On the landscape ruggedness of the quadratic assignment problem

Authors:
Eric Angela;Vassilis Zissimopoulosb
Affiliations:
Univ. de Paris Sud, Orsay, France;Univ. Paris, Villetaneuse, France
Venue:
Theoretical Computer Science
Year:
2001

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Abstract

Local-search-based heuristics have been demonstrated to give very good results to approximately solve the quadratic assignment problem (QAP). In this paper, following the works of Weinberger and Stadler, we introduce a parameter, called the ruggedness coeffcient, which measures the ruggedness of the QAP landscape which is the union of a cost function and a neighborhood. We give an exact expression, and a sharp lower bound for this parameter. We are able toderive from it that the landscape of the QAP is rather flat, and so it gives a theoretical justification of the effectiveness of local-search-based heuristics for this problem. Experimental results with simulated annealing are presented which con8rm this conclusion and also the influence of the ruggedness coe5cient on the quality of results obtained.