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UBC Theses and Dissertations

Performance modelling and automated algorithm design for NP-hard problems Xu, Lin


In practical applications, some important classes of problems are NP-complete. Although no worst-case polynomial time algorithm exists for solving them, state-of-the-art algorithms can solve very large problem instances quickly, and algorithm performance varies significantly across instances. In addition, such algorithms are rather complex and have largely resisted theoretical average-case analysis. Empirical studies are often the only practical means for understanding algorithms’ behavior and for comparing their performance. My thesis focuses on two types of research questions. On the science side, the thesis seeks a in better understanding of relations among problem instances, algorithm performance, and algorithm design. I propose many instance features/characteristics based on instance formulation, instance graph representations, as well as progress statistics from running some solvers. With such informative features, I show that solvers’ runtime can be predicted by predictive performance models with high accuracy. Perhaps more surprisingly, I demonstrate that the solution of NP-complete decision problems (e.g., whether a given propositional satisfiability problem instance is satisfiable) can also be predicted with high accuracy. On the engineering side, I propose three new automated techniques for achieving state-of-the-art performance in solving NP-complete problems. In particular, I construct portfolio-based algorithm selectors that outperform any single solver on heterogeneous benchmarks. By adopting automated algorithm configuration, our highly parameterized local search solver, SATenstein-LS, achieves state-of- the-art performance across many different types of SAT benchmarks. Finally, I show that portfolio-based algorithm selection and automated algorithm configuration could be combined into an automated portfolio construction procedure. It requires significant less domain knowledge, and achieved similar or better performance than portfolio-based selectors based on known high-performance candidate solvers. The experimental results on many solvers and benchmarks demonstrate that the proposed prediction methods achieve high predictive accuracy for predicting algorithm performance as well as predicting solutions, while our automatically constructed solvers are state of the art for solving the propositional satisfiability problem (SAT) and the mixed integer programming problem (MIP). Overall, my research results in more than 8 publications including the 2010 IJCAI/JAIR best paper award. The portfolio-based algorithm selector, SATzilla, won 17 medals in the international SAT solver competitions from 2007 to 2012.

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Attribution-NonCommercial-NoDerivs 2.5 Canada