Research On Multi-objective Evolutionary Algorithm Considering Convergence And Diversity

With the rapid development of science and technology,multi-objective optimization problem has become one of the most crucial problems in the field of artificial intelligence and other related fields.In recent years,the multi-objective optimization problem has become more and more complicated,which leads to the appearance of new types such as disconnected multi-objective optimization problem,many-objective optimization problem and constrained multi-objective optimization problem.The distinctive character of these problems poses a challenge for solving.Therefore,how to solve the new types of multi-objective optimization problem efficiently has become a research focus of optimization field.As an important branch of evolutionary computation,multi-objective evolutionary algorithm has become one of the most effective and popular methods to solve multi-objective optimization problem.Convergence(refining the solution set)and diversity(searching new Pareto-optimal solutions)are the basic characters of multi-objective evolutionary algorithm.However,with the emergence of the new type multi-objective optimization problem and the demand of the user,the multi-objective evolutionary algorithms' performances deteriorate severely when handling new type multi-objective optimization problem.The reason of this phenomenon can be summarized as follows:for specific types of multi-objective optimization problem,the traditional algorithms which emphasize on maintaining one basic character could not balance convergence and diversity of algorithm,resulting in wasting of search resources or searching in a wrong direction.Aiming at the above problem,we propose four multi-objective evolutionary algorithms to solve four representative multi-objective optimization problems.Based on the characteristics of each type,we adjust the diversity and convergence maintenance mechanism to balance the convergence and diversity of the proposed algorithms.To make up for some shortcomings of traditional criterions,dimension convergence is proposed as a new convergence criterion,and search space diversity and two space diversity are presented as new diversity criterion.All new criterions balance the convergence and diversity of algorithm with the traditional evaluation criterions.The contribution is reflected in the following aspects:(1)When solving disconnected multi-objective optimization problem,the diversity maintenance mechanism of traditional multi-objective optimization algorithm could not suppress the wasting and unequal allocation of the search resource.To address this issue,we propose a search space diversity-oriented evolutionary algorithm.The proposed algorithm use search space diversity maintenance mechanism to balance the convergence and diversity.A good search space diversity could keep search behavior out of local search,while maintaining a good objective space diversity.An exploratory reproduction operation is presented to enhance the explorative search ability of the algorithm and avoid the local search.The comparison experimental results show that the proposed algorithm could effectively avoid the waste of search resources with respect to chosen state-of-the-art designs.(2)When solving connected and unconstrained multi-objective optimization problem,most of the researches related to diversity maintenance scheme are dedicated to the diversity of objective space and ignore the diversity of decision space.To address this issue,we propose a two space density-oriented multi-objective evolutionary algorithm.Two-space-density is defined to reflect the diversity in both the objective space and the decision space.Based on two-space-density,TSD-mating selection is presented to balance the convergence and the diversity of population;TSD-selection is designed to fully explore the objective space and the decision space.The experimental results show that,diversity maintenance of the search space and objective space make proposed algorithm perform competitively with respect to chosen state-of-the-art designs.(3)When solving many-objective optimization problem,the traditional convergence criterion failed to distinguish the convergence among the non-dominated solutions.To address this issue,we propose a dimension convergence based many-objective evolutionary algorithm.Dimension convergence can further evaluate the convergence among the non-dominated solutions,which ensures a more accurately individual selection.A dimension convergence-based mating selection is presented to enhance the convergence ability of the proposed algorithm.The experimental results show that,dimension convergence-based convergence maintenance mechanism could effectively improve the convergence speed of the algorithm.(4)When solving constrained multi-objective optimization problem,most of the researches ignore the influence of constraint in objective space.To address this issue,we propose a comprehensive evaluation based constraint many-objective evolutionary algorithm.The comprehensive evaluation mechanism considers constraint feasibility,constraint violation,non-dominance level,dimension convergence degree and diversity based on reference point to balance the convergence and diversity of proposed algorithm.The comprehensive evaluation mechanism also can assist the individual selection operator work effectively.The experimental results show that,comprehensive evaluation of the proposed algorithm could overcome constraints' influence on the objective space.On the background of multi-objective optimization problem,this thesis investigated evolutionary multi-objective algorithms for four types of multi-objective optimization problems from the aspects of convergence and diversity.This study has not only important significance to the multi-objective evolutionary algorithm research,but also certain instruction value to the research of various types of multi-objective optimization problems.