Publication Date

5-30-2023

Description

The quadratic assignment problem (QAP) is perhaps the most widely studied nonlinear combinatorial optimization problem. It has many applications in various fields, yet has proven to be extremely difficult to solve. This difficulty has motivated researchers to identify special objective function structures that permit an optimal solution to be found efficiently. Previous work has shown that certain such structures can be explained in terms of a mixed 0-1 linear reformulation of the QAP known as the level-1 reformulation-linearization-technique (RLT) form. Specifically, the objective function structures were shown to ensure that a binary optimal extreme point solution exists to the continuous relaxation. This paper extends that work by considering classes of solvable cases in which the objective function coefficients have special chess-board and graded structures, and similarly characterizing them in terms of the level-1 RLT form. As part of this characterization, we develop a new relaxed version of the level-1 RLT form, the structure of which can be readily exploited to study the special instances under consideration.

Journal

Journal of Combinatorial Optimization

Volume

45

Department

Mathematics

Publisher Statement

This preprint has not undergone any post-submission improvements or corrections. The Version of Record of this article is published in the Journal of Combinatorial Optimization, and is available online at https://doi.org/10.1007/s10878-023-01044-3.

DOI

10.1007/s10878-023-01044-3

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