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An Empirical Investigation of the Effectiveness of a Vertex Substitution Heuristic

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  • K E Rosing

    (Department of Applied Economics and Tinbergen Institute, Erasmus University Rotterdam, PO Box 1738, NL3000 Rotterdam, The Netherlands)

Abstract

Many problems require the identification of a subset of points to minimize (or maximize) some function. A vertex substitution heuristic (VSH) employs a strategy of one-by-one replacement to approximate, or perhaps find, the optimal set. The Teitz and Bart heuristic is the archetype of this procedure and is the heuristic most frequently used for the solution of the p -median problem. One study of the performance of this heuristic with increasing numbers of facilities ( p ) in problems with a very small number of demand nodes ( n ) has been published. However, no study satisfactorily indicates the relative effectiveness of this heuristic method with increasing values of n or p. In this paper we compare optimal and heuristic solutions for ninety problems varying the values of n and p systematically. The results indicate that there is a definite reduction in the effectiveness of the heuristic with increasing values of n or p.

Suggested Citation

  • K E Rosing, 1997. "An Empirical Investigation of the Effectiveness of a Vertex Substitution Heuristic," Environment and Planning B, , vol. 24(1), pages 59-67, February.
    • Handle: RePEc:sae:envirb:v:24:y:1997:i:1:p:59-67
    DOI: 10.1068/b240059
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    References listed on IDEAS

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    1. Michael B. Teitz & Polly Bart, 1968. "Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph," Operations Research, INFORMS, vol. 16(5), pages 955-961, October.
    2. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Mauricio Resende & Renato Werneck, 2007. "A fast swap-based local search procedure for location problems," Annals of Operations Research, Springer, vol. 150(1), pages 205-230, March.

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