On the Use of the Doubly Stochastic Matrix Models for the Quadratic Assignment Problem

Permutation problems have captured the attention of the combinatorial optimization community for decades due to the challenge they pose. Although their solutions are naturally encoded as permutations, in each problem, the information to be used to optimize them can vary substantially. In this paper,...

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Vydáno v:Evolutionary computation Ročník 33; číslo 3; s. 425
Hlavní autoři: Santucci, Valentino, Ceberio, Josu
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 02.09.2025
Témata:
Algorithms
Computer Simulation
Models, Statistical
Probability
Stochastic Processes
Fourier transform
Ordering vs. Assignment Problems
Estimation of Distribution Algorithm
Doubly Stochastic Matrix
Quadratic Assignment Problem
ISSN:1530-9304, 1530-9304
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Shrnutí:Permutation problems have captured the attention of the combinatorial optimization community for decades due to the challenge they pose. Although their solutions are naturally encoded as permutations, in each problem, the information to be used to optimize them can vary substantially. In this paper, we consider the Quadratic Assignment Problem (QAP) as a case study, and propose using Doubly Stochastic Matrices (DSMs) under the framework of Estimation of Distribution Algorithms. To that end, we design efficient learning and sampling schemes that enable an effective iterative update of the probability model. Conducted experiments on commonly adopted benchmarks for the QAP prove doubly stochastic matrices to be preferred to the other four models for permutations, both in terms of effectiveness and computational efficiency. Moreover, additional analyses performed on the structure of the QAP and the Linear Ordering Problem (LOP) show that DSMs are good to deal with assignment problems, but they have interesting capabilities to deal also with ordering problems such as the LOP. The paper concludes with a description of the potential uses of DSMs for other optimization paradigms, such as genetic algorithms or model-based gradient search.
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ISSN:1530-9304
1530-9304
DOI:10.1162/evco_a_00369