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Estimation distribution algorithms based on extreme elitism and their application in engineering optimization problems Gao, Shujun

Abstract

This dissertation modifies several estimation distribution algorithms (EDAs) and implements them in engineering optimization problems. The EDAs are population-based evolutionary algorithms, which employ extreme elitism selection. The main work of the present study is outlined below. First, an approach of extreme elitism selection is developed for EDAs. This selection highlights the effect of a few top solutions and advances EDAs to form a primary evolutionary direction. Simultaneously, this selection can also maintain population diversity to make EDAs avoid premature convergence. EDAs with the new selection approach are tested using a set of benchmark low-dimensional and high-dimensional optimization problems. The experimental results show that the EDA based on univariate marginal Gaussian distribution (UMGD) with extreme elitism selection can outperform some other classical evolution algorithms for most problems. Second, the EDA based on UMGD with extreme elitism is implemented for solving the inverse displacement problem (IDP) of a robotic manipulator. This EDA is compared with the EDAs with other selection methods in solving the IDP of a 4-degree-of-freedom (DOF) robotic arm. Next the algorithm is integrated with differential mutation to solve the IDP of a 7-DOF robotic arm. After that, the proposed algorithm is used to search for satisfactory solutions as a continuous curve. The simulation results show this algorithm can reach real time speeds, in practical applications. Third, EDAs based on five different Gaussian distributions are proposed to solve optimization problems with various types of constraints like equality, inequality, linear, nonlinear, continuous or discontinuous. It is found the EDA based on a single multivariate Gaussian distribution with extreme elitism selection can outperform other EDAs. Besides, this EDA has good performance for four engineering design problems. Fourth, EDA is combined with differential mutation to solve multi-objective optimization problems (MOPs). The hybrid algorithm seeks to find the Pareto optimal front for MOPs. EDAs guide the search direction in the evolution while differential mutation keeps a diversified population. A new sampling method that uses more Gaussian models to generate offspring is specially designed for the EDAs for MOPs. In light of no-free-lunch theorem, different probabilistic models and programing codes are adopted for different MOPs.

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Attribution-NoDerivatives 4.0 International

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