## Neighborhood Composition: A Parallelization of Local Search Algorithms

Citations: | 1 - 0 self |

### BibTeX

@MISC{H_neighborhoodcomposition:,

author = {Yuichi H and Hirotaka Ono and Kunihiko Sadakane and Masafumi Yamashita},

title = {Neighborhood Composition: A Parallelization of Local Search Algorithms},

year = {}

}

### OpenURL

### Abstract

Abstract. To practically solve NP-hard combinatorial optimization problems, local search algorithms and their parallel implementations on PVM or MPI have been frequently discussed. Since a huge number of neighbors may be examined to discover a locally optimal neighbor in each of local search calls, many of parallelization schemes, excluding so-called the multi-start parallel scheme, try to extract parallelism from a local search by distributing the examinations of neighbors to processors. However, in straightforward implementations, when the next local search starts, all the processors will be assigned to the neighbors of the latest solution, and the results of all (but one) examinations in the previous local search are thus discarded in vain, despite that they would contain useful information on further search. This paper explores the possibility of extracting information even from unsuccessful neighbor examinations in a systematic way to boost parallel local search algorithms. Our key concept is neighborhood composition. We demonstrate how this idea improves parallel implementations on PVM, by taking as examples well-known local search algorithms for the Traveling Salesman Problem. 1

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Citation Context ...Salesman Problem. 1 Introduction Most of combinatorial problems which frequently arise in various real-world situations, such as machine scheduling, vehicle routing and so on, are known to be NP-hard =-=[3]-=-, and are believed that there would not exist polynomial time algorithms to find optimal solutions. Many researchers are hence interested in approximation algorithms [8] that can find near-optimal sol... |

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Citation Context ...so on, are known to be NP-hard [3], and are believed that there would not exist polynomial time algorithms to find optimal solutions. Many researchers are hence interested in approximation algorithms =-=[8]-=- that can find near-optimal solutions in reasonable time. Among them are metaheuristics algorithms based on local search very popular [4, 1, 10] because of their simplicity and robustness. A generic o... |

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Citation Context ... search its own neighborhood while other slaves communicate with the master, which hide the communication overhead. To confirm the availability of our method, we choose the Traveling Salesman Problem =-=[6]-=- (TSP, for short) and 2OPT (or Or-OPT) and Lin-Kernighan [5] neighborhood local search algorithms as a model problem and its algorithms. We implemented these algorithms on PVM, and then conducted comp... |

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Citation Context ...with the master, which hide the communication overhead. To confirm the availability of our method, we choose the Traveling Salesman Problem [6] (TSP, for short) and 2OPT (or Or-OPT) and Lin-Kernighan =-=[5]-=- neighborhood local search algorithms as a model problem and its algorithms. We implemented these algorithms on PVM, and then conducted computational experiments. The reasons why we adopt TSP and thes... |

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Citation Context ...y researchers are hence interested in approximation algorithms [8] that can find near-optimal solutions in reasonable time. Among them are metaheuristics algorithms based on local search very popular =-=[4, 1, 10]-=- because of their simplicity and robustness. A generic outline of a local search algorithm starts with an initial feasible solution and repeats replacing it with a better solution in its neighborhood ... |

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Citation Context ...endently execute the same algorithm from randomly selected initial solution and returns the best solution among those obtained by the processors, mainly to increase the quality of solution (see e.g., =-=[2]-=-). A parallelized GRASP is an application of multi-start paradigm; while original GRASP randomly generates initial solutions in greedy manner then applies local search for each initial solution, in pa... |

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