Fast Separation Algorithms for Three-Index Assignment Problems
In polyhedral combinatorics, the polytope related to a combinatorial optimization problem is examined in order to obtain families of valid inequalities. To incorporate such families of inequalities within a ‘Branch & Cut’ algorithm requires one further step: that of deriving an algorithm which determines whether an inequality of a specific family is violated by a given vector (the separation problem). The idea put forward in this work is to consider a compact representation of the given vector, and measure the complexity of a separation algorithm in terms of this compact representation. We illustrate the idea on the separation of known inequalities for the three index assignment polytope. It turns out that we find new separation algorithms with better complexities than the current ones (that were called best possible).
KeywordsAssignment Problem Valid Inequality Separation Problem Separation Algorithm Single Machine Schedule Problem
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- 1.Applegate, D., Bixby, R., Chvátal, V., Cook, W.: The Traveling Salesman Problem: A Computational Study. Princeton University Press (2006) ISBN 978-0-691-12993-8Google Scholar
- 8.Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley (1988)Google Scholar
- 9.Qi, L., Sun, D.: Polyhedral methods for solving three index assignment problems. In: Pardalos, P.M., Pitsoulis, L. (eds.) Nonlinear Assignment Problems: Algorithms and Applications, Kluwer Academic Publisher, Nowell (2000)Google Scholar