Linearizable special cases of the QAP
Eranda Cela, Vladimir G. Deineko, Gerhard J. Woeginger
TL;DR
This paper characterizes specific cases of the quadratic assignment problem that can be simplified to linear problems, providing new insights and solvable instances for related combinatorial optimization problems.
Contribution
It offers combinatorial characterizations of linearizable instances of certain QAP variants, including feedback arc set and TSP cases, and introduces a new solvable case.
Findings
Characterization of linearizable weighted feedback arc set QAP
Characterization of linearizable traveling salesman QAP
Introduction of a new solvable feedback arc set case
Abstract
We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem.
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Taxonomy
TopicsOptimization and Search Problems · Vehicle Routing Optimization Methods · Optimization and Packing Problems