Use of Multiple Grids with Different Scalarizing Functions in MOEA/D

Abstract

Recently MOEA/D (multi-objective evolutionary algorithm based on decomposition) was proposed by Zhang and Li (2007) for difficult multi-objective optimization problems. The main feature of MOEA/D is the decomposition of a multi-objective problem into a number of single-objective problems to simultaneously optimize a scalarizing function with different weight vectors. The point is the use of a neighborhood structure of weight vectors to optimize similar single-objective problems in a cooperative manner. Each weight vector has an elite solution with respect to the corresponding single-objective optimization problem. The diversity of solutions is maintained by the use of uniformly distributed weight vectors while the convergence of solutions is realized by the use of scalarizing function-based fitness evaluation. One important issue in the implementation of MOEA/D is the choice of an appropriate scalarizing function. In our former study, we proposed a simple idea of simultaneously using two different scalarizing functions. In this paper, we further examine this idea. That is, we discuss how to choose two scalarizing functions. We also examine the simultaneous use of three or more scalarizing functions.