Chained Lin-Kernighan for Large Traveling Salesman Problems

Applegate, David; Cook, William J.; Rohe, André

doi:10.1287/ijoc.15.1.82.15157

Cited by 350 publications

(221 citation statements)

References 22 publications

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“…Recently, for TSP and GPP, the VDS-based heuristics have been incorporated into several metaheuristic frameworks, such as iterated local search [16], [17], [18], [19] and evolutionary algorithm [20], [21], [22]. The general performance of metaheuristics embedded with VDS-based local search is remarkably effective for the hard problems TSP and GPP.…”

Section: B Variable Depth Search Methodsmentioning

confidence: 99%

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

Katayama

Yamashita

Narihisa

2007

2007 IEEE Congress on Evolutionary Computation

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Abstract-We address a problem of finding an optimal node placement that minimizes the amount of traffics by reducing the weighted hop distances in multihop lightwave networks. The problem is called Node Placement Problem (NPP). NPP is known to be NP-hard and one of the most important problems in wavelength division multiplexing (WDM) based networks.In this paper we propose a new local search algorithm for the NPP based on variable depth search, and show its extension to an iterated local search algorithm. To evaluate the performance of the proposed methods, we provided the benchmark instances with known optimal solutions, and performed extensive experiments on the instances. The computational results showed that our iterated local search outperformed multistart local search methods and the best available metaheuristic for the problem.

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Section: B Variable Depth Search Methodsmentioning

confidence: 99%

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

Katayama

Yamashita

Narihisa

2007

2007 IEEE Congress on Evolutionary Computation

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“…This algorithm is reported to outperform the PD-TPLS of Paquete and Stützle. The main differences are that (i) the single-objective algorithm used to tackle the scalarized problems is an effective implementation of the chained LinKernighan heuristic [6], which is presumably more effective than the iterated local search algorithm used by the PD-TPLS, and (ii) a full version of PLS is used (more precisely, the version of Angel et al [4]) instead of the restricted one in the PD-TPLS method. This algorithm is nowadays, to the best of our knowledge, the state of the art for the bTSP.…”

Section: Hybrid Tpls+plsmentioning

confidence: 99%

Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search

Dubois-Lacoste

López-Ibáñez

Stützle

2013

Hybrid Metaheuristics

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In this chapter, we review metaheuristics for solving multi-objective combinatorial optimization problems, when no information about the decision maker's preferences is available, that is, when problems are tackled in the sense of Pareto optimization. Most of these metaheuristics follow one of the two main paradigms to tackle such problems using metaheuristics. The first paradigm is to rely on Pareto dominance when exploring the search space. The second paradigm is to tackle several single-objective problems to find several solutions that are non-dominated for the original problem; in this case, one may exploit existing, efficient single-objective algorithms, but the performance depends on the definition of the set of scalarized problems. There are also a number of approaches in the literature that combine both paradigms. However, this is usually done in a relatively ad-hoc way. In this paper, we review two conceptually simple methods representative of each paradigm: Pareto local search and Two-phase Local Search. The hybridization of these two strategies provides a general framework for engineering stochastic local search algorithms that can be used to improve over the state-of-the-art for several, widely studied problems.

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“…Variations and implementations for CLK were proposed e.g. by Applegate, Bixby, Chvátal and Cook [8] (ABCC-CLK) and Applegate, Bixby and Rohe [9] (ABR-CLK).…”

Section: Algorithmsmentioning

confidence: 99%

“…The Quick-Borůvka heuristics for TSP tours sorts the vertices of the problem instance by coordinates (if possible) and processes each vertex by adding an adjacent edge to the tour that has a minimal weight and is feasible (no subtour will be generated by adding). As stated in [8,9], this construction algorithm's tour quality is worse than other greedy algorithms, while requiring less time to build a tour. This algorithm is suited for further Chained Lin-Kernighan processing, too, and can be efficiently implemented by kd-trees [14].…”

Section: Algorithmsmentioning

confidence: 99%

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Embedding a Chained Lin-Kernighan Algorithm into a Distributed Algorithm

Fischer

Merz

Metaheuristics

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The Chained Lin-Kernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) network-based framework the resulting tours are modified and exchanged with neighboring nodes. We show that the distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050% above the optimum, compared to CLK's average solution of 0.119% above the optimum given the same total CPU time (10 4 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033% above the optimum and the CLK algorithm 0.099%.

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Chained Lin-Kernighan for Large Traveling Salesman Problems

Cited by 350 publications

References 22 publications

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

Variable depth search and iterated local search for the node placement problem in multihop WDM lightwave networks

Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search

Embedding a Chained Lin-Kernighan Algorithm into a Distributed Algorithm

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