Performance Analysis of ACO on the Quadratic Assignment Problem

Abstract

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.