Research On Multi-objective And Many-objective Evolutionary Algorithm Based On Decomposition

With the development of society,the increase in the number of optimization goals has led to the current hot topic of solving multi-objective optimization problems(MOPs)and many-objective optimization problems(MaOPs),and the difficulty of solving problems has also increased significantly.The increase in the number of objectives not only makes the number of non-dominated solutions increase sharply,but also greatly reduces the selection pressure of the algorithm,so it slows down the convergence speed and reduces the search efficiency of the algorithm.The framework of decomposition-based multi-objective evolutionary algorithm(MOEA/D)is very suitable for solving MOPs and MaOPs.Therefore,this article has made some improvements under the framework of MOEA/D and proposed two improved algorithms to better solve MOPs and MaOPs.The work of this paper is mainly summarized as follows:1.In order to improve the convergence speed of MOEA/D and the overall performance of the algorithm,this paper proposes a multi-objective invasive weed optimization algorithm based on decomposition,referred to as MOEA/D-IWO.This algorithm combines MOEA/D with Invasive Weed Optimization(IWO)method and inherits their excellent characteristics,i.e.,it decomposes a MOPs to be solved into several single-objective subproblems with the help of MOEA/D,and these subproblems are solved in parallel in each generation.The population consists of the best solution that is searched for each subproblem so far,and each subproblem is optimized by using the extended IWO algorithm.In order to prove the effectiveness of the algorithm,the proposed MOEA/D-IWO was verified on 19 test questions of F1-F9 and UF1-UF10,and compared with other advanced algorithms.Experimental results show that MOEA/D-IWO is competitive in solving these complex multi-objective optimization problems.2.In order to make the diversity and convergence of MOEA/D in solving many-objective optimization problems as balanced as possible,this paper proposes a decomposition method based on random objective division(ROD)for MOEA/D in many-objective optimization,referred to as MOEA/D-ROD.This algorithm combines the idea of the MOEA/D with the random objective division method.Firstly,the proposed algorithm converts MaOPs into several MOPs,and then a decomposition method is randomly assigned to each MOPs.Finally,the decomposition method is used to turn each MOPs into many single-objective optimization problems for collaborative optimization.Thus MOEA/D-ROD can take advantage of different decomposition methods to solve MaOPs.In order to confirm the effectiveness of the MOEA/D-ROD,the MOEA/D-ROD was verified on the two sets of test problems(DTLZ 1-4 and WFG 1-9)with 3-8,10,and 15 objectives,and compared with some other advanced algorithms.The experimental results prove that the proposed algorithm has certain advantages in solving these many-objective optimization problems.