Evolutionary Algorithms For Solving Many-objective Optimization Problems

Multi-objective optimization problems are widely used in scientific research and engineering applications,such as automatic control,portfolio and decision-making,job shop scheduling,biomedicine,image processing and data mining.A multi-objective problem refers to a problem that contains multiple optimization functions,but with the increase of the number of objectives,the traditional multi-objective evolutionary algorithms can only converge to local optimization.Many-objective optimization problems have gradually become a kind of research hotspot.Specifically,in many-objective optimization problems,the number of nondominated solutions accounts for the majority,and the traditional multi-objective evolutionary algorithms lose the convergence pressure because they cannot identify the solutions.In order to promote the convergence pressure of many-objective evolutionary algorithms,this paper mainly considers the following aspects:(1)For a large number of solutions that are not dominated by each other,how to choose potential solutions to promote the convergence ability of the algorithm;(2)How to improve the dominance relation of the solutions and slow down the rising speed of the proportion of non-dominated solutions in the population.In order to solve the above problems,the research work of this paper includes:(1)An evolutionary algorithm based on generational distance indicator and an improved niching method is proposed.The indicator is designed to compare the optimal solution set of different algorithms.In the process of population evolution,the convergence ability of the algorithm can be optimized by selecting the next generation population based on the indicator.Generational distance(GD)is a reliable indicator to measure the convergence.Therefore,in view of the large proportion of non-dominated solutions in many-objective optimization problems,an evolutionary algorithm based on GD indicator is proposed to further select potential individuals to enter the next generation population(called GD/Ma OEA).Firstly,for the non-dominated solution with the same rank,the proximity distance of the individual is introduced as the indicator to select the potential solution.Secondly,in order to maintain the good diversity at the same time,an improved niching method based on the angle between the candidate solutions is proposed to assign new ranks to the solutions.An individual can only be compared with the individuals in the same niche.Finally,a new comparison method is proposed to eliminate the influence of comparison order on individuals and give higher priority to the individuals with better diversity.The results of numerical experiments show that compared with the state of the art algorithms,the proposed algorithm is effective.(2)A nonlinear expanded dominance relation based evolutionary algorithm is proposed.Multi-objective evolutionary algorithms do not perform well in many-objective optimization problems.Because with the increase of the number of objectives,the traditional Pareto dominance cannot identify the solution,resulting in a sharp rise in the proportion of nondominated solutions and it can only converge to the local optimum.For a feasible solution,it can dominate the solutions which are slightly better in some objectives but significantly worse in most other objectives,and this dominance should be gradually expanded.Based on this motivation,a nonlinear expanded domination relation is proposed.Firstly,in order to unify the order of magnitude of different objectives,the objective function values of individuals in the population are normalized.Secondly,the objective function values of individuals are modified according to the proposed dominance relation,and the domination region of the solution is expanded nonlinearly.Finally,in order to maintain the diversity and wideness,a niching method is used to limit the comparison range of individuals.The proposed nonlinear expanded dominance relation replaces the non-dominated sorting in the classic many-objective evolutionary algorithm NSGA-III.The numerical experiment results show that the algorithm has good performance compared with the state of the art algorithms.