The Research On High-dimensional Multi-objective Evolutionary Algorithm Based On Reference Point

In daily life,many applications involve the problem of multi-objective optimization at the same time,which is called multi-objective optimization problem.Evolutionary algorithm is widely used in multi-objective optimization problems because of its good convergence and diversity.At present,the research on two to three objective optimization problems accounts for the majority,but the number of objectives involved in practical problems is often more than three.The evolutionary algorithm based on Pareto domination is one of the most commonly used methods to solve this kind of problems.However,it faces many problems in dealing with this kind of problems,such as the ineffectiveness of Pareto domination,the time-consuming of Pareto hierarchical sorting,and the difficulty in maintaining the balance between convergence and diversity.For the research of these problems,some researchers have developed a method based on reference points,which can generate a group of reference vectors in advance during the optimization process,so that the population can maintain good diversity.However,the Pareto frontier of different test problems will seriously affect the performance of MOEAs in the search process.Therefore,based on the reference point based evolutionary method,this paper studies the above problems,and the main research contents are summarized as follows:Firstly,in order to solve the problems of slow convergence of Pareto domination,poor distribution of PBI aggregation on the discontinuous Pareto front and low efficiency of operation,a multi-objective optimization algorithm is proposed based on the three-level selection of two-stage reference points.The algorithm first proposes two-stage reference point strategy,which sets fewer reference points at the early stage of the algorithm to make the population quickly converge and improve the operation efficiency;and sets more reference points at the later stage of the algorithm to improve the diversity of the population.Secondly,a three-level selection strategy is proposed.In the first level,in order to accelerate convergence,effective non dominated selection is adopted;in the second level,PBI is adopted to consider convergence and diversity;in the third level,niche selection is adopted to increase diversity.Through the comparison of the results of five standard test functions,it can be concluded that the performance of this algorithm is better than that of the comparison algorithm in most test functions,which verifies the feasibility and effectiveness of the proposed algorithm.Secondly,a hybrid multi-objective evolutionary algorithm based on two-stage adaptive adjustment is proposed to solve the problems of Pareto dominance,which is difficult to converge in high-dimensional case,edge effect and computational complexity brought by using index selection.In the first stage,the algorithm mainly considers the convergence of the algorithm,and adopts index selection to solve the problem that Pareto dominates in the high-dimensional case is difficult to converge;in the second stage,it mainly considers the diversity of the algorithm,and adopts three-level selection strategy to solve the problem At the same time,the two-stage adaptive switching is carried out by using the magnitude of the change of the extreme value,which makes the index based algorithm only run in the first stage,greatly reducing the computational complexity.The algorithm in this paper is compared with five classical algorithms on dtlz series standard test functions.The experimental results show that the algorithm has strong competitiveness compared with other algorithms.Then,based on the existing Pareto frontier approximation to get the conflict information,the existing algorithms still have the disadvantages of poor diversity and large computational complexity in the process of solving the significant problem of target conflict.This paper proposes a high-dimensional multi-objective parallel evolution algorithm using the conflict information partition.Firstly,the target space is divided into several sub intervals by using the conflict information among the targets,and each sub interval evolves independently to reduce the difficulty of solving the problem;secondly,the global information is considered to avoid local convergence,and the aggregation information of other sub intervals is added to each sub interval;finally,according to the different target numbers in the sub interval,the parallel independent optimization strategy is adopted,and the search space is reduced to avoid local convergence To avoid weakening the function of evolutionary operators and improve the optimization performance of the algorithm.The proposed algorithm is applied to wfg2 Standard Test and compared with seven kinds of algorithms.The experimental results show that the algorithm has strong competitiveness.Finally,the algorithm is applied to the vehicle routing problem.Based on the consideration of the actual situation,firstly,this paper comprehensively considers the classic vehicle routing problem,from a single objective to a high-dimensional objective;from a single perspective to a different perspective of suppliers and customers;secondly,based on the consideration of environmental factors,this paper studies the VRP considering carbon emissions.There are four objective functions and three constraints to establish the model for the above three aspects: to minimize the total path length;to minimize the cost(vehicle cost,time window penalty cost,fuel cost and carbon trading cost);to minimize the transportation time;to minimize the maximum capacity difference;and to meet the time window constraint,vehicle capacity constraint and maximum driving distance constraint.In order to further verify the optimization performance of the proposed algorithm,the test of urban distribution problem is promoted from single car park to three car park.Three classical algorithms are selected to compare with the algorithm in this paper to verify the advantages and disadvantages of this algorithm.