Research And Application Of Multi-objective Optimization Evolutionary Algorithm

Multi-objective optimization is widely used in engineering practice,scientific research and many other fields.The common methods to solve multi-objective problems include traditional solutions and intelligent algorithms.Genetic Algorithms(GA)is one kind of intelligent algorithms and a bionic one based on adaptive evolution,which is famous for its good global search ability and parallel search ability.The genetic algorithm shows well performance in solving single objective and multi-objective problems.Based on the introducing the theory of the genetic algorithm,this paper designs an improved genetic algorithm for solving multi-objective problems and evaluate its performance.The main research work and results are as follows:Firstly,based on the study of multi-objective optimization theory and traditional multi-objective optimization algorithm,we further focused on the basic theory of multi-objective evolutionary algorithm and several typical benchmark algorithms in multi-objective evolutionary domain.Moreover,a benchmark algorithm in the field of multi-objective evolutionary algorithm,non-dominated sorting genetic algorithm ?(NSGA-?),is emphatically introduced.Secondly,a non-dominated sorting genetic algorithm based on dominance matrix is designed to solve multi-objective optimization problems.This algorithm improves the diversity of solution sets and the non-dominated sorting method based on the framework of the non-dominated sorting genetic algorithm ?(NSGA-?).Generally speaking,the main focuses of multi-objective algorithms include convergence and diversity.NSGA-? gives priority to convergence than diversity and improves the diversity in some degree and achieves good results.In order to further improve the diversity of NSGA-? algorithm,this paper uses the partition selection algorithm(PSA)to redefine the crowding distance between individuals to maintain the population diversity.Partition selection algorithm can obtain a diversity subset from any given set,and based on this feature of the algorithm,it can screen the individuals with diversity from the current population into the next generation evolution process,so as to obtain the diversify solution set.In addition,owing to the guidance of Pareto dominance,the NSGA-? algorithm adopts Pareto dominant to guide individuals to converge to the Pareto front,the search process includes non-dominant-sorting,dominant-counting and other methods.These methods are usually time-consuming,and the execution time will increase with the dimension of the objective function.Therefore,a more effective non-dominated sorting method,namely DDA-NS based on dominance matrix,is proposed to reduce the running time of the whole algorithm.Two improved strategies,PSA and DDA-NS,are embedded in NSGA-?,which is denoted as DNSGA2-PSA.Finally,the performance of the improved algorithm is tested by numerical experiments.In this paper,the execution time,the convergence and uniform distribution index of the final solution set are used to evaluate the algorithm.The experimental results show that the running time of DNSGA2-PSA algorithm is significantly shorter than that of NSGA-? algorithm added by PSA alone(NSGA2-PSA),which shows that the non-dominated sorting method based on dominance matrix can greatly reduce the running time of the whole algorithm.Experiments show that DNSGA2-PSA is performed better than NSGA-II that joined DDA-NS and PSA lonely with regard to convergence index GD,IGD and diversity index HV and Spacing,and DNSGA2-PSA still shows good applicability in high-dimensional situations.