The Research On Preference Multiobjective Evolutionary Method Based On Objective Proportion

Multiobjective evolutionary algorithms(MOEAs)are commonly used methods to solve multiobjective optimization problems(MOPs)in real life.MOEAs can search and provide decision maker(DM)with a series of trade-off solutions.With the increase of the number of optimization objectives in traditional MOEAs,the difficulty of optimization also increases.Therefore,researchers have proposed a way to add preference information during the search process,so that DM can get the region of interest(ROI)in the objective space.To a certain extent,this method can solve the problems of insufficient selection pressure in high-dimensional algorithms and insufficient number of individuals to express a complete Pareto Front.Aiming at the problem that the preference information in the preference MOEAs affects the convergence of the algorithm and the population distribution in the ROI,this paper proposes a preference algorithm based on objective proportion(PAOP)for evolutionary multiobjective optimization.According to the preference information provided by the DM—the objective proportion,the PAOP algorithm generates reference points uniformly on the unit hyperplane,and integrates the preference information with each reference point evenly distributed on the hyperplane,and finally establishes a preference model located on the hyperplane corresponding to the preference information.Without the need for the DM to provide the size of the ROI,the model can control the range of the preference optimal solution,so as to meet the DM’s expectation of the ROI range,and can avoid the influence of preference information on the performance of the algorithm.The PAOP algorithm integrates the preference model into the decomposition-based algorithm,and guides the population from searching for solutions in the entire objective space to searching for solutions only in the ROI,maintaining the convergence and diversity in the ROI.In each iteration of the evolution process,the algorithm calculates the weight-based aggregation function value for the individuals in the population,compares this value with the aggregation function value of the newly generated individual,and performs the same comparison operation with the neighbors of the individual.So as to achieve the effect of survival of the fittest.By combining the preference model with decomposition,the PAOP algorithm can also find a set of solutions with good convergence in high-dimensional problems.The PAOP algorithm has low requirements on the degree of DM participation.It only needs to provide the proportion of each objective,and the final solution obtained can reflect the partial order relationship between the objectives.This paper selects four preference MOEAs(g-NSGA-II,r-NSGA-II,MOEA/D-PRE,NUMS)that have certain influence in the field of preference as the comparison algorithm,and selects classics such as ZDT,DTLZ,WFG,etc.The multiobjective test problem set is used as the optimization problem in the experiment.The experimental results show that the performance of the PAOP algorithm proposed in this paper is stable and can overcome the influence of the position of preference information;and when the number of objectives increases,the PAOP algorithm still has certain advantages and competitiveness compared with the above four preference algorithms.