Improvement of convergence properties in adaptive weighted aggregation for multiobjective continuous optimization

This paper presents a new weight adaptation method for Adaptive Weighted Aggregation (AWA) that is a powerful multi-start framework of scalarized decent methods for multi-objective function optimization. AWA iteratively adapts weight vectors for a scalarized decent method in order to improve the coverage of an approximate solution set. AWA has been reported to show better performance than conventional multi-start methods. However, we observe that AWA often fails to make weight vectors converge to the correct ones when applied to problems with strong non-linearity, which causes performance deterioration in terms of coverage. In order to remedy the problem of AWA, we propose a new weight adaptation method named the step size control weight adaptation method (SSCWA). In order to investigate the effectiveness of SSCWA, we compared the performance of AWA with SSCWA (AWA-SSCWA) with that of the original AWA on two to five objectives benchmark problems with ten variables. As the result, we confirmed that AWA-SSCWA outperformed the original AWA on the benchmark problems.