Download e-book for iPad: Approximation and Optimization: Proceedings of the by Juan A. Gomez-Fernandez, Francisco Guerra-Vazquez, Miguel A.

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By Juan A. Gomez-Fernandez, Francisco Guerra-Vazquez, Miguel A. Jimenez-Pozo, Guillermo Lopez-Lagomasino

ISBN-10: 3540504435

ISBN-13: 9783540504436

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Read Online or Download Approximation and Optimization: Proceedings of the International Seminar, held in Havana, Cuba, January 12-16, 1987 PDF

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Additional resources for Approximation and Optimization: Proceedings of the International Seminar, held in Havana, Cuba, January 12-16, 1987

Sample text

The algorithm proceeds rather steadily through the tree, finding a new incumbent solution in row 9. This solution has a within-cluster sum of dissimilarities value of f2(λ*) = 211, and corresponds to the partition {1, 2, 3}, {4, 5, 6}. 4. 2. The partial solution associated with this row shows an assignment of objects 1 and 2 to cluster 1 and object 3 to cluster 2 (thus, three positions have been assigned; so, p = 3). Cluster 1, therefore, produces the within-cluster dissimilarity value of a12 = 35, whereas cluster 2 does not yield any direct contribution to the bound.

2, with minor modification for the computation of the change in within-cluster dissimilarity sums instead of diameters, illustrates the basic implementation of the Banfiled and Bassil (1977) procedure. 2) produced by this heuristic process is denoted f2(λ*). For the remainder of this chapter, this notation refers to the best found solution at any point in the branch-and-bound process. 3 The PARTIAL SOLUTION EVALUATION Step Klein and Aronson’s (1991) evaluation of partial solutions requires consideration of three bound components.

For p = 2, objects 3, 4, 5, and 6 are unassigned, and the minimum number of possible terms collected among these four objects in the criterion function is two. Thus, when p = 2, the Component 3 bound is the sum of the minimum two elements among (a34 = 43, a35 = 63, a36 = 53, a45 = 37, a46 = 29, a56 = 34), which is 29 + 34 = 63. Finally, when p = 1, objects 2 through 6 are unassigned. The minimum number of collected terms will occur when three of the n – p = 6 – 1 = 5 unassigned objects are placed in one cluster and two of the unassigned objects in the other cluster.

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Approximation and Optimization: Proceedings of the International Seminar, held in Havana, Cuba, January 12-16, 1987 by Juan A. Gomez-Fernandez, Francisco Guerra-Vazquez, Miguel A. Jimenez-Pozo, Guillermo Lopez-Lagomasino


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