Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem

The multi-objective minimum weighted vertex cover problem aims to minimize the sum of different single type weights simultaneously. In this paper, we focus on the bi-objective minimum weighted vertex cover and propose a multi-objective algorithm integrating iterated neighborhood search with decomposition technique to solve this problem. Initially, we adopt the decomposition method to divide the multi-objective problem into several scalar optimization sub-problems. Meanwhile, to find more possible optimal solutions, we design a mixed score function according to the problem feature, which is applied in initializing procedure and neighborhood search. During the neighborhood search, three operators (Add, Delete, Swap) explore the search space effectively. We performed numerical experiments on many instances, and the results show the effectiveness of our new algorithm (combining decomposition and neighborhood search with mixed score) on several experimental metrics. We compared our experimental results with the classical multi-objective algorithm non-dominated sorting genetic algorithm II. It was obviously shown that our algorithm can provide much better results than the comparative algorithm considering the different metrics.