XIA Xiaoyun and ZHOU Yuren, “Performance Analysis of ACO on the Quadratic Assignment Problem,” Chinese Journal of Electronics, vol. 27, no. 1, pp. 26-34, 2018, doi: 10.1049/cje.2017.06.004
Citation: XIA Xiaoyun and ZHOU Yuren, “Performance Analysis of ACO on the Quadratic Assignment Problem,” Chinese Journal of Electronics, vol. 27, no. 1, pp. 26-34, 2018, doi: 10.1049/cje.2017.06.004

Performance Analysis of ACO on the Quadratic Assignment Problem

doi: 10.1049/cje.2017.06.004
Funds:  This work is supported by the National Natural Science Foundation of China (No.61703183, No.61773410), the Scientific Research Special Plan of Guangzhou Science and Technology Programme (No.201607010045), the Education Scientific Planning Project of Zhejiang Province (No.2017SCG048), and the Natural Science Foundation of Jiangxi Province of China (No.20151BAB217008).
  • Received Date: 2016-03-15
  • Rev Recd Date: 2016-12-01
  • Publish Date: 2018-01-10
  • 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.
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