Decomposition-Based Evolutionary Multiobjective Algorithm

It is common to face a number of optimization problems in many areas of the real world especially in the science and engineering fields. Generally we need to consider several objectives in some optimization problems known as multi-objective optimization problems (MOP). Moreover we also need consider some constrained in some problems. In such problems the objectives often conflict with each other. That is there is no solution can optimize all the objectives simultaneously. Therefore the traditional optimization approach cannot independently solve it. Evolutionary algorithms search the solution by the population. It has a significant advantage to solve MOP and has received a lot of researcher’s attention. In the past few decades a number of evolutionary multiobjective optimization algorithms (EMOA) have been proposed. In this paper we made an intensive exploration and research on EMOA proposed a hybrid EMOA and constraint handling technique and carried out the theoretical analysis and experimental research. Specifically the study of this paper includes the following two issues:(1) A hybrid EMOA with adaptive multi-fitness assignment:Each EMOA has its own strengths and weaknesses. We know from "no free lunch" theorems that any EMOA over one class of problems is offset by the performance over another class and do not know which kind of EMOA is most suitable for the spatial MOP in advance. Thus hybridizing different EMOAs in one single algorithmic framework is a natural way to deal with hard MOPs. There are several studies on hybrid multi-operator recombination methods while few works have been proposed in the area of combining different fitness assignment in a framework. On the other hand it is known that fitness assignment has a marked impact on the performance of EMOA. In this paper a hybrid EMOA is proposed which divides the population into several smaller subpopulations according to their distribution in the objective space. Each subpopulation is evolved by an individual EMOA and a hybrid performance measure estimates the performance of these EMOAs. We focus on the fitness assignment and assume that all EMOAs used in the subpopulations adopt the same recombination operator. To evaluate performance of the proposed algorithm we compare it with MOEA/D-M2M MOEA/D SMS-EMOA and NSGA-Ⅱ on sixteen test instances. Experimental results show that the proposed algorithm performs better than or similar to those compared EMOAs.(2) A decomposition-based constrained EMOA:Currently the constrained optimization has become a hot and hard research field in evolutionary computation. Penalty function method is simple and easy to implement except designing a general penalty factor which determines the severity of the punishment for CMOPs. If penalty factor is too low the algorithm will cost too much time in exploring the infeasible space and final infeasible solutions may result. And if it is too high the algorithm will be pushed inside the feasible region very quickly cannot make the best of the infeasible individuals. In this paper we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problem(CMOP) named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. A novel constraint handling technique based on the boundary search and archive is proposed in this paper. Each subproblem has its one subpopulation and one temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation while the temporary register consists of those individuals ever found before. To improve the efficiency of the algorithm the boundary search method is designed. This method makes the feasible individuals with a higher probability to perform genetic operator with the infeasible individuals. Especially when the constraints are active at the Pareto solutions it can play its leading role. Compared with two algorithms i.e. CMOEA/D-DE-CDP and Gary’s algorithm on eighteen CMOPs the results show the effectiveness of the proposed constraint handle technique.