The Research On Hierarchical Preference Algorithm Based On Decomposition Multiobjective Optimization

The existing classical multi-objective optimization evolutionary algorithms(MOEAs)perform well in dealing with two-dimensional or three-dimensional multi-objective optimization problems(MOPs).However,with the deepening of the research,how to find the overall Pareto optimal frontier has become an important and challenging problem in the practical application of multi-objective optimization.In the process of studying highdimensional optimization problems,researchers found that the ultimate goal of multi-objective optimization is to support decision makers to find the solution that can best meet their preferences.Providing too many solutions for decision-makers not only costs a lot of time and energy,but also leads to a lot of irrelevant interference information in the decision-making process,making it difficult for decision-makers to choose the appropriate solution.In addition,with the increase of the number of targets,it is difficult to cover the whole PF surface with only a limited number of individuals.Therefore,only searching the target preference region by the DM can not only reduce the difficulty of convergence,but also help decision-makers make better choices.In some practical problems,decision makers(DM)may only be interested in a local region(ROI),instead of requiring all solutions to be distributed in the entire Pareto optimal Frontier(POF).Based on this demand,many researchers guide the population to converge to the designated region by forming a new dominant relationship or directly limiting the convergence region.However,the existing preference algorithms are lack of density control and contrast fairness.To solve this problem,we propose a systematic approach to integrate decision makers' preference information into a decomposition based multi-objective optimization algorithm framework(MOEA/D-HP).Different from most existing preference algorithms,MOEA/DHP guides the population to converge to the preference region by generating a series of hierarchical reference points in the preference region,and forms some hierarchical solutions for decision makers to compare and select.In addition,the MOEA/D-HP reference vector generation method makes the solution no longer uniformly distributed in ROI,but the closer to the preference point,the denser the solution.In this way,the decision maker can get more solutions in the region of more interest.In this paper,five advanced preference algorithms(g-NSGAII,r-NSGAII,p-NSGAII,MOEA/D-STM,MOEA/D-PRE)are selected and compared on ZDT series,DTLZ series,WFG series and Ma OP test problems.From the results of GD index,we can see that the method proposed in this paper is feasible and competitive.