On scalability of Adaptive Weighted Aggregation for multiobjective function optimization

In our previous study, we have proposed Adaptive Weighted Aggregation (AWA), a framework of multi-starting optimization methods based on scalarization for solving multi-objective function optimization problems. The experiments in the proposal show that AWA outperforms conventional multi-starting descent methods at coverage of solutions. However, the suitable termination condition for AWA has not been understood. Coverage of AWA's solutions and computational cost of AWA strongly depends on the termination condition. In this paper, we derive the necessary and sufficient iteration count to achieve high coverage and the number of approximate solutions generated until AWA stops. Numerical experiments show that AWA still achieves better coverage than the conventional methods under the derived termination condition.