Improving the anytime behavior of two-phase local search

Algorithms based on the two-phase local search (TPLS) framework are a powerful method to efficiently tackle multi-objective combinatorial optimization problems. TPLS algorithms solve a sequence of scalarizations, that is, weighted sum aggregations, of the multi-objective problem. Each successive scalarization uses a different weight from a predefined sequence of weights. TPLS requires defining the stopping criterion (the number of weights) a priori, and it does not produce satisfactory results if stopped before completion. Therefore, TPLS has poor "anytime" behavior. This article examines variants of TPLS that improve its "anytime" behavior by adaptively generating the sequence of weights while solving the problem. The aim is to fill the "largest gap" in the current approximation to the Pareto front. The results presented here show that the best adaptive TPLS variants are superior to the "classical" TPLS strategies in terms of anytime behavior, matching, and often surpassing, them in terms of final quality, even if the latter run until completion.