Randomized heuristics for the max-cut problem

Given an undirected graph with edge weights, the max-cutproblem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. It is a well-known NP-hard problem with applications in several fields, including very large scale integration design and statistical physics. In this article, a greedy randomized adaptive search procedure (GRASP), a variable neighborhood search (VNS), and a path-relinking (PR) intensification heuristic for max-cut are proposed and tested. New hybrid heuristics that combine GRASP, VNS, and PR are also proposed and tested. Computational results indicate that these randomized heuristics find near-optimal solutions. On a set of standard test problems, new best known solutions were produced for many of the instances.