Combining Clustered Adaptive Multistart and Discrete Dynamic Convexized Method for the Max-Cut Problem

Abstract

Given an undirected graph with edge weights, the max-cut problem is to find a partition of the vertices into two subsets, such that the sum of the weights of the edges crossing different subsets is maximized. Heuristics based on auxiliary function can obtain high-quality solutions of the max-cut problem, but suffer high solution cost when instances grow large. In this paper, we combine clustered adaptive multistart and discrete dynamic convexized method to obtain high-quality solutions in a reasonable time. Computational experiments on two sets of benchmark instances from the literature were performed. Numerical results and comparisons with some heuristics based on auxiliary function show that the proposed algorithm is much faster and can obtain better solutions. Comparisons with several state-ofthe-science heuristics demonstrate that the proposed algorithm is competitive.