Research On Evolutionary Algorithms For Large Scale Multi-objective Optimization Problems Based On Dimensionality Reduction

In the academic sector of evolutionary computation,multi-objective is a significant and challenging field.During the past few years,a large number of researchers have devoted themselves to finding solutions to such optimization problems,and many classical multiobjective evolutionary algorithms(MOEAs)have been proposed one after another.Although these multi-objective evolutionary algorithms have been proved to be able to solve some test problems well and have been well applied in practical problems.However,when we use traditional MOEAs to solve multi-objective optimization problems with large-scale decision variables,their performance will decline sharply.The reason for this phenomenon is that when the dimension increases,the search space will expand exponentially,which is called "the curse of dimensionality".In practical applications,there are many such highdimensional problems that need to be solved,which urgently requires us to design a new multi-objective evolutionary algorithm to solve these problems.Cooperative coevolution framework is one of the most effective methods to deal with large-scale multi-objective problems.The cooperative coevolution method divides decision variables into mutually exclusive subgroups,and then optimizes each subproblem independently.In this thesis,we integrate dimensionality reduction method as well as diversity optimization technology and introduce a new grouping mechanism to solve large scale multi-objective problems(LSMOPs).The specific content is as follows: 1.A new clustering and dimensionality reduction based evolutionary algorithm PCA-MOEA is proposed to solve multi-objective optimization problems with high-dimensional decision variables.Mainstream evolutionary algorithms ignore the relationship between variables in search space and optimize all decision variables as a whole,which brings many difficulties to the optimization process.In PCA-MOEA,a clustering strategy is adopted to classify decision variables into two categories,namely,convergence-related variables and diversityrelated variables.Clustering method adopts the angle between sampling solution and convergence direction as feature and uses k-means to group decision variables.Then,the low-dimensional representation of convergence-related variables is obtained by principal component analysis,after that,the reduced decision variables are decomposed into several independent sub-components,which are optimized independently in the framework of cooperative coevolution finally.Compared with several state-of-the-art algorithms,the statistical results show that PCA-MOEA can solve the large scale multi-objective optimization problems well.2.A diversity variable optimization based multi-objective evolutionary algorithm PCA-DVMOEA is proposed.The performance of PCA-MOEA can be further improved on population diversity.We know that PCA-MOEA divides decision variables into two categories: convergence-related variables and diversity-related variables,which affect the convergence rate of the population and the evenness of the final solution distributed on the Pareto front,respectively.Therefore,for different groups of decision variables,adopting different selection strategies will produce better results.In the process of diversity variable optimization,we use the dominance-based approach and distance measure to improve the diversity of population.The experimental results show that PCA-DV-MOEA has advantages in solving multi-objective optimization problems with high-dimensional decision variables,and it can effectively improve the diversity of the population.3.A novel overlapped grouping mechanism is proposed to solve large-scale multi-objective problems,named PCA-OG.Traditional cooperative coevolution framework divides all decision variables into a set of groups which are mutually exclusive,but most of the grouping strategies only consider the dependence relationship between variables and ignore another characteristic,that is,the influence of decision variables on the value of fitness.For a specific problem,each dimension of decision variables may have different effects on optimization.The algorithm uses delta perturbation strategy to detect decision variables that have a significant impact on fitness values,and then overlaps them based on general grouping results.In the optimization process,influence variables are overlapped in different groups and thus optimized many times,which means that they are given more computing resources.This mechanism will increase the diversity of the population and avoid falling into local optimum.