Preference Multi-Objective Evolutionary Optimization Based On Angle Decomposition

Multi-objective evolutionary optimization performs operations such as selection,crossover and mutation on the initial population.According to the idea of survival of the fittest,the solution with better performance is retained and the next generation solution set is continuously generated,and finally all optimal solutions in the feasible interval are obtained,which is a set of solutions.In reality,problems such as planning and scheduling involve multiple solutions,and decision makers often need to choose the appropriate solution according to their own needs.The algorithm that gives an appropriate solution according to the individual requirements provided by the decision maker before the algorithm is executed is the multiobjective evolutionary optimization preference algorithm.Due to its widespread existence in practical problems,the research on preference algorithms has become a popular direction.How to accurately give feasible solutions according to the preference information given by decision makers is an important criterion for judging the pros and cons of preference algorithms.The ultimate goal of multi-objective evolutionary optimization is to support decision makers to find solutions that best satisfy their preferences.Multi-objective optimization provides a large number of solutions for decision makers,and a large amount of irrelevant interference information will be generated during the decision-making process.Centrally searching for the optimal solution set in the preference area can not only concentrate the search resources,but also help the decision maker to select the optimal solution set from a large number of solution sets.The current preference multi-objective optimization algorithms can be divided into dominance-based optimization algorithms represented by r-dominance and weight aggregation-based optimization algorithms represented by MOEA/D-PRE and MOEA/D-STM.However,these algorithms still have shortcomings in dealing with practical problems.Therefore,in order to improve the performance of the algorithm in practical problems,according to the preference information given by the decision maker,the optimal solution set that meets the needs of the decision maker is called a new research field in the multi-objective evolutionary optimization algorithm.Rather than a whole Pareto optimal front(PF),which demands too many solutions,the decision maker(DM)may only be interested in a partial region,called the region of interest(ROI).In this paper,we propose an idea based on the angle decomposition between objectives(MOEA/D-DAP),so that the information represented by individuals is different relative to the preference points,thus avoiding the loss of preference information due to the increase in dimensions.This paper summarizes and analyzes the problems existing in the traditional way of defining preference regions,and proposes a new method for defining preference regions.At the same time,the proposed algorithm avoids the phenomenon of partial preference information being lost due to the increase of dimensions,so that the final results are more in line with decision makers.Preferences.Finally,the reference vector generation method of the algorithm proposed in this paper makes the final solution no longer evenly distributed in the ROI,but gradually changes the distribution density of the solution in space according to its proximity to the preference point.A large number of experiments on benchmark problems with two to ten objectives prove the effectiveness of proposed method in the ROI.These experimental results show that our algorithm is feasible in solving multi-objective optimization problems(MOPs).