 100% of them are in small patch sizes (<40 hectares). Figure 4.28 and 4.29 show the temporal changes of old stands (>100 years) and patches in layer 2. Similar to layer 1, it takes 95 years to reach the old stand target. The old patch targets are met by period 7, at which point the desired states are maintained for the remainder of the planning horizon (within a 10% tolerance). 73 100 90 80 70 60 •] 50 40 30 20 10 1 Old (>100 years) stands over time (%) Target -Achieved 5 7 9 11 13 15 17 19 Period (10 years/period) Figure 4.26 - Old (>100 years) stands in layer 1 for scenario S4.3.4 (Polygon ages are randomly 0-50 years at the start). Figure 4.27 - Old (>100 years) patches in layer 1 for scenario S4.3.4 (Polygon ages are randomly 0-50 years at the start). 100 90 80 70 60 50 40 30 20 10 0 Old (>100 years) stands over time (%) Target •Achieved 5 7 9 11 13 15 17 19 Period (10 years/period) Figure 4.28 - Old (>100 years) stands in layer 2 for scenario S4.3.4 (Polygon ages are randomly 0-50 years at the start). Figure 4.29 - Old (>100 years) patches in layer 2 for scenario S4.3.4 (Polygon ages are randomly 0-50 years at the start). Figure 4.30 shows the four snapshots of the old (>100 years) patches at years 2000, 2100, 2150 and 2200 (or years 0, 100, 150, and 200, respectively). The current forest does not have any old (>100 years) stands or patches. The desired states are met in year 2100 and maintained for the remainder of planning horizon. Period 0, Year 2000 No old_patches_ Period 10, Year 2100 Period 15, Year 2150 Period 20, Year 2200 I " I MM I I mil HEM Layer boundary. Figure 4.30 - Four snapshots of old (>100 years) stands for scenario S4.3.4 (Polygon ages are randomly 0-50 years at the start). 76 From these four scenarios, I conclude that F S O S can achieve the desired forest states from different initial inventories, and that the time to achieve the desired state increases the further the target is from the initial inventory. 4.4 Sensitivity of Timber Flows and Old Patches to Natural Disturbances To analyze the sensitivity of timber flows to natural disturbance rates and test whether the model can build desired age and patch size distributions with different natural disturbance rates, three scenarios (Table 4.9, Figures 4.35 and 4.36) are developed. To create a complex forest transformation problem, the following assumptions are made: 1) the existing forest is created by following 10-year adjacency constraints for 30 years, 2) 25% of the area is recently regenerated; 3) 25% of the area is 10-year old forest; 25% of the area is 20-year old forest; and 4) 25% of the area is 175-year old forest. The following age structure targets (in % of area) are applied. 1) Maximum target for young stands (<=20 years) is 25%, and minimum target for old stands (>=100 years) is 20%. The old (>=100 years) patch targets (in % of old stand area) are: 1) maximum target for small size patches (<=10 hectares) is 33%, 2) maximum target for medium size patches (<10 and <40 hectares) is 33%, and 3) minimum target for larger size patches (>=40 hectares) is 34%. Natural disturbances are randomly generated before each run. 77 Table 4.9 - Timber flows with different natural disturbance scenarios. Scenario S4.4.1 S4.4.2 S4.4.3 Natural disturbance rate 0%/year 0.125%/year 0.25%/year Average timber flows (% reduced) 22,680(0%) 16,958(25.2%) 12,201 (46.2%) Timber flows (cubic meters / period) 300000 250000 200000 150000 100000 50000 0 -S4.4.1 •S4.4.2 •S4.4.3 1 3 5 7 9 11 13 15 17 19 21 Period (10 years/period) Figure 4.31 - Timber flows with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3. On average, timber flows are reduced 25.2% with a 0.125%/year natural disturbance rate and reduced 46.2% with a 0.25%/year natural disturbance rate (Table 4.9 and Figure 4.31). Timber flows are low from period 1 to 10 because there are excessive young stands at periods 1 and 2 (Figure 4.32) and there not enough old stands from period 2 to 10 (Figure 4.33). Patch targets can not be achieved until period 10 (Figure 4.34). The age class and patch targets greatly affect timber flows. 78 60 50 40 30 20 10 0 Young (<=20 years) stands over time (%) 7 9 11 13 15 17 Period (10 years/period) 19 21 Target -S4.4.1 •S4.4.2 •S4.4.3 Figure 4.32 - Young stands (<=20 years) with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3. 60 50 40 30 20 10 0 Old (>=100 years) stands over time (%) 5 7 9 11 13 15 17 Period (10 years/period) 19 21 Target •S4.4.1 •S4.4.2 •S4.4.3 Figure 4.33 - Old stands (>=100 years) with different natural disturbance rates for scenarios S4.4.1, S4.4.2, and S4.4.3. 79 Patches <= 10 ha 100 80 H 60 40 20 0 100 80 60 40 3 5 7 9 11 13 15 17 19 21 Period (10 years/period) Patches >10 ha and <= 40 ha 1 3 5 7 9 11 13 15 17 19 21 Period (10 years/period) Patches > 40 ha -Target -S4.4.1 -S4.4.2 •S4.4.3 Target -S4.4.1 • S4.4.2 •S4.4.3 I -Target -S4.4.1 -S4.4.2 • S4.4.3 Period (10 years/period) Figure 4.34 - Old (>=100 years) patches with natural disturbance for scenarios S4.4.1, S4.4.2, and S4.4.3. Natural Disturbance Period: m u m 2000 - 2050 0-5 • • 2051 -2100 6-10 I 12101-2150 H-15 • • 2151 -2200 l ° - 2 0 Figure 4.35 - The natural disturbance pattern for scenario S4.4.2 (0.125% / year random). Natural Disturbance Period: B 2000-2050 0-5 2051 -2100 6-10 12101-2150 H-15 • • 2151 -2200 1 6 - 2 0 Figure 4.36 - The natural disturbance pattern for scenario S4.4.3 (0.25%/year random). 81 Figures 4.37, 4.38 and 4.39 show that the natural disturbance rates slightly affect old stands and large old patch achievements. However, the natural disturbances greatly impact the timber flows (Figure 4.31). With the three natural disturbance rates, the same old stand and large old patch targets can be achieved. Therefore, I conclude that the model is working as designed, and that it is able to find harvest strategies that meet the targets (Figures 4.37, 4.38 and 4.39). This is an advantage of target-oriented forest planning. 82 Period 0, Year 2000 Period 10, Year 2100 tiiiiiiiliiiij r-™— t i*^J V?'.{<\:y\ ! Period 15, Year 2150 Period 20, Year 2200 Figure 4.37 - Snapshots of old patches without natural disturbance (Scenario S4.4.1). 83 Period 0, Year 2000 Period 10, Year 2100 Period 0, Year 2000 Period 10, Year 2100 m n . h n • • • • • • • • • • • • • • • • • • • • • • • • • • • • • a d • • • • • • • • • • 1 j 1 1 [ j ! j I 1 1 J L_l 1 ! L J 1 _ B B B I JM MM uWm m m m MM mmm g isd IBS MB SB EH flfi H BBS BE! BBj 71 • LTaT • "• Period 15, Year 2150 Period 20, Year 2200 T^-T""k- aB a u Figure 4.39 - Snapshots of old patches with 0.25%/year natural disturbance rate (scenario S4.4.3). 4.5 Comparison with ATLAS The objective of comparing F S O S and ATLAS is to demonstrate differences between a rule-based, simulation model and a target-oriented model. ATLAS (A Tactical Landscape Analysis System, Nelson 1995) is a typical time-step rule-based simulation model developed at the University of British Columbia and has been used for about a decade. A 400-grid data set is used for all F S O S and ATLAS runs in this section. To make the forest transformation more difficult, the 400-grid polygons are sorted into 4 non-adjacent groups and are assigned ages 0, 10, 20, and 175 years, respectively. All stands use the same yield curves. The minimum harvest age is 80 years and all polygons are 10 hectares. Three ATLAS runs with different harvest rules and three F S O S runs with different weighting scenarios are made. The targets for F S O S runs are used as constraints for ATLAS runs. 4.5.1 A T L A S Runs The harvest-scheduling rules are identified first. The age structure constraints for the entire area are: 1) maximum 25% of area less than or equal to 20 years old, and 2) minimum 20% of area greater than or equal to 100 years. Instead of specifying a patch size distribution, ATLAS created a block size distribution by aggregating polygons before the runs. The distribution is: 86 1) 33% of area in 10 ha blocks, 2) 33% of area in 40 ha blocks, and 3) 34% of area in 120 ha blocks. A 20-year adjacency green-up constraint is applied to all three scenarios. The differences in the three scenarios are described in Table 4.10. A harvest , priority list of potential cutblocks is established based on the stand ages. The harvest-rule is "oldest first", subject to all constraints. In scenario S4.5.1.3, blocks are sorted into four non-adjacent groups. Each group is assigned a harvest priority and the "oldest first" rule is applied within the group. Table 4 .10 - Descriptions of ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3. Scenario S4.5.1.1 S4.5.1.2 S4.5.1.3 Description Whole block can not be harvested if one or more polygons are under the minimum harvest age. Polygons that are at least as old as the minimum harvest age can be cut within a block. Blocks are sorted into 4, non-adjacent groups. These groups are used as harvest priorities. The result is a non-adjacency cutting pattern. 87 Timber flows (cubic meters / period) 300000 -| P e r i o d (10 y e a r s / p e r i o d ) Figure 4.40 - Timber flow for ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1. 3. Figure 4.40 shows the timber flows from the three ATLAS runs. The timber flow during first two decades is zero because the young stand requirement is binding (Figure 4.41). During periods 4-8, the old stand requirement is binding (Figure 4.42). The timber flows are similar for the three scenarios when the forest reaches a stable state after period 9. The timber flow for Scenario S4.5.1.1 is lower than Scenario S.4.5.1.2 between period 4 and 9 (Figure 4.40) because a less flexible minimum harvest age within cut blocks is applied for Scenario S4.5.1.1. The three scenarios have similar results in terms of timber flows, forest age structures and old patch patterns (Figures 4.43, 5.44, 5.45, and 5.46). F S O S was used to calculate age structures and patches from the A T L A S simulations. Figure 4.41 shows the temporal changes of young stands (<=20 years) for the A T L A S runs. The percentage of young stands in the existing forest exceeds the 88 constraint, and this prevents timber harvests for more than 2 periods. Figure 4.42 shows that the percentage of old stands (>=100 years) is limiting timber production from periods 4 to 8. Figure 4.43 illustrates that the patch targets cannot be reached until period 8 because of the existing forest patterns (Figure 4.44, 4.45 and 4.46). After period 8, most of the old stands are in patches greater than 40 hectares. The results show that block size distributions can not guarantee the patch size distributions. In this example, very few small old patches are created even when 33% of the blocks are 10 hectares and 33% are 40 hectares. The small blocks (<=40 ha) are aggregated to large patches (Figures 5.44, 5.45, and 5.46) over time. Scenarios S4.5.1.1 and S4.5.1.2 created similar patch patterns (Figure 5.44 and 5.45) because the harvest rules'are quiet similar, especially over the long-term. Scenario 4.5.1.3 generated a very different patch pattern from other scenarios because of the "non-adjacency grouping" harvest rule. 89 Young (<=20 years) stands overtime (%) • Target -S4.5.1.1 • S4.5.1.2 • S4.5.1.3 5 7 9 11 13 15 17 Period (10 years/period) 19 21 Figure 4.41 - Young (<=20 years) stands for ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3. 70 60 50 40 30 20 10 0 Old (>=100 years) stands overtime (%) 5 7 9 11 13 15 17 Period (10 years/period) 19 21 - - - Target S4.5.1.1 S4.5.1.2 — S 4 . 5 . 1 . 3 Figure 4.42 - Old (>=100 years) stands for ATLAS scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3. Patches <= 10 ha (ATLAS) 100 80 60 40 20 0 — I — i — I I ^ 13 15 17 7 9 11 Per iod (10 years/per iod) 19 21 -Target -S4.5.1.1 -S4.5.1.2 -S4.5.1.3 I 100 80 60 40 20 0 Patches >10 ha and <= 40 ha (ATLAS) T — i — i — i — i — r 3 5 7 9 11 13 15 Per iod (10 years/per iod) Target -S4.5.1.1 -S4.5.1.2 •S4.5.1.3 Patches > 40 ha (ATLAS) 100 80 60 40 20 5 7 9 11 Period (10 years/period) i — i — \ — ] — \ — i — i i i i 13 15 17 19 21 •Target -S4.5.1.1 -S4.5.1.2 • S4.5.1.3 Figure 4.43 - Old (>=100 years) patches for A T L A S scenarios S4.5.1.1, S4.5.1.2, and S4.5.1.3. Figure 4.45 - Four snapshots of old patches for the A T L A S scenario S4.5.1 .2. Period 0, Year 2000 Period 10, Year 2100 wmmmmm • • • • • • • • • • • • • • Period 15, Year 2150 Period 20, Year 2200 Figure 4.46 - Four snapshots of old patches for the A T L A S scenario S 4 . 5 . 1 . 3 . After finding that young and old stand requirements are binding, the analysts can relax the constraints for the binding periods and re-run the simulations. This is repeated until an acceptable solution, in terms of forest structure and timber supply, is found. 94 4.5.2 FSOS Runs Because the two models are so different, it is difficult to compare F S O S and ATLAS directly. The parameters for the F S O S runs were set as close as possible to the constraints of the ATLAS runs. The age structure targets (in % of the area) are: 1) maximum target for young stands (<=20 years) is 25%, and minimum target for old stands (>=100 years) is 20%. The old (>=100 years) patch targets (expressed in % of the old stand area) are: 1) maximum target for the small size patches (<=10 hectares) is 33%, 2) maximum target for the medium size patches (<10 and <40 hectares) is 33%, and 3) minimum target for the larger size patches (>=40 hectares) is 34%. An important difference between ATLAS and F S O S is in this larger patch size. ATLAS uses pre-blocked 120 ha blocks while F S O S tries to build blocks >= 40 ha (not 120 ha). Because the age structure is the major factor that impacts timber flows for ATLAS simulation runs, three scenarios (Table 4.11) with different weightings of age structures are tested. These three scenarios differ only in the age structure weightings. Table 4.11 -Age structure weights for scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3. Scenario S4.5.2.1 S4.5.2.2 S4.5.2.3 Weight for age structure 0.0001 0.01 1 Figure 4.47 illustrates the timber flows of the three F S O S runs. In scenario S4.5.2.1 and S4.5.2.2, even timber flows within a 10% tolerance can be 95 achieved and maintained over the entire planning horizon. It requires a few decades to achieve the age structure (Figures 4.48 and 4.49). In scenario S4.5.2.3, the age structure can be achieved earlier if the weight of the age structure is increased (Figures 4.48 and 49). However, the timber flows must be reduced during first few decades similar to the ATLAS runs (Figure 4.47). Figures 4.50 shows that the patch targets cannot be reached until period 9 (90 years later). The old (>=100 years) large patches (>40 ha) targets are achieved one period earlier in scenario S4.5.2.3 than scenario S4.5.2.1 because higher age structure weights are used in the patch penalty function. Note that the young stand requirement is not met in periods 1-2 and the old stand requirement is not met in periods 1-9 (Figure 4.49). Where old stands are already scarce, harvesting as in Scenarios S4.5.2.1 and S4.5.2.2 is probably unacceptable. Timber flows (cubic meters / period) 350000 -, 1 3 5 7 9 11 13 15 17 19 21 Period (10 years/period) Figure 4.47 - Timber flows for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3. 96 Young (<=20 years) stands overtime (% - - Target S4.5.2.1 S4 .5 .2 .2 ^ — S 4 . 5 . 2 . 3 5 7 9 11 P e r i o d (10 y e a r s / p e r i o d ) Figure 4.48 - Young (<=20 years) stands for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3. 60 50 40 30 20 10 0 Old (>=100 years) stands overtime (%) 3 5 7 9 11 13 15 17 19 21 Period (10 years/period) Target •S4.5.2.1 •S4.5.2.2 •S4.5.2.3 Figure 4.49 - Old (>=100 years) stands for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3. Patches <= 10 ha - - - -Target S4.5.2.1 S4 .5 .2 .2 S4 .5 .2 .3 1 3 5 7 9 11 13 15 17 19 21 P e r i o d (10 y e a r s / p e r i o d ) Patches >10 ha and <= 40 ha 100 i 80 . . . . Target 60 - S4.5.2.1 40 - A S4.5 .2 .2 A S4 .5 .2 .3 20 -u - -i— i i i * i—i—i 1 3 5 7 9 11 13 15 17 19 21 P e r i o d (10 y e a r s / p e r i o d ) Patches > 40 ha - - - -Target S4.5.2.1 S4 .5 .2 .2 S4 .5 .2 .3 1 3 5 7 9 11 13 15 17 19 21 P e r i o d (10 y e a r s / p e r i o d ) Figure 4.50 - Old (>=100 years) patches for F S O S scenarios S4.5.2.1, S4.5.2.2, and S4.5.2.3. Figures 4.51, 4.52, and 4.53 show that the desired patterns are achieved in period 10 (year 2100), and maintained for the remainder of the planning horizon. The patterns for the three scenarios are similar because the same targets are used. Period 0, Year 2000 • • • • • m a • • • • • n • • m m • u • n • • • B D D D D D Period 10, Year 2100 Period 15, Year 2150 Period 20, Year 2200 Figure 4.51 - Four snapshots of old patches for F S O S scenario S4.5.2.1 99 Figure 4.52 - Four snapshots of old patches for F S O S scenario S4.5.2.2. Period, Year 2000 Period 10, Year 2100 1 1 1 1 Bj Bj BJ E • L_ _ _ • • • • • • • i i • B • m • • d I i i • • E • i d i - ± : " j " 1 ' H E S • M l I j ^ J J • • • • • • • • • q • ^ • • • • • • • E a Period 15, Year 2150 Period 20, Year 2200 •' ••: • • EH • B^Bj • • 1 • zFb WW __ Mflf'L j flti B jHBBS ^ B B B T " 1 upj^ ^pj ^ B l B^^BIBJ^B^^^B I B ™ I • • T i m H l l l l Figure 4.53 - Four snapshots of old patches for F S O S scenario S4.5.2.3. In all ATLAS runs, no timber production is allowed during the first few decades. It requires 20 years to achieve the maximum young stand targets, and it takes 80 years to achieve the old large patch targets. It is the duty of the analysts to use this information to modify the constraints and re-run the model until acceptable solutions are found. Both desired forest states can be maintained (in the absence of natural disturbance) once they reach the targets. 101 With F S O S scenario S4.5.2.1, timber flows can be maintained a level that ranges from 18,144 m 3/year to 27,139 m 3/year for the entire planning horizon, however, it requires 90 years to reach the stable old stand requirements, and it depletes an already scarce supply of old stands during periods 1-9. It requires 15 years to reach a maintainable young stand requirement, and it requires 90 years to reach the patch targets (Table 4.12). Table 4.12 - Summary of ATLAS runs (S4.5.1.1, S4.5.1.2, and S4.5.1.3) and F S O S runs (S4.5.1.1, S4.5.2.2, and S4.5.2.3). ATLAS runs F S O S runs Scenario 4.5.1.1 4.5.1.2 4.5.1.3 4.5.2.1 4.5.2.2 4.5.2.3 Average timber (m J/year) 17,915 18,519 18,504 22,680 20,940 21,074 Maximum timber (mJ/year) 27,730 28,514 25,330 27,139 24,940 31,611 Minimum timber (rrfVyear) 0 0 0 18,144 16,668 0 Years to achieve old (>=100 years)target 0 0 0 90 80 0 Years to achieve young (<=20 years) target 10 10 10 15 15 10 Years to achieve large old (>=100 years) patch target 80 80 80 90 85 80 With the F S O S scenario S4.5.2.2, age structure weighting is increased, and the timber flows, on average, are reduced to 20,940 from 22,680 cubic meters per year. Both the old stand targets and old large patch targets can be achieved about 5 years earlier than in scenario S4.5.2.1. However, the depletion of old stands during periods 1-9 is similar to S5.4.2.1. With F S O S scenario S4.5.2.3, the age structure weighting is increased again, and the age structures can be achieved and maintained for the entire planning horizon in a similar 102 fashion to the ATLAS runs. The timber flows are also similar to the ATLAS runs (Table 4.12). In summary, F S O S uses weights to manage tradeoffs between forest structure and timber flows, while ATLAS relies on explicit interventions of the analysts to adjust constraints in order to make similar tradeoffs. 103 Chapter 5 Case Study The Forest Simulation Optimization System was used on Tree Farm License (TFL) #3 (Slocan Forest Product Limited, 1998). TFL 3 is located in the Nelson Forest Region (Arrow Forest District) near the village of Slocan, B.C. (Figure 5.1 - tenure map). The TFL is located predominantly within the Interior Cedar Hemlock (ICH), Engelmann Spruce - Subalpine Fir (ESSF) and Alpine Tundra (AT) biogeoclimatic zones. The total area of the TFL is 79,796 hectares, with forested, operable and inoperable areas listed in Table 5.1. The forest industry is an important sector, providing long-term social and economic development in the region. Slocan Forest Product (SFP) is the largest employer in the Slocan Valley and has a significant economic impact not only in the Slocan Valley, but throughout the West Kootenay region. Currently, it is difficult for S F P to harvest timber because different groups have conflicting interests. To accommodate the concerns of all interest groups, S F P asked experts in relevant fields to clearly define the desired forest structures (age structure + patches) required to sustain non-timber resources within the TFL. F S O S was used to develop a 20-year harvest plan based on these long-term management objectives. The forest transitions projected by F S O S were analyzed by monitoring timber flows and forest conditions. Comparisons between the achieved values and the desired values were made. 104 A R R O W F O R E S T D I S T R I C T U.S.A. Figure 5.1 - TFL3 tenure map. 0 10 20 Kilometers Figure 5.2 - Resultant polygons in TFL #3. Overlaying the resource layers (Table 5.2) and forest cover generated 17,642 resultant polygons (Figure 5.2). 10 106 Table 5. 1 - Summary of TFL #3 area. Area (hectares) % of TFL Area TFL#3 79,796 100 Total Forest 60,174 75.4 Operable Forest 35,585 44.6 Inoperable Forest 24,589 30.8 The F S O S results are also compared with the A T L A S model by using the F S O S targets as constraints. Sensitivity analyses are used to determine the response of forest structure and timber flows to changes in objective weights in F S O S runs. The rest of this chapter will be divided into four sections. Section 5.1 describes the resource layers, and the desired states; section 5.2 states the harvest criteria; section 5.3 provides the objective weighting scenarios; and section 5.4 contains the results and discussion. 5.1 Management Layers and Their Objectives There are 46 layers in this case study (Table 5.2) and each layer has a desired state in terms of age structures and patch size distributions. The most complicated layers are natural disturbance type layers, which require both age structures and patch size distributions. The 46 layers combined with the forest cover layer created 18,000 resultant polygons. A 200-year planning horizon with forty 5-year periods was used. The current and desired states of these layers will be described in the subsequent sections. 107 Table 5.2 - Resource Emphasis Layers. Layer ID Name Area (ha) 1 Connectivity 11,608 2 V Q O Retention 1,894 3 V Q O Partial Retention 4,269 5 V Q O Maximum Modification 152 6 V Q O Modification 4,559 7 Small Business 1,909 8 Robertson Face Watershed 170 9 Airy Face Watershed 577 10 South Tedesco Watershed 220 11 Talbot Watershed 221 12 East Little Slocan Watershed 455 13 Airy/Slocan Residual Watershed 1,411 14 Airy 31.3A Watershed 1,837 15 Airy 31.3B Watershed 278 16 Airy 31.3C Watershed 343 17 Airy 31.3D Watershed 463 18 Airy 31.3E Watershed 328 19 Airy 31.3F Watershed 996 20 Airy 31.3G Watershed 318 21 NDT1 Landscape UnitA16 19,363 22 NDT1 Landscape UnitA17 3,542 23 NDT1 Landscape Unit A36 14,213 24 NDT2 Landscape Unit A16 12,746 26 NDT2 Landscape Unit A36 9,194 27 NDT3 Landscape Unit A16 1,599 28 NDT3 Landscape Unit A17 11,796 29 NDT3 Landscape Unit A36 6,453 51 Bannock Burn non-domestic watershed 3,840 52 Cougar non-domestic watershed 1,630 53 Dago non-domestic watershed 1,287 54 Greasybill non-domestic watershed 4,133 55 Heimdal non-domestic watershed 1,519 56 Hoder non-domestic watershed 6,734 57 Koch Residual non-domestic watershed 4,022 58 Lower Grizzly non-domestic watershed 2,214 59 Lower LS Residual non-domestic watershed 3,914 60 Ludlow non-domestic watershed 2,051 61 Mista non-domestic watershed 1,079 62 Russel non-domestic watershed 3,059 63 Slocan Lake non-domestic watershed 160 64 Upper Grizzly non-domestic watershed 3,074 65 Upper Koch Residual non-domestic 5,818 66 Upper LS Residual non-domestic watershed 4,625 67 Woden non-domestic watershed 4,207 5.1.1 Visual Quality Objectives (VQOs) There are 4 levels of visual quality objectives (Figure 5.3). Age class structure percentage targets for V Q O s are defined in Table 5.3. Figure 5.3 - Visual Quality Objective areas in TFL #3. Table 5.3 - Visual quality objectives (VQO) Layer ID V Q O Levels Forested Area Operable Area % (< 25 years) Current Maximum Target 2 Retention 1,894 829 6 5 3 Partial Retention 4,269 2,625 5 15 5 Modification 4,559 3,267 12 25 6 Maximum modification 152 15 0 40 109 5.1.2 Caribou Connectivity Corridors The caribou connectivity corridor (Figure 5.4) has 2,675 polygons and covers 11,608 hectares of which 5,087 hectares are operable. The mature stand target for the corridor is a minimum of 70% older than 100 years, however, the current state is only 49.5% older than 100 years. Figure 5.4 - Caribou Connectivity Corridors. no 5.1.3 Wildlife Trees (Stand-level Biodiversity) Wildlife tree retention was accounted for through a percentage netdown applied to each block. Approximately 50% of the wildlife tree retention objective will be met through riparian management areas and inoperable areas; therefore, initial wildlife tree requirements have been reduced. The percentage reductions are in Table 5.4. Table 5.4 - Wildlife tree reserve percentages. Layer ID Landscape Unit NDT* Biodiversity Emphasis Forest Area Operable Area Wildlife tree reduction (%) 21 16 1 Low 19,363 10,114 2 24 16 2 Low 12,746 11,426 2 27 16 3 Low 1,599 1,420 2 22 17 1 Intermediate 3,542 1,981 2 25 17 2 Intermediate 0 0 2 28 17 3 Intermediate 11,796 2,616 3 23 36 1 Low 14,232 3,632 2 26 36 2 Low 9,194 3,767 2 29 36 3 Low 6,453 1,630 2 *NDT is Natural Disturbance Type (Biodiversity Guidebook, MOF, 1995) 1 = ecosystems with rare stand-initiating events 2 = ecosystems with infrequent stand-initiating events 3 = ecosystems with frequent stand-initiating events 5.1.4 Landscape-level Biodiversity There 4 biogeoclimatic zones in TFL #3 (Figure 5.5). Age class structure targets are applied to individual Natural Disturbance Types (NDTs) based on the biodiversity emphasis options (Table 5.5). i n • The young stand age for all NDTs is <= 40 years; • the mature stand age for NDT 1 is >40 and <=120 years, for NDT 2 and 3 it is >40 and <=100 years; and • the old stand age for NDT 1 and 2 is >250, for NDT 3 is >140. Figure 5.5 - Biogeoclimatic zones in TFL #3. 112 Table 5.5 - Biodiversity age class structure targets and current states. Landscape Unit NDT Biodiversity Emphasis Young Stand (%) Mature Stand (%) Old Stand (%) Current Target Current Target Current Target 16 1 Low 14.4 36 41.8 - 9.6 19* 16 2 Low 13.6 36 22.4 - 12.8 9 16 3 Low 20.6 36 16.9 - 8.4 14* 17 1 Intermediate 1.4 22 44.4 22 4.2 19* 17 3 Intermediate 7.8 22 24.2 9 7.5 14* 36 1 Low 12.2 36 56.2 - 4.1 19* 36 2 Low 11.8 36 29.3 - 3.0 9* 36 3 Low 4.2 36 28.2 - 5.2 14* * = currently does not meet target. Patch size distribution percentage targets for each NDT are assigned according to Biodiversity Guidebook by MOF, 1995 (Table 5.6). Table 5.6 - Patch size distribution targets for young and old stands. Layer ID Landscape Unit NDT Biodiversity Emphasis % Area of 0-40 ha patch targets % Area of 41-80 ha patch targets % Area of 81-150 ha patch targets 21 16 1 Low 35 35 30 24 16 2 Low 35 35 30 27 16 3 Low 25 35 40 22 17 1 Intermediate 35 35 30 25 17 2 Intermediate 35 35 30 28 17 3 Intermediate 25 25 40 23 36 1 Low 35 35 30 26 36 2 Low 35 35 30 29 36 3 Low 25 35 40 5.1.5 Riparian Zones Riparian zones were excluded from the harvestable land base. However, they still contribute to age class structure and patch size distribution targets. 113 5.1.6 Watersheds There are 30 watersheds in TFL 3 (Figure 5.6 and Table 5.7). Age structure rules were applied to watersheds based on their respective equivalent clear cut area (ECA) and the age to reach a 9 m hydrological green-up. With a 30% E C A applied, the age structure target is a maximum of 30% of the watershed area in stands, which are 35 years or younger (time for stands to reach 9 meters). Watersheds Airy Airy Face Airy/Slocan Residual Bannock Burn Cougar Dago East Little Slocan Greasybill Heimdal Hotter Koch Residual Lower Grizzly Lower LS Residual Ludlow Msta Robertson Face Slocan Lake South Ted esco Talbot Upper Grizzly Upper Koch Residual Upper LS Residual Woden N Figure 5.6 - Watersheds in TFL #3. 114 Table 5.7 - Watershed young stand (<=35 years) targets and current states. Layer ID Watershed Name Upper Bound(%) Current(%) 8 Robertson Face Watershed 30 0 9 Airy Face Watershed 20 15 10 South Tedesco Watershed 30 9 11 Talbot Watershed 30 0 12 East Little Slocan Watershed 30 6 13 Airy/Slocan Residual Watershed 20 25 14 Airy 31.3A Watershed 20 18 15 Airy 31.3B Watershed 20 24* 16 Airy 31.3C Watershed 20 26* 17 Airy 31.3D Watershed 20 28* 18 Airy 31.3E Watershed 20 40* 19 Airy 31.3F Watershed 20 31* 20 Airy 31.3G Watershed 20 33* 51 Bannock Burn non-domestic watershed 35 14 52 Cougar non-domestic watershed 35 10 53 Dago non-domestic watershed 35 10 54 Greasybill non-domestic watershed 35 11 55 Heimdal non-domestic watershed 35 44* 56 Hoder non-domestic watershed 35 17 57 Koch Residual non-domestic watershed 35 13 58 Lower Grizzly non-domestic watershed 35 2 59 Lower LS Residual non-domestic watershed 35 16 60 Ludlow non-domestic watershed 35 7 61 Mista non-domestic watershed 35 1 62 Russel non-domestic watershed 35 5 63 Slocan Lake non-domestic watershed 35 2 64 Upper Grizzly non-domestic watershed 35 13 65 Upper Koch Residual non-domestic watershed 35 10 66 Upper LS Residual non-domestic watershed 35 4 67 Woden non-domestic watershed 35 10 * = currently does not meet target. 5.2 Harvest Criteria The first five years of harvest are fixed according to Slocan Forest Product's 5-year forest development plan. Resultant polygons generated by GIS overlays are used as the basic planning units. Resultant polygons are amalgamated to create openings; and the openings then aggregate over time to 115 create patches. Stand-level growth and yield curves were generated with the growth and yield models V D Y P (Variable Density Yield Program) for natural stands and TIPSY (Table Interpolation Program for Stand Yield) for managed stands. 5.3 Objective Weightings Weighting of the objectives and parameters is a key process in the operation of the model, and the choice of weighting is specific to the forest being modeled. Table 5.8 shows the weighting used in this analysis (3 scenarios). The absolute value of the weights is not relevant, rather, the weightings show the relative importance of each parameter (i.e. in scenario S5.2, patch size distribution is 1.6 times more important than total volume flow). Generally, the higher the weighting, the sooner the target can be achieved. The weightings are only control parameters, and they depend on the difficulty of achieving the targets within time limits. By placing a high priority on biodiversity objectives, a relatively higher importance is attributed to patch size and age class structure objectives. Low weight was applied to the even volume flow parameter because it is an easy target to achieve. A cut block size objective was added to control cut block size. The block size range can be specified for each layer; and the block size must meet the requirements of all the layers that share the block. A high weight was given to the cut block size because it proved to be a different target to achieve. 116 Table 5.8 - Weighting parameters. Weight Parameters Scenario Scenario Scenario Atlas S5.1 S5.2 S5.3 Total volume 1 1 1 — Patch size distribution 16 1.6 0.16 — Age class structure 15 1.5 0.15 ~ Even volume flow 0.2 0.2 0.2 — Cut block size 20 2 0.2 — 5.4 Results and Discussions Figure 5.7 shows the performance of the objective function values for weighting Scenario S5.2 (1 million iterations). Performances for other scenarios are similar to Scenario S5.2. In Figure 5.7, "Total Obj" is the total objective function value; "Total Timber" is the total timber volume produced over the planning horizon; "Patch Size" is the patch size distribution penalty; "Age Class" is the age class structure penalty; "Block Size" is the cut block size penalty; and "Timber Flows" is the timber even flow penalty. All objective function indicators continue to improve as the number of iterations increases until further iterations do not yield significant improvements. When the indicators level off, a good solution has been achieved. Table 5.9 gives the solution time with a Pentium 266 MHZ and 98 MB R A M computer. Table 5.9 - Solution Times. Iterations 200,000 400,000 600,000 8,00,000 1,000,000 % of the best solution 32.5 72.4 91.3 98.8 100 Time (hour) 1.8 3.5 5.3 7.2 8.8 117 o > c o u CD > • o o Iterations —Total Obj — Total Timber Patch Size — Block Size -»- Age Qass -•- Timber Rows 1,000,000 Figure 5.7 - Objective function values for Scenario S5.2 over 1 million iterations. Figure 5.8 shows the 20-year plan harvest blocks. The minimum cutblock size target was set at 10 hectares. Results show that the average size is greater than the minimum desired cutblock size (Figure 5.9), and that less than 10% of the cut blocks in number, or 2% by area, in all periods are smaller than 10 hectares. 118 Figure 5.8 - Harvest blocks for 20 years (by 5-year period). 119 T- O I I I I I I I I I I I I I I I I I I I I I I I I I I I I I c o c £ ) 0 ) C M u n c o T - T j - r - o T - T - T - C N C M C M r O C O C O ^ r Period (5 year period) Figure 5.9 - Average cut block size over all periods. 5.4.1 Timber Flows Figure 5.10 shows the timber flows for three F S O S runs and an ATLAS run. In Scenario S5.1, timber has the lowest weighting compared with scenarios 2 and 3, and it has the lowest timber flows (Figure 5.10 and Table 5.10). With Scenario S5.2, over the long-term (200 years), Atlas and F S O S produce almost the same timber flows. However, in the short-term (40 years), F S O S achieved higher volume flows because the lower weightings on age and patch targets allowed it to harvest more. Atlas uses "hard" constraints and if the analyst does not relax them, the timber harvest is seriously limited during the first 40 years. 120 o > e a CD u 3 o — S5.1 - • - S 5 . 2 — S5.3 — A t l a s i M 1111 M i M 1 1 1 1 1 1 1 m cs co N T - ifl O) co N T - CN CN CN CO CO Period (5-year period) Figure 5.10 - Timber volume flows over all periods. Table 5.10 - Timber volume flows of TFL #3. Scenario S5.1 Scenario S5.2 Scenario S5.3 ATLAS Average volume flows (m 3 / year) 77,301 84,756 91,145 81,867 Figure 5.10 demonstrates that the timber flows increase after 150 years (30 periods). Two additional runs were conducted with a 400-year planning horizon, which confirmed that the forest reaches a stable state and high timber flows can be maintained after 150 years. 121 5.4.2 Watersheds Figure 5.11 demonstrates how the targets are achieved in one typical watershed over time. The maximum allowable young stand target (<35 years) is 20%. The spikes at periods 3 and 4 are caused by a large amount of stands which have to be harvested to meet patch target and/or age structure targets. With Scenario S5.3, timber has the highest weighting and age class structure has the lowest weighting. The achieved age class structure is close to the target. With Scenario S5.1, where timber has the lowest weighting and age class structure has the highest weighting, the achieved age class structure is far below the target. The targets for other watersheds are achieved within a number of periods, depending on the current state. 25 i 5 0 I i 11 I I i M i 11 i i 11 i i 11 i M i 1111 i i I I i i 11 I I T - m c o c o h - T - i n c o c o r - -T — T— CN CN CN CO OO Period (5-year period) Figure 5.11 - Young (<35 years) stands of Airy 31.3D watershed. 122 5.4.3 V isua ls Figure 5.12 presents an example of how visual resource objectives are achieved and maintained over time. With Scenario S5.3, timber has the highest weighting and age class structure has the lowest weighting; so the achieved age class structure is close to the target (10% tolerance). With Scenario S5.1, where timber has the lowest weighting and age class structure has the highest weighting, the achieved age class structure is farther below the target. 1 0 •Target • S5.1 S5.2 •S5.3 I I I I I I ! I I I I I I I I I I I I I I I I I I l O c o r o N - T - i n c o c o r * -T — T — CM CN CM OO 00 Period (5-year period) Figure 5.12 - Young (<20 years) stands of V Q O retention area. 5.4.4 Natural Disturbance Type and Biodiversi ty Figure 5.13 shows the old (>250 years) stand percentage targets achieved in a NDT1 area of landscape unit 16 during each period. The old stand targets for NDT 1 of landscape unit 16 are met in 60 years. In this specific case, a surplus of old stands develops because natural disturbance is not considered 123 and the inoperable stands are aging. The inoperable area alone is sufficient for the old stand target, so the weight has almost no effect on the results. 5 H T - m c > c o r > - T - i r ) o > e o r * -T— CM CM CM CO CO Period (5-year period) Figure 5.13 - Old (>250 years) stands of NDT1, landscape unit 16. Figures 5.14 (A1 - B4) show the achieved and desired patch size distributions for NDT1 of landscape unit 16. Graphs A1 - A4 are for young stands and graph B1 - B4 are for old stands. The targets for the smaller sized old patches are maximum targets, whereas the targets for smaller sized young patches are minimum targets. The target percentages of small sized patches for young and old stands are the same (35%, Figure 5.14 A1 and B1). However, fewer small old patches are desired, whereas more small young patches are desired. 124 The targets for the large-size (>250 hectares) old (>250 years) patches are minimum targets, whereas the targets for the larger sized young patches are maximum targets. The percentages of large (>250 ha) patches for young and old stands can be 0% (A3, B3, A4 and B4). However, more large old patches are desired, whereas less large young patches are desired. Some large (>250 ha) young (<=40 years) patches are created around period 6 (Figure 5.16 and Figure 5.14 A4) because these stands are "over mature" and have to be harvested under the assumptions of the model (stands older than maximum harvest age must be harvested or they will "collapse" and regenerate naturally). Figure 5.15 and Figure 5.16 show the achieved patch size distributions of old and young stands in NDT1 of landscape unit 16. For the old (>250 years) stands, the percentage of large (>250 hectares) patches is increasing and the percentage of small patches is decreasing over time. For the young (<40 years) stands (Figure 5.16), the percentage of large (>250 hectares) patch size is decreasing and the percentage of small (<40 hectares) patches is increasing over time. This implies that we can build large old patches while harvesting with small openings. A large old patch surplus occurs because the inoperable stands are aging in the absence of natural disturbance. 125 A1 80 60 40 20 0 • inffv. in CM s -eriod (5-years period) Target -S1(>35%) • S2(>35%) •S3 (>35%) © i S 3 CM II A 80 60 40 20 0 B1 - • S N 8 8 Period (5-year period) Target -S1(<35%) -S2(<35%) •S3(<35%) 2 5 f 50 40 30 20 10 0 A2 - * 5P « 8 8 Period (5-year period) Target -S1(35%) • S2(35%) •S3(35%) 2 A f V 15 10 A4 i- oo m a a 8 Period (5-year period) Target -S1(0%) -S2(0%) •S3(0%) ra O s A i o IO N II A 50 40 30 20 10 0 B4 " 0 0 5 Rl 83 8 Per iod (5-year period) Target -S1(>=0%) -S2(>=0%) •S3(>=0%) Figure 5.14 - Patch size distribution for NDT 1 of Landscape unit 16 126 lO CO CO T - 10 ai co h-r- CN CM CM CO CO Period (5 year period) Patch Size(Targets): •>250ha(>=0) • 80-250 ha (>30%) •40-80 ha (35%) •(M0ha(<35%) Figure 5.15 - Old (>250 years) patches of NDT1, Landscape Unit 16. Period (5 year period) Figure 5.16 - Young (<40 years) patches of NDT1, Landscape Unit 16. 5.4.5 Wildlife Connectivity Corridors Figure 5.17 shows the mature stand percentage achieved in connectivity corridors during each period. The target is met at period 8 (40 years) and is 127 maintained over the remaining planning horizon. A surplus occurs because the inoperable stands are aging in the absence of natural disturbance. In all scenarios, no area in the corridor is harvested during the first 8 periods, so the results are insensitive to the weightings. 90 n 80 -years) 7 0 -years) 6 0 - / T a r g e t years) 5 0 - S 5 . 1 o o 4 0 - ^ — S 5 . 2 30 - S 5 . 3 2 0 -10 -u i i i i i I I i i i i i i i i i i i i i i i I I I i - i o a ) c o r ^ " - m a > r o r ^ T - T - CN CN CN CO CO Period (5-year period) Figure 5.17 - Caribou connectivity corridor mature stands over time. 5.4.6 General Observat ions The desired states of all layers can be achieved within 200 years. Some layers are achieved earlier while others are not satisfied until period 15. A stable timber flow is maintained and the impacts of non-timber resources on timber flow are reduced. If these are unacceptable, objective weights should be adjusted and the model re-run. 128 Chapter 6 Conclusions and Recommendations Conclusions A Target-oriented Forest landscape Blocking and Scheduling (TFBS) theory was developed. A tool, the Forest Simulation Optimization System (FSOS) model was built based on the T F B S theory to produce strategies for forest treatment blocking and scheduling while transforming forest landscapes to desired states. A simulated annealing algorithm was used in F S O S to make tradeoffs between conflicting resource values. F S O S was tested on a sample data set and used to prepare a 20-year and 200-year plan for a 80,000 ha Tree Farm in British Columbia. The conclusions drawn from this study are: 1. The thesis has shown that age-structure and patch-size distributions are effective landscape-level indicators for non-timber resources. By using these two indicators, the forest landscape can be easily measured and monitored. 2. Combining blocking and scheduling is an effective way to achieve and maintain patch size distribution targets over the planning horizon while maximizing timber flows. 3. Sensitivity analysis of the sample data set demonstrates that the TFBS approach can produce strategies to transform forest landscapes from different initial states to the same desired state. It can also identify treatment strategies under different natural disturbance regimes. 129 4. The case study showed that the T F B S approach integrates the short- and long-term planning processes. It produces a long-term (up to several rotations) treatment schedule according to current states, desired states, projected dynamics and the sustainability of resources. The short-term schedule (1 - 20 years) is a subset of the long-term schedule, which guides current forest operations. 5. F S O S is an efficient tool for adaptive forest management. Forest treatment schedules can be modified when forest engineers reconfigure the blocks, update the database or when natural disturbance occurs. 6. The case study demonstrated that the T F B S approach allows simultaneous planning for multiple layers and multiple rotations. Tradeoffs can be made between resources and between rotations by adjusting objective weights. This differs from time-step simulation, which requires explicit intervention of the analyst to examine tradeoffs between resources and between rotations (or periods). 7. The case study demonstrated that forest management aimed at achieving sustainability of all objectives requires gradual modification of forest ecosystems. Developing the recommended age class structures and patches for a landscape unit should be implemented gradually and adapted to local conditions. It may be difficult to achieve the recommended age class structure in landscapes with an extensive harvesting history, and it may take several rotations to meet the old age class structure objectives. 130 8. One must exercise caution when using F S O S . Improper weightings can result in unacceptable solutions such as the short-term depletion of old growth when meeting long-term patch targets (Figures 5.10 and 5.12). There are numerous high quality solutions to the problems, and each solution has a different spatial pattern. From operations research perspectives, it is frustrating that there is no global "optimal" solution. However, from a forest management perspective, this is good news because it indicates robustness in the harvest schedule. The thesis has made a unique contribution by developing and demonstrating a multiple objective model capable of handling large scale and long-term planning problems. The modeling approach is flexible and can be extended to problems where the consequences of conflicting objectives need to be evaluated. Recommendations for future research • More efficient algorithms should be researched to improve the speed (or allow for larger problems - i.e. entire Timber Supply Areas). • Easier ways of identifying weightings and cooling rates should be identified. • Efficient map overlay tools are needed to reduce the number of resultant polygons. • An ability to schedule from multiple treatments is needed. Examples are alternative silvicultural systems and regeneration options. 131 Literature Cited Barahona, F., Weintraub, A. R. 1992. Habitat dispersion in forest planning and stable set problem. Operations Research 40 Supp. No. 1, S14 S21. Borges, J .G . , Goganson, H.M. and D.W. Rose. 1999. Combining a decomposition strategy with dynamic programming to solve spatially constrained forest management scheduling problems. Forestry Science 45(2): 201-212. Boston, K. and P. Bettinger. 1999. An analysis of Monte Carlo integer programming, Simulated annealing, and Tabu Search heuristics for solving spatial harvest scheduling problems. Forestry Science 45(2): 292-301. Brumelle, S. , Granot, D. Halme, M. and Vertinsky, I., 1998. A tabu search algorithm for finding good forest harvest schedules satisfying green-up constraints. European Journal of Operational Research, 106 (1998) 408-424. Camenson, Daniel M. 1998. Hierarchical design support tools for ecologically-based planning and management. Forest Scenario Modelling for Ecosystem Management at Landscape Level EFI Proceedings No. 19, 1998. Clements, S. E., Dallain, P. L. and Jamnick, M. S. 1990. An operational, spatially constrained harvest scheduling model. Can. J . For. Res. 20, 1438-1447. De Werra, D. and Hertz, A. 1989. Tabu search techniques: a tutorial and an application to neural networks. OR Spektrum 11, 131-141. Forman, R.T.T., and M. Godron, 1986. Landscape Ecology. John Wiley, Chichester, pp. 1 -16 . Forman, R.T.T., and Godron, M. 1981. Patches and structural components for a landscape ecology. Bioscience 31(10): 737-740. Glover, F. 1990. Tabu search: a tutorial. Interfaces 20, 264-280. Glover, F. 1989. Tabu search- part I. O R S A Journal on computing 1, 190-206. Gustafson E J . and Crow TR. 1996. Simulating the effects of alternative forest management strategies on landscape structure, Journal of Environmental Management. 46(1): 77-95. Haley, D. 1996. Paying the piper, paper prepared for working with the B. C. Forest Practices Code, an Insight Information Inc. Conference, sponsored by the Globe and Mail, Vancouver B.C. April 1 6 - 17, 1996. 132 Hof, J . , Becers, M., Joice, L , and Kent, B. 1994. An integer programming approach for spatially and temporally optimizing wildlife populations, Forest Science, Vol. 40, No. 1, pp. 177-191. Jamnick, M. S. and Walters, K. 1991. Harvest blocking, adjacency constraints and timber harvest volumes. Systems Analysis in Forest Resources Symposium, South Carolina, March 3-7, 255-261. Johnson, K.N., T.W. Stuart and S.A. Crim. 1986. F O R P L A N version 2: an overview. USDA Forest Service, Land management planning systems section, Washington D.C. 98 p. Jones, J .G . , Meneghim, B.J. , and Kirby, M.W. 1991. Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning. Forest Science. 37: 1283-1297. Kent, M. B., Kelly, J . W., and Flowers, W. R. 1985. Experience with the solution of USDA Forest Service FORPLAN models, Proceedings of a Society of American Foresters Symposium held in Athens, Georgia, December 9-11, 85. Kimmins, J .P . (Hamish), 1995. Sustainable development in Canadian forestry in the face of changing paradigms. January/February 1995, Vol. 71, No. 1, The Forestry Chronicle. Kirby, M., Hager, W. and Wong, P. 1986. Simultaneous planning of wild land management and transportation alternatives. TIMS Studies in the Management Sciences 21, 371-387. Kirkpatrick, S., Gelatt, C. and Vecchi, M. 1983. Optimization by simulated annealing. Science 220, 671-680. Lockwood, O , and Moore, T. 1993. Harvest scheduling with adjacency constraints: a simulated annealing approach. Can. J . For. Res. 23:468-478. Liu, Guoliang. 1995. Evolution programs, simulated annealing and hill climbing applied to harvest scheduling problems. Master's thesis, Department of Forest Resource Management, The University of British Columbia, Vancouver, Canada, pp. 45 - 60. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. 1953. Equation of state calculations by fast computing machine, Journal of Chemical Physics 21, 1887-1092. Michalewicz, Z. 1991, Genetic algorithms + data structures = evolution programs, Dept. of Computer Science, University of North Carolina, 133 Charlotte, NC 28223, USA, pp. 1 - 35. MOF, 1995. Forest Practices Code, Ministry of Forests, British Columbia, Biodiversity Guidebook, Victoria, British Columbia, Canada. Murphy, G. 1999. Allocation of Stands and Cutting Patterns to Logging Crews Using a Tabu Search Heuristic. Journal of Forest Engineering. Murray, A. T., and Church, R. L. 1993. Heuristic solution approaches to operational forest planning problems. OR Spectrum, 20p. Navon, Daniel I. 1971. Timber RAM, a long-range planning method for commercial timber lands under multiple-use management. P S W For. and Range Exp. Stn. USDA Forest Service Res. Rap. PSW-70. 22p. Nelson, J . D., Gizowski, D., and Shannon T. 1995, Menu for ATLAS V2.87 windows edition. Faculty of Forestry, University of British Columbia. Nelson, J.D. and Liu, G. 1994. Simulated annealing and forest planning problems, in Proceedings of 1994 International Conference of International Union of Forest Research Organisation, July 25 - 28, Harbin, China. 1994, pp. 28 - 36. Nelson, J . D. 1993. Analyzing integrated resource management options, Seminar Proceedings, Determining Timber Supply & Allowable Cuts in BC, pp. 45 - 51. Nelson, J . D. and Finn, S. T. 1991. The influence of cut-block size and adjacency rules on harvest levels and road networks. Can. J . For. Res. 21:595-600. Nelson, J . D. and Brodie, J . D. 1990. Comparison of a random search algorithm and mixed-integer program for solving area-based forest plans. Can. J . For. Res. 20: 934-942. Nute, D. et al., 1999. Goals in Decision Support Systems for Ecosystem management, Artificial Intelligence Center and Department of Philosophy, University of Georgia. O'Hara, A., Faaland, B. and Bare, B. 1989. Spatially constrained timber harvest scheduling. Can. J . For. Res. 19, 715-724. Sessions, J . , and Sessions, J . B. 1991. Tactical forest planning. In Proc. Soc. Am. For. National Convention, Soc. Am. For., San Francisco, CA , Aug. 4-7. Synder, S. and Revelle, C. 1995. The Grid Packing Problem: Selecting a Harvesting Pattern in an Area with Forbidden Regions, For. Sci . 42(1):27-34. 134 Thompson, E. F., Halterman, B. G. , Lyon, T. J . and Miller, R. L. 1973. Integrating timber and wildlife management planning. Forestry Chronicle 49, 247-250. Torres, R., J . M. and Brodie, J . D. 1990. Adjacency constraints in harvest scheduling: an aggregation heuristic. Can. J . For. Res. 20, 978-986. Wardoyo, W. and Jordan G. , 1996. Measuring and assessing management of forested landscapes. The Forestry Chronicle, Vol. 72, No. 6. Nov./Dec. 1996. Walters, C . J . 1986. Adaptive management of renewable resources. Macmillan, New York, USA. Weintraub A., Jones G. , Meacham M., Magendzo A. and Malchuk D., 1995. Heuristic procedures for solving mixed-integer harvest scheduling -transportation planning models, Canadian Journal of Forest Research-Journal, 25(10):1618-1626, 1995 Oct. 135 

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