On the use of the Doubly Stochastic Matrix models for the Quadratic Assignment Problem

Valentino Santucci, Josu Ceberio

Keywords: Combinatorial optimization, doubly stochastic matrix, estimation of distribution algorithm

TL;DR: We propose using doubly stochastic matrices to model permutation solutions of quadratic problems within the framework of EDAs

Abstract: 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 article, 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 other four models for permutations, both in terms of effectiveness and computational efficiency.

Submission Number: 1