Performance Analysis of ACO on the Quadratic Assignment Problem

• Published in: Chinese Journal of Electronics Vol. 27; no. 1; pp. 26 - 34
• Main Authors: Xia, Xiaoyun, Zhou, Yuren
• Format: Journal Article
• Language: English
• Published: Published by the IET on behalf of the CIE 01.01.2018
• Subjects: ACO; Algorithms analysis; ant colony optimisation; ant colony optimization; Ant colony optimization (ACO); approximation algorithm; Approximation algorithms; approximation theory; computational complexity; Local search; max‐min ant algorithm; NP‐hard combinatorial optimization problem; quadratic assignment problem; Quadratic assignment problem (QAP); Runtime analysis; search problems; two‐exchange local search algorithm; Algorithms analysis; approximation theory; Local search; Runtime analysis; two-exchange local search algorithm; max-min ant algorithm; Quadratic assignment problem (QAP); NP-hard combinatorial optimization problem; ACO; quadratic assignment problem; ant colony optimization; approximation algorithm; Approximation algorithms; ant colony optimisation; Ant colony optimization (ACO); search problems; computational complexity
• ISSN: 1022-4653; 2075-5597
• DOI: 10.1049/cje.2017.06.004

The Quadratic assignment problem(QAP)is to assign a set of facilities to a set of locations with given distances between the locations and given flows between the facilities such that the sum of the products between flows and distances is minimized, which is a notoriously difficult NP-hard combinatorial optimization problem. A lot of heuristics have been proposed for the QAP problem, and some of them have proved to be efficient approximation algorithms for this problem. Ant colony optimization(ACO) is a general-purpose heuristic and usually considered as an approximation algorithms for NP-hard optimization problems. However, we know little about the performance of ACO for QAP from a theoretical perspective. This paper contributes to a theoretical understanding of ACO on the QAP problem. The worst-case bound on a simple ACO algorithm called(1+1) Max-min ant algorithm((1+1) MMAA) for the QAP problem is presented.It is shown that a degenerate(1+1) MMAA finds an approximate solution on the QAP problem. Finally, we reveal that ACO can outperform the 2-exchange local search algorithm on an instance of the QAP problem.