Research On Multi-objective Evolutionary Optimization Method Based On Decision Space Search

There are many multi-objective optimization problems(MOPs)in the real world.Multi-objective optimization is the simultaneous optimization of multiple objectives.Multi-objective optimization algorithm has been applied in many scientific and engineering fields.Multi-objective evolutionary algorithm(MOEAs)is a kind of iterative optimization algorithm based on swarm intelligence.Because it can find a set of solutions in a single run,it is widely used to solve multi-objective optimization problems,and has attracted more and more researchers' attention.Traditional multi-objective evolutionary algorithms(MOEAs)have good performance when solving low dimensional continuous multi-objective optimization problems.However,as the optimization problems' dimensions increase,the difficulty of optimization will also increase dramatically.The main reasons are the lack of algorithms' search ability,and the smaller selection pressure when the dimension increases as well as the difficulty to balance convergence and distribution conflicts.In this paper,after analyzing the characteristics of the continuous multi-objective optimization problem,a directional search strategy based on decision space(DS)is proposed to solve high dimensional multi-objective optimization problems.This strategy can be combined with the MOEAs based on the dominating relationship.DS first samples solutions from the population and analyzes them,and obtains the controlling vectors of convergence subspace and distribution subspace by analyzing the problem characteristics.The algorithm is divided into convergence search stage and distribution search stage,which correspond to convergent subspace and distributive subspace respectively.In different stages of search,we use sampling analysis results to macroscopically control the region of offspring generation.The convergence and distribution are divided and emphasized in different stages to avoid the difficulty of balancing them.Additionally,it can also relatively focuses the search resources on certain aspect in certain stages,which facilitates the searching ability of the algorithm.To prove the effectiveness of DS strategy in the experiment,we compare NSGA-II and SPEA2 algorithms combining DS strategy with original NSGA-II and SPEA2 algorithms,and use DS-NSGA-II as an example to compare it with other state-of-the-art high-dimensional algorithms,such as MOEAD-PBI,NSGA-III,Hype,MSOPS,LMEA.The experimental results show that the introduction of the DS strategy greatly improves the performance of NSGA-II and SPEA2 when addressing high dimensional multi-objective optimization problems.It is also shown that DS-NSGA-II is more competitive when compared the existing classical high dimensional multi-objective algorithms.