Breakout Local Search for the Max-Cutproblem

Abstract

Given an undirected graph G = (V, E) where each edge of E is weighted with an integer number, the maximum cut problem (Max-Cut) is to partition the vertices of V into two disjoint subsets so as to maximize the total weight of the edges between the two subsets. As one of Karp's 21 NP-complete problems, Max-Cut has attracted considerable attention over the last decades. In this paper, we present Breakout Local Search (BLS) for Max-Cut. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. The proposed algorithm shows excellent performance on the set of well-known maximum cut benchmark instances in terms of both solution quality and computational time. Out of the 71 benchmark instances, BLS is capable of finding new improved results in 33 cases and attaining the previous best-known result for 35 instances, within a computational time ranging from less than one second to 5.6 hours for the largest instance with 20000 vertices.

Breakout local search for the Steiner tree problem with revenue, budget and hop constraints

“…For example, Fig. 1 illustrates the process for generating a neighboring solution by M ove 2(8, 7), where the profitable vertices with r i > 0 are drawn in box (i.e., vertices 1,3,4,7,8,9,11,13,14), and the others are drawn in circle (i.e., vertices 2, 5, 6, 10, 12). As shown in Fig.…”

“…BLS follows the general Iterated Local Search scheme (Lourenco et al, 2003) and alternates between a neighborhood search phase and a perturbation phase. BLS has recently shown its effectiveness for solving several combinatorial optimization problems, such as sum coloring (Benlic and Hao, 2012), maximum clique (Benlic and Hao, 2013a), quadratic assignment (Benlic and Hao, 2013b), and max-cut (Benlic and Hao, 2013c). For the STPRBH, the proposed BLS algorithm integrates a probabilistic constructive procedure to generate its initial solution, a Neighborhood Search (NS) procedure based on three specifically designed move operators to discover local optima, and an adaptive perturbation strategy to continually move from one local optimum to another one, by varying its perturbations depending on the search status.…”

Hypervolume-Based Multi-level Algorithm for the Bi-criteria Max-Cut Problem

“…In order to conduct the experiments on the bi-objective max-cut problem, we use two single-objective benchmark instances of max-cut problem with the same dimension provided in [7] 1 to generate one bi-objective max-cut problem instance. All the instances used for experiments are presented in Table 1 below.…”

“…As one of Karps 21 NP-complete problems with numerous practical applications [7], a large number of metaheuristics have been proposed to tackle this problem, including tabu search [2], breakout local search [7], variable neighborhood search [9], scatter search [11], global equilibrium search [13], hybrid approaches [14], etc.…”

A Study of Adaptive Perturbation Strategy for Iterated Local Search

“…In this paper, we investigate the contribution of a new adaptive diversification strategy (ADS) employed by a recent breakout local search (BLS) metaheuristic [3,4,5,6]. BLS is a variation of iterated local search (ILS) [9] since it combines a descent-based local search with a perturbation mechanism.…”