A Weight Design Method Based on Power Transformation for Multi-Objective Evolutionary Algorithm MOEA/D

In multi-objective optimization problems, it is very important to find a group of uniformly distributed Pareto optimal solutions on Pareto fronts. MOEA/D is one of the promising evolutionary algorithms for multi-objective optimization at present. When the Pareto front is some known types of shape, the MOEA/D can find uniformly distributed Pareto-optimal solutions by using the advanced decomposition. Nevertheless, it is a nontrivial task for the MOEA/D for a general shape of the Pareto front. In this paper, each objective function is transformed by the power function, which makes the Pareto front of multi-objective optimization close to the desired shape. Furthermore, a kind of weight design method of MOEA/D is proposed to solve general multi-objective optimization problem. This paper also discusses the distance preserving character of Pareto front by mathematics transform. MOEA/D, making use of proposed weight design method, easily finds uniformly distributed Pareto optimal solutions for general multi-objective optimization problem. Numerical results show the effectiveness of MOEA/D with the proposed weight design method.