Studies Of MOEA/D For Complex Pareto Fronts

Multi-objective evolutionary algorithm based on decomposition obtains more and more attention and studies in the field of multi-objective optimization field.Many studies have verified the performance of multi-objective evolutionary algorithm based on decomposition,but there are still some problems.For example,it is more sensitive to the shape of Pareto fronts and when dealing with multi-objective optimization issues with complex Pareto fronts,it often leads to uneven distribution of solution sets which can not cover the whole Pareto fronts.This thesis conducts studies according to this problem so as to improve the ability of multi-objective evolutionary algorithm based on decomposition to solve complex Pareto fronts.Main study contents can be summarized as follows:1.To deal with discontinuous Pareto fronts in complex Pareto fronts,it proposes a two-section MOEA/D algorithm frame.It divides this algorithm into two sections and in the first section,it will explore the shape of Pareto fronts to judge if it is discontinuous;if yes,in the second section,it will transform the discontinuous shape into an issue of optimizing several continuous Pareto fronts and evolve them collaboratively.In this algorithm frame,it puts forward the idea of using reference points sets instead of reference points to guide population evolution and this algorithm also includes generating array weight vectors and redistributing the population.It uses these operations to improve the algorithm frame's ability dealing with discontinuous Pareto fronts.During regenerating weight vectors,it proposes a method of using the target vector space ratio of subclass populations to determine the number of weight vectors generated by each group so as to make the allocation of computing resources more reasonable in the space.During redistributing populations,it puts forward a population redistribution strategy based on greedy method.With this strategy,it can fast allocate resources while preserving the diversity of the population as much as possible.2.Based on the two-section MOEA/D algorithm frame as mentioned above,it combines the classic multi-objective evolutionary algorithm MOEA/D-DE based on decomposition with a density-based clustering algorithm DBSCAN.DBSCAN is used to judge if the Pareto front is discontinuous.It also puts forward an individual selection strategy for parents between neighbors,intraclasses and interclasses which makes it possible for population evolution to take not only the advantage of its neighbors but also the advantage of subclass populations so as to accelerate the speed of convergence.We name this algorithm as MOEA/D-DE-DC.The experimental results show that the proposed algorithm's ability of dealing with multi-objective optimization problem with discontinuous Pareto fronts is greatly improved compared with traditional algorithms and it can also gives more even distribution of approximate solution sets compared with traditional algorithms.3.To improve this algorithm's ability of dealing with various Pareto fronts,it puts forward a probability-adaptive algorithm MOEA/D-DE.This algorithm can automatically and non-linearly adjust the probability of selecting parent individual,the probability of differential evolution and the probability of mutation of each child problem.When the solutions of children problems are distributed sparsely,it will decrease the probability of selecting parent individual from its neighbors but increase the probability of differential evolution and mutation;when the solutions of children problems are distributed densely,it will increase of selecting parent individual from its neighbors but decrease the probability of differential evolution and mutation.Finally,it uses experiments to verify the performance of MOEA/D-ACP.