Kernels of Mallows Models under the Hamming Distance for solving the Quadratic Assignment Problem

TL;DR

This paper introduces a novel kernel of Mallows models under Hamming distance within EDAs to effectively solve the Quadratic Assignment Problem, outperforming existing permutation-based EDAs.

Contribution

The paper proposes a new kernel of Mallows model under Hamming distance for EDAs, tailored for the QAP, demonstrating superior performance over existing methods.

Findings

Proposed kernel outperforms classical EDAs on QAP instances.

New approach achieves better solution quality than existing permutation-based EDAs.

Experimental results validate the effectiveness of the Hamming distance kernel.

Abstract

The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it has captured the attention of the optimization community for decades. As a result, a large number of algorithms have been proposed to tackle this problem. Among these, exact methods are only able to solve instances of size $n<40$. To overcome this limitation, many metaheuristic methods have been applied to the QAP. In this work, we follow this direction by approaching the QAP through Estimation of Distribution Algorithms (EDAs). Particularly, a non-parametric distance-based exponential probabilistic model is used. Based on the analysis of the characteristics of the QAP, and previous work in the area, we introduce Kernels of Mallows Model under the Hamming distance to the context of EDAs. Conducted experiments point out that the performance of the proposed algorithm in the QAP is superior to (i) the classical EDAs adapted to deal with the QAP, and also (ii) to the specific EDAs proposed in the literature to deal with permutation problems.