Abstract
This paper presents a new relocation method for Adaptive Weighted Aggregation with Step Size Control Weight Adaptation (AWA-SSCWA) that is a powerful multi-start framework of scalarized decent methods for multi-objective continuous function optimization. AWA-SSCWA repeats two procedures: subdivision and relocation. Subdivision decides initial weight vectors and solutions for relocation. Relocation iteratively adapts weight vectors by repeating two procedures of optimization and weight adaptation in order to improve the coverage of an approximate solution set. Weight adaptation uses neighborhood relationship between weight vectors and solutions to estimate appropriate weight vectors which achieve an approximate solution set with good coverage. AWA-SSCWA employs lattice points, called addresses, to quickly calculate the neighborhood relationship between weight vectors and solutions. AWA-SSCWA has been reported to find good approximate solution sets in terms of coverage. However, AWA-SSCWA has a serious problem in that the performance of AWA-SSCWA deteriorates in terms of coverage when the neighborhood relationship of addresses does not match that of solutions. In order to remedy the problem, we propose a new version of AWA-SSCWA, named AWA with Enhanced Relocation (AWA-ER). In order to investigate the effectiveness of AWA-ER, we compared the performance of AWA-ER with that of AWA-SSCWA on three to five objective benchmark problems with twenty variables. As the result, we confirmed that AWA-ER outperformed AWA-SSCWA on the benchmark problems.
