Study Of Preference-based Multi-objective Evolutionary With Preference Radius Selection Mechanism

In real life,optimization problems with multi-objective,nonlinear and high-complicated are difficult to solve.The traditional optimization methods cannot solve those problems very well,but Evolutionary Algorithms(EAs)which randomly search individuals for problems especially multi-objective evolutionary algorithms can deal with them easily.Evolutionary Algorithms are one kind of global searching algorithm,and they simulate the biological evolutionary mechanisms to solve actual optimization problems.EAs can be divided into single-objective optimization evolutionary algorithms and multi-objective evolutionary algorithms.Most actual optimization problems are multi-objective optimization problems,so study of Multi-objective Evolutionary Algorithms(MOEAs)are becoming one of hotspot in the EAs.With an increasingly popular study of MOEAs,the researchers tend to obtain high performance algorithms and these algorithms can solve problems with more objectives.However,with the increase of the number of dimensions of the optimization problems,the number of pareto non-domination solutions increase exponentially.These solutions will affect the convergence and distribution of algorithms,which is hard to the decision makers(DMs)to make accurate choices.Later,the researchers find that the MOEAs joined the decision maker's preference information can not only reduce the time complexity of the algorithm,but also can improve the convergence of the algorithm.Consequently,preference information provided by the DMs based on multi-objective evolutionary algorithms become one of hotspot in the research of MOEAs.In the traditional preference-based multi-objective evolutionary algorithms,reference points as preference information carrier in different objective space(the infeasible region,true Pareto front,the feasible region)sometimes seriously affect the performance of the algorithm.The algorithm can not accurately obtain the region that the decision maker interest.On the high-dimensional problems,the number of non-dominated solutions is far lager than the number of dominated solutions,which is bad for layered selection based on Pareto ranking and affects the convergence performance of the algorithm.To solve the above problems,this paper proposes a new preference information with reference point based on multi-objective evolutionary algorithm.In this newalgorithm,we construct a preference radius selection model and divide the objective space into two region: preference region and non-preference region.The solutions also divide two distinct parts: a preference set where solutions located in preference region and non-preference set where solutions located in non-preference region.If the number of the preference set is bigger than the evolutionary population size,then the superfluous solution by Pareto dominance relationship are removed,or if the number of preference set is smaller than the size,those solutions which have smaller distances to the preference direction in the non-preference set are selected until the number matches the evolutionary population size.In comparison with the state-of-the-art algorithms: g-NSGA-II,r-NSGA-II and a-NSGA-II,experimental results show that the proposed algorithm applying the mechanism is able to adapt to different reference points in varying regions in objective space and obtain the region which the decision maker interests.Moreover,this paper has better performance in most of test instances compared with other three algorithms in high-dimensional problems.