Phased local search for the maximum clique problem

Pullan, Wayne

doi:10.1007/s10878-006-9635-y

Cited by 61 publications

(81 citation statements)

References 14 publications

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“…(1) Reactive Local Search (RLS) [5]-an advanced tabu search method which is complemented by a feedback scheme to determine the amount of diversification; (2) Variable Neighbourhood Search (VNS) [12] -a basic variable neighorhood search heuristic that combines greedy with the simplicial vertex test in its descent step; (3) Phased Local Search (PLS) [23]-a stohastic local search algorithm which alterantes between phases of iterative improvement and plateau search. Tables 2 and 3 show performance results for BLS in comparison with the results reported by the three reference approaches on the set of DIMACS instances.…”

Section: Comparative Results For Mcpmentioning

confidence: 99%

“…Over the past decades, much effort has been made in devising exact algorithms [17,20,26] as well as powerful heuristics including tabu search [10,18,30], reactive search [5,23,24], stochastic local search [9,15,[22][23][24], variable neighbourhood search [12], ant colony optimization [28] and hybrid methods [27,31]. Most of these approaches have mainly been applied to MCP.…”

Section: Introductionmentioning

confidence: 99%

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Breakout Local Search for maximum clique problems

Benlic

Hao

2013

Computers & Operations Research

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The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current state-of-art heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.

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Section: Comparative Results For Mcpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Breakout Local Search for maximum clique problems

Benlic

Hao

2013

Computers & Operations Research

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“…The algorithm is realized through efficient supporting data structures leads to smaller overall CPU times. The family of stochastic local search algorithms, dynamic local search (DLS) [27], phased local search (PLS) [28] and cooperating local search (CLS) [29], share similar strategies of clique expansion, plateau search, and search stagnation.…”

Section: Such That |N (I ) ∩ N(c)| Is Maximum;mentioning

confidence: 99%

“…The phased Based local search (PLS) [28], to cope with graphs of different structures, combines three subalgorithms which use different vertex selection rules: random selection, random selection among those with the highest vertex degree, and random selection within those with the lowest vertex penalty. For each of the sub problem the procedure of DLS-MC is adopted.…”

Section: The K-opt Algorithm (Kls)mentioning

confidence: 99%

Survey of Algorithms on Maximum Clique Problem

Singh¹,

Pandey²

2015

International Advanced Research Journal in Science, Engineering

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Abstract:The maximum clique problem (MCP) is to determine a sub graph of maximum cardinality. A clique is a sub graph in which all pairs of vertices are mutually adjacent. Based on existing surveys, the main goal of this paper is to provide a simplified version and comprehensive review on Maximum clique problem. This review intends to encourage and motivate new researchers in this area. Though capturing the complete literature in this regard is beyond scope of the paper, but it is tried to capture most of the representative papers from similar approaches.

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“…When neither improvement nor new plateau steps are possible, search restarts from a single vertex. The DLS-MC algorithm has since evolved into the Phased Local Search algorithm [15], which eliminates the need for tuning a parameter while producing similar results.…”

Section: Maximum Clique and Independent Setmentioning

confidence: 99%

A Stochastic Local Search Approach to Vertex Cover

Richter

Helmert

Gretton

2007

Lecture Notes in Computer Science

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Abstract. We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used DIMACS benchmarks for the related clique problem, finding that our approach is competitive with the current best stochastic local search algorithm for finding cliques. On three very large problem instances, our algorithm establishes new records in solution quality.

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Phased local search for the maximum clique problem

Cited by 61 publications

References 14 publications

Breakout Local Search for maximum clique problems

Breakout Local Search for maximum clique problems

Survey of Algorithms on Maximum Clique Problem

A Stochastic Local Search Approach to Vertex Cover

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