Solving large scale Max Cut problems via tabu search

Abstract

In recent years many algorithms have been proposed in the literature for solving the Max-Cut problem. In this paper we report on the application of a new Tabu Search algorithm to large scale Max-cut test problems. Our method provides best known solutions for many well-known test problems of size up to 10,000 variables, although it is designed for the general unconstrained quadratic binary program (UBQP), and is not specialized in any way for the Max-Cut problem.

Area Efficient Annealing Processor for Ising Model without Random Number Generator

“…(3) to the energy minimization of the Ising model in Eq. (2). By comparing these equations, they become equivalent when we associate the variables as…”

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

“…In this second experimental study, we focus on comparing the performance of the proposed algorithm CAM_DCM with respect to scatter search (SS) [28], rank-two relaxation heuristic [5], tabu search (TS) [18], breakout local search (BLS) [3]. These heuristics are able to obtain high-quality solutions of the max-cut problem.…”

“…The column ''CAM_DCM'' of Table 4 presents the best cut values of the test instances among 20 runs of CAM_DCM. For comparison purposes, the best cut values of the test instances obtained by scatter search [28], rank-two relaxation heuristic [5], tabu search [18], breakout local search [3] are also cited in the columns ''SS'', ''CirCut'', ''TS'', and ''BLS'' of Table 4, respectively. A ''-'' in the Table 4 means that the algorithm does not report result for the test instance.…”

“…The data under the columns ''SS'' and ''TS'' are from [18]. [18] presented the best cut values found by tabu search [18] in 2.…”

“…[18] presented the best cut values found by tabu search [18] in 2. 36,8,12,20, and 24 h on their computer for instances with n 6 3 000, 5 000 6 n 6 7 000, n ¼ 8 000, n ¼ 9 000, and n ¼ 10 000, respectively.…”