%0 Journal Article
%T A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization
%A Cai Dai
%A Yuping Wang
%J Journal of Applied Mathematics
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/906147
%X In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms. 1. Introduction Since there are many problems with several optimization problems or criteria in real world [1], multiobjective optimization has become a hot research topic. Unlike single-objective optimization problem, multiobjective optimization problem has a series of noninferior alternative solutions, also known as Pareto optimal solutions (the set of Pareto optimal solutions is called Pareto front [2]), which represent the possible trade-off among various conflicting objectives. Therefore, multiobjective optimization algorithms for MOP should be able to discover solutions as close to the optimal solutions as possible; find solutions as uniform as possible in the obtained nondominated front; determine solutions to cover the true Pareto front (PF) as broad as possible. However, achieving these three goals simultaneously is still a challenge for multiobjective optimization algorithms. Among various multiobjective optimization algorithms, multiobjective evolutionary algorithms (MOEA), which make use of the strategy of the population evolutionary to optimize the problems, are an effective method for solving MOPs. In recent years, many MOEAs have been proposed for solving the multiobjective optimization problems [3¨C18]. In the MOEA literatures, Goldberg¡¯s population categorization strategy [19] based on nondominance is important. Many algorithms use the strategy to assign a fitness value based on the nondominance rank of members. For example, the
%U http://www.hindawi.com/journals/jam/2014/906147/