The Study Of Evolutionary Algorithm On Solving Multi-Trap And Imbalance Optimization Problems

Evolutionary Algorithm (EA), a random search method inspired by biological evolution,plays an important role in solving complex global optimization and multi-objectiveoptimization problems, especially the multi-trap imbalance and constrained optimizationproblems, and draws the wide attention of the optimization community. At present, due to itshigh generality and usability, EAs have been gradually used in project management, computerapplications, engineering optimization design, automation control and other fields. In contrastto the traditional deterministic algorithms, EAs' search ability and robustness have becomethe key factors that influence their widespread applications. This paper mainly studies EAs insolving multi-trap imbalance and constrained optimization problems, and proposes severalmodified algorithms. The main contributions and innovations are brought forward, including:(1) For single objective problems, an evolutionary algorithm with sorted race mechanismfor global optimization is proposed. Unlike EAs that evolve populations directly according tofitness values, our method selects better solution from two individuals with similarchromosomes to maintain the diversity and convergence of population, this method needs noadditional external set for diversity of population and has a low time complexity. Besides, aself-adaption crossover and mutation operator related to evolution time is used to enhance thesearch ability of EAs. Finally, the numerical experiments for a group of benchmark problemsand the comparison of numerous existing elite algorithms indicate that the algorithm iseffective. Especially, the proposed algorithm finds a solution of a test function with100variables even better than the best reported result.(2) After discussing the shortcomings of some common fitness functions, a group ofevenly distributed weights and a transform function is designed to improve the fitnessfunction that enable algorithm to select a set of solutions distributed evenly in objective space,but if the selected solutions are not distributed evenly, some sub-domains should be sparselyor no solution appeared, then a dynamic adjusted mechanism is proposed to increase thesearch probability in these sub-domains, also the good solutions in dynamic adjacent domainsare exploited to enhance the algorithm's search efficiency. Experimental results have showthat the proposed algorithm is more efficient than the other two state-of-the-art algorithms.(3) The essay first presents the detailed analysis of individual selection of the min-maxstrategy. The best individual can be obtained by searching the solution of each sub-objectivein different areas. Based on this observation, a direction selection search method is proposed.Moreover, in order to prevent large deviation between solutions searched in different direction in the same sub-region, a dynamic threshold is designed and an external set is added to shareinformation between individuals. At last, some common and difficult multi-objective testfunctions are tested, the experiments show that the proposed algorithm solves most problems.(4) In order to handle the constraints, the method not only considers the violation ofinfeasible solutions and preference relations, but also the distribution of infeasible solutionsinfluences on population updating, thus it improves selection of infeasible solutions. Inaddition, an effective judge mechanism to determine whether holes appear on Pareto Front isproposed to reduce the invalid search for constrained multi-objective optimization problem.The results suggest that this algorithm outperforms or performs comparably to otheralgorithms for many difficult constrained test functions.(5) The problem about loss of optimal solutions and selecting poor solutions is studied inselecting solutions by weights. A method of selecting weights by solutions is proposed, and itstheoretical analysis is presented. Generally, in the selection process we employ grouping andthe local comparison strategies to reduce the time complexity of the algorithm. In addition,the algorithm gives a new induced operator based on statistics to dynamically adjust theprobability of solutions searching in different regions. It works well on many constrained andunconstrained multi-objective optimization test instances.