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Breakout Local Search for the Max-Cut Problem
, 2012
"... 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 problem ..."
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Cited by 8 (6 self)
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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 quadratic assignment problem
- Applied Mathematics and Computation
"... The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present Breakout Local Search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation str ..."
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Cited by 8 (4 self)
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The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present Breakout Local Search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Experimental evalua-tions on the set of QAPLIB benchmark instances show that the proposed approach is able to attain current best-known results for all but two instances with an average computing time of less than 4.5 hours. Comparisons are also provided to show the competitiveness of the proposed approach with respect to the best-performing QAP algorithms from the literature.
A study of Breakout Local Search for the minimum sum coloring problem
"... Abstract. Given an undirected graph G = (V, E), the minimum sum coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of G such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present Breakout Local S ..."
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Cited by 7 (7 self)
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Abstract. Given an undirected graph G = (V, E), the minimum sum coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of G such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present Breakout Local Search (BLS) for MSCP which combines some essential features of several well-established metaheuristics. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Tested on 27 commonly used benchmark instances, our algorithm shows competitive performance with respect to recently proposed heuristics and is able to find new record-breaking results for 4 instances.
Breakout local search for the Steiner tree problem with revenue, budget and hop constraints
- Eur. J. Oper. Res
, 2014
"... The Steiner tree problem (STP) is one of the most popular combinatorial optimiza-tion problems with various practical applications. In this paper, we propose a Break-out Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop con ..."
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Cited by 4 (2 self)
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The Steiner tree problem (STP) is one of the most popular combinatorial optimiza-tion problems with various practical applications. In this paper, we propose a Break-out Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop constraints (STPRBH), which consists of determining a subtree of a given undirected graph which maximizes the collected revenues, subject to both budget and hop constraints. Starting from a probabilistically constructed initial solution, BLS uses a Neighborhood Search (NS) procedure based on several specifically designed move operators for local optimiza-tion, and employs an adaptive diversification strategy to escape from local optima. The diversification mechanism is implemented by adaptive perturbations, guided by dedicated information of discovered high-quality solutions. Computational results based on 240 benchmarks show that BLS produces competitive results with respect to several previous approaches. For the 56 most challenging instances with unknown optimal results, BLS succeeds in improving 49 and matching one best known results within reasonable time. For the 184 instances which have been solved to optimality, BLS can also match 167 optimal results.
Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata
- International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
, 2015
"... Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, ev ..."
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Cited by 4 (2 self)
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Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, every feature of the graph such as path, clique, spanning tree and dominating set, to mention a few, should be treated as a stochastic feature. For example, choosing stochastic graph as the graph model of an online social network and defining community structure in terms of clique, and the associations among the individuals within the community as random variables, the concept of stochastic clique may be used to study community structure properties. In this paper maximum clique in stochastic graph is first defined and then several learning automata-based algorithms are proposed for solving maximum clique problem in stochastic graph where the probability distribution functions of the weights associated with the edges of the graph are unknown. It is shown that by a proper choice of the parameters of the proposed algorithms, one can make the probability of finding maximum clique in stochastic graph as close to unity as possible. Experimental results show that the proposed algorithms significantly reduce the number of samples needed to be taken from the edges of the stochastic graph as compared to the number of samples needed by standard sampling method at a given confidence level.
Breakout local search for the vertex separator problem
"... In this paper, we propose the first heuristic approach for the vertex separator problem (VSP), based on Breakout Local Search (BLS). BLS is a recent meta-heuristic that follows the general framework of the popular Iterated Local Search (ILS) with a particular focus on the perturbation strategy. Base ..."
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Cited by 3 (1 self)
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In this paper, we propose the first heuristic approach for the vertex separator problem (VSP), based on Breakout Local Search (BLS). BLS is a recent meta-heuristic that follows the general framework of the popular Iterated Local Search (ILS) with a particular focus on the perturbation strategy. Based on some relevant information on search history, it tries to introduce the most suitable degree of diversification by determining adaptively the number and type of moves for the next perturbation phase. The proposed heuristic is highly competitive with the exact state-of-art approaches from the literature on the current VSP benchmark. Moreover, we present for the first time computational results for a set of large graphs with up to 3000 vertices, which constitutes a new challenging benchmark for VSP approaches.
Memetic search for the quadratic assignment problem
, 2014
"... The quadratic assignment problem (QAP) is one of the most studied NP-hard problems with various practical applications. In this work, we propose a powerful population-based memetic algorithm (called BMA) for QAP. BMA in-tegrates an effective local optimization algorithm called Breakout Local Search ..."
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Cited by 1 (0 self)
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The quadratic assignment problem (QAP) is one of the most studied NP-hard problems with various practical applications. In this work, we propose a powerful population-based memetic algorithm (called BMA) for QAP. BMA in-tegrates an effective local optimization algorithm called Breakout Local Search (BLS) within the evolutionary computing framework which itself is based on a uniform crossover, a fitness-based pool updating strategy and an adaptive mu-tation procedure. Extensive computational studies on the set of 135 well-known benchmark instances from the QAPLIB revealed that the proposed algorithm is able to attain the best-known results for 133 instances and thus competes very favorably with the current most effective QAP approaches. A study of the search landscape and crossover operators is also proposed to shed light on the behavior of the algorithm.
A Study of Adaptive Perturbation Strategy for Iterated Local Search
"... Abstract. We investigate the contribution of a recently proposed adaptive diversification strategy (ADS) to the performance of an iterated local search (ILS) algorithm. ADS is used as a diversification mechanism by breakout local search (BLS), which is a new variant of the ILS metaheuristic. The pro ..."
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Abstract. We investigate the contribution of a recently proposed adaptive diversification strategy (ADS) to the performance of an iterated local search (ILS) algorithm. ADS is used as a diversification mechanism by breakout local search (BLS), which is a new variant of the ILS metaheuristic. The proposed perturbation strategy adaptively selects between two types of perturbations (directed or random moves) of different intensities, depending on the current state of search. We experimentally evaluate the performance of ADS on the quadratic assignment problem (QAP) and the maximum clique problem (MAX-CLQ). Computational results accentuate the benefit of combining adaptively multiple perturbation types of different intensities. Moreover, we provide some guidance on when to introduce a weaker and when to introduce a stronger diversification into the search.
