Very Large-Scale Neighborhood Search for the Quadratic Assignment Problem

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Very Large-Scale Neighborhood Search for the Quadratic Assignment Problem (2002)

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by Ravindra K. Ahuja , Krishna C. Jha , James B. Orlin , Dushyant Sharma

Venue:	DISCRETE APPLIED MATHEMATICS
Citations:	150 - 13 self

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@ARTICLE{Ahuja02verylarge-scale,
    author = {Ravindra K. Ahuja and Krishna C. Jha and James B. Orlin and Dushyant Sharma},
    title = {Very Large-Scale Neighborhood Search for the Quadratic Assignment Problem},
    journal = {DISCRETE APPLIED MATHEMATICS},
    year = {2002},
    volume = {123},
    pages = {75--102}
}

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Abstract

The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very large-scale neighborhood search algorithms give consistently better solutions compared the popular 2-exchange neighborhood algorithms considering both the solution time and solution accuracy.

Keyphrases

large-scale neighborhood search quadratic assignment problem novel search procedure solution time 2-exchange neighborhood standard benchmark instance size instance search procedure relies used neighborhood structure search algorithm good neighbor improvement graph largescale neighborhood small size instance previous effort size neighborhood qap arises present extensive computational result neighborhood search algorithm popular 2-exchange neighborhood algorithm solution accuracy popular heuristic algorithm many diverse setting 4-exchange neighborhood

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