A proximal DC approach for quadratic assignment problem

Zhuoxuan Jiang (), Xinyuan Zhao () and Chao Ding ()
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Zhuoxuan Jiang: Beijing University of Technology
Xinyuan Zhao: Beijing University of Technology
Chao Ding: Chinese Academy of Sciences

Computational Optimization and Applications, 2021, vol. 78, issue 3, No 6, 825-851

Abstract: Abstract In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under the framework of the difference of convex functions (DC) approach, a semi-proximal DC algorithm is proposed for solving the relaxation of the rank constrained DNN problem whose subproblems can be solved by the semi-proximal augmented Lagrangian method. We show that the generated sequence converges to a stationary point of the corresponding DC problem, which is feasible to the rank constrained DNN problem under some suitable assumptions. Moreover, numerical experiments demonstrate that for most QAP instances, the proposed approach can find the global optimal solutions efficiently, and for others, the proposed algorithm is able to provide good feasible solutions in a reasonable time.

Keywords: Quadratic assignment problem; Doubly nonnegative programming; Augmented Lagrangian method; Rank constraint; 90C22; 90C25; 90C26; 90C27 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-020-00252-5

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