This paper presents a hybrid metaheuristic approach (HMA) for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. By incorporating a tabu search procedure into the framework of evolutionary algorithms, the proposed approach exhibits several distinguishing features, including a diversification-based combination operator and a distance-and-quality based replacement criterion for pool updating. The proposed algorithm is able to easily obtain the best-known solutions for 31 large random instances up to 7000 variables (which no previous algorithm has done) and find new best solutions for 3 of 9 instances derived from the set partitioning problem, demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency. Furthermore, some key elements and properties of the HMA algorithm are also analyzed.
This paper describes a Diversification-Driven Tabu Search (D 2 TS) algorithm for solving unconstrained binary quadratic problems. D 2 TS is distinguished by the introduction of a perturbation-based diversification strategy guided by long-term memory. The performance of the proposed algorithm is assessed on the largest instances from the ORLIB library (up to 2500 variables) as well as still larger instances from the literature (up to 7000 variables). The computational results show that D 2 TS is highly competitive in terms of both solution quality and computational efficiency relative to some of the best performing heuristics in the literature.
This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by introducing a population management strategy. Both algorithms are based on a dedicated randomized greedy construction heuristic and a tabu search procedure. We show extensive computational results on two sets of 31 large random UBQP instances and one set of 54 structured instances derived from the MaxCut problem. Comparisons with state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that the reinforced GRASP-Tabu Search algorithm is able to improve the previous best known results for 19 MaxCut instances.
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.
In certain settings, difficulties arise that limit the effectiveness of LP formulations for the discriminant problem. Explanations and possible remedies have been offered, but these have had only limited success. We provide a simple way to overcome these problems based on an appropriate use and interpretation of normalizations. In addition, we demonstrate a normalization that is invariant under all translations of the problem data, providing a stability property not shared by previous approaches. Finally, we discuss the possibility of using more general models to improve discrimination.
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