An Improved NSGA-? Algorithm Based On Differential Evolution And Farthest Distance Priority

In scientific research and engineering practice,people often encounter some multi-objective optimization problems.There are more than one things to be optimized in these problems,always conflicting with each other.Different from the single objective optimization problem,the solution to a multi-objective optimization problem is usually not a single one,but an assemble of a set of Pareto optimal solutions.Therefore,it is more complex to solve the multi-objective optimization problem than the single objective optimization problem.Over the years,scholars have made many attempts to resolve this kind of problems and also put forward some methods,such as constraint method,weighted method,goal programming method etc.,but these methods request more in subjective factors and related parameters,so they are difficult to be widely used in engineering practice.Evolutionary algorithm is a kind of algorithm that simulated the biological evolution process,it doesn't need gradient information,while having the advantages of easy implementation and high robustness,it can effectively deal with the complex problems that traditional methods can not do.Since 1960s-1970 s many representative algorithms have appeared,such as NSGA-?,SPEA2,MOEA/D and so on,these algorithms have been widely applied in engineering practice.In the design of multi-objective evolutionary algorithm,convergence and diversity are two key elements.The former refers to the degree of approximation between computed approximate solution and actual Pareto front in the search space,while the latter measures the distribution of computed approximate solutions in the search space,including uniformity and universality.Convergence and diversity are always conflicting:Improving convergence to a certain extent will do damage to the diversity,and vice versa.Therefore,an excellent multi-objective evolutionary algorithm is supposed to make a good balance between the two elements.NSGA-? ensures the convergence of algorithm by fast non-dominated sorting,meanwhile introduces crowding distance to maintain the diversity.In those two-objective optimization problems,crowding distance can measure the distribution of solutions,however,when the objective quantity increases,the crowding distance cannot reflect the individual density effectively.The reason is that crowding distance just consider only one objective's distribution each time but not all of them.Secondly,NSGA-? algorithm select multiple individuals into the next generation one-time according to the crowding distance,which will also affect the diversity of final solution set.In order to improve the convergence and diversity of NSGA-? algorithm then make a balance between the two,this paper proposed NSGAIIDE algorithm.There are two aspects where NSGAIIDE is ahead of NSGA-?:One is introducing differential evolution algorithm to replace the simulated binary crossover operation in NSGA-? algorithm,and adding the information of globel optimal solution adaptively into the new individuals to enhance the convergence of the algorithm;the other is using global dynamic insertion mechanism based on distance priority,which replaces the static insert operation based on crowding distance in NSGA-?,this way the diversity of the algorithm is guaranteed.To verify the validity of the improved scheme,this paper chooses DTLZ,ZDT and WFG test set of benchmark problems(21)and uses six performance indicators to compare NSGAIIDE algorithm with other nine mainstream algorithms.The experimental results show that the proposed NSGAIIDE algorithm' performance really dominates other algorithms.Compared with the NSGA-?,the distribution of populations has improved significantly.The work of this paper has a certain reference value in improving multi-objective evolutionary algorithm,desighing the new algorithms and the practical application of algorithms.