Cluster Analysis: An Application of Lagrangian Relaxation

John M. Mulvey and Harlan P. Crowder
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John M. Mulvey: Princeton University
Harlan P. Crowder: IBM T. J. Watson Research Center

Management Science, 1979, vol. 25, issue 4, 329-340

Abstract: This paper presents and tests an effective optimization algorithm for clustering homogeneous data. The algorithm iteratively employs a subgradient method for determining lower bounds and a simple search procedure for determining upper bounds. The overall objective is to assign n objects to m mutually exclusive "clusters" such that the sum of the distances from each object to a designated cluster median is minimum. The model represents a special case of the uncapacitated facility location and m-median problems. This technique has proven efficient for examples with n \le 200 (i.e., the number of 0-1 variables \le 40,000); computational experiences with 10 real-world clustering applications are provided. A comparison with a hierarchical agglomerative heuristic, the minimum squared error method, is included. It is shown that the optimization algorithm is an effective solution technique for the homogeneous clustering problem, and also a good method for providing tight lower bounds for evaluating the quality of solutions generated by other procedures.

Keywords: cluster analysis; integer programming applications; Lagrangian relaxation; heuristics (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (33)

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