FixedSum: An improved algorithm for generation of weight vectors for decomposition-based multiobjective optimization

Abstract

Many multiobjective optimization algorithms employ weight vectors for decomposing a problem into multiple subproblems by associating each subproblem with a single weight vector (WV). These weight vectors should be uniformly spread in the space so as to get a diversified set of solutions along the Pareto front. In the recent past, different studies involving the development of decomposition-based multiobjective evolutionary algorithms (including MOEA/D and MOEA/DD) have adopted different methods for generating weight vectors. However these WVs lack the needed diversity and are either biased near the boundary or the inner regions of the search space. In this paper, we have proposed an improved algorithm, FixedSum, for the generation of weight vectors and graphically compared its results with other methods on 2-, 5-, 8- and 10-D weight vectors. For further validation of our approach, we have applied our weight vectors along with WVs of two other methods for solving the DTLZ4 problem using a popular decomposition-based algorithm MOEA/DD. All the results are graphically shown which demonstrate the improved spread ability of our approach as compared to the competing approaches.