Research On Multi-objective Evolutionary Algorithm Based On Decomposition Thought

It is often necessary to optimize multiple objectives in engineering and science problems.At the same time,these objectives are often mutually exclusive.In order to solve these problems,the decomposition-based evolutionary algorithm(MOEA/D)has received extensive attention since it was put forward.MOEA/D decomposes a multi-objective problem into several sub-problems and optimizes these sub-problems simultaneously,and a set of evenly-distributed reference points should be generated to represent each sub-problem.Also,the scalar function is used in the evolutionary process to evaluate the individual.Although,MOEA/D has achieved good performance for solving multi-objective optimization problem(MOP),its performance would be degraded a lot for some complex problems.The solution set obtained by MOEA/D is not uniform for MOP with complex front.Also,for many-objective problems,MOEA/D cannot do well in the diversity of the obtained solutions.To tackle these two problems,this paper proposes the methods based on the decomposition thought to design two algorithms.For the MOP with complex front,a uniform distribution of weight vectors cannot be guaranteed to obtain a set of evenly distributed solutions on the Pareto-optimal front(POF)in MOEA/D.For example,the POF may have disconnected regions and a long tail and a sharp peak and a degenerate geometry,which significantly degrades the performance of the original MOEA/D.In order to solve the defect of the standard MOEA/D,two aspects which containing scalar function and reference point adjustment are proposed in this study.First,a modified PBI(Penalty-Based Boundary Intersection)approach(MPBI)is proposed to deal with the POF with long tail and sharp peak.Moreover,adjusting reference point(ARP)is proposed to handle these POFs with discontinuous regions and degradation,so that the obtained solutions are more evenly distributed on the POF,and some reference points which could not guide the selection will be deleted.Finally,the two strategies are mixed into the framework based on Pareto dominance algorithms,and a comparative experiment is carried out on 22 test instances.The experiment shows that the algorithm is better than other algorithms on 20/22 test instances.For the many-objective optimization problems,the traditional method based on Pareto dominance or based on decomposition cannot achieve more satisfactory results.In this case,a greed-based selection strategy and an angle-based selection are proposed.The proposed algorithm decomposes a multi-objective optimization problem into several sub-problems based on the idea of decomposition-based algorithm.Meanwhile,a greedy strategy is used to select the solutions to minimize the scalar function of each solution attached to the corresponding sub-problem.At the same time,in order to maintain the distribution of the solutions,a parameter topK is set up to limit the depth of the search.Finally,a partial solutions based on the angle selection is used to maintain the distribution.In order to verify the performance of the algorithm on many-objective optimization problems,some popular algorithms are tested on DTLZ and WFG series problems,and proved that the proposed algorithm has a better performance than other algorithms on 47/70 test instances.