Fast separation for the three-index assignment problem

Dokka Venkata Satyanaraya, Trivikram and Mourtos, Ioannis and Spieksma, Frits C R (2017) Fast separation for the three-index assignment problem. Mathematical Programming Computation, 9 (1). pp. 39-59. ISSN 1867-2949

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Abstract

A critical step in a cutting plane algorithm is separation, i.e., establishing whether a given vector x violates an inequality belonging to a specific class. It is customary to express the time complexity of a separation algorithm in the number of variables n. Here, we argue that a separation algorithm may instead process the vector containing the positive components of x, denoted as supp(x), which offers a more compact representation, especially if x is sparse; we also propose to express the time complexity in terms of |supp(x)|. Although several well-known separation algorithms exploit the sparsity of x, we revisit this idea in order to take sparsity explicitly into account in the time-complexity of separation and also design faster algorithms. We apply this approach to two classes of facet-defining inequalities for the three-index assignment problem, and obtain separation algorithms whose time complexity is linear in |supp(x)| instead of n. We indicate that this can be generalized to the axial k-index assignment problem and we show empirically how the separation algorithms exploiting sparsity improve on existing ones by running them on the largest instances reported in the literature.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Programming Computation
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1700/1712
Subjects:
ID Code:
79458
Deposited By:
Deposited On:
11 May 2016 14:22
Refereed?:
Yes
Published?:
Published
Last Modified:
06 Aug 2020 03:32