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-Opt Neural Approaches to Quadratic Assignment Problems

Nara Institute of Science and Technology, Ikoma-shi, Nara, 630-0101 Japan and ATR Human Information Processing Research Laboratories, Soraku-gun, Kyoto, 619-0288 Japan

Hirotaka Niitsuma

Nara Institute of Science and Technology, Ikoma-shi, Nara, 630-0101 Japan

In this article, we propose new analog neural approaches to combinatorial optimization problems, in particular, quadratic assignment problems (QAPs). Our proposed methods are based on an analog version of the -opt heuristics, which simultaneously changes assignments for elements in a permutation. Since we can take a relatively large value, our new methods can achieve a middle-range search over possible solutions, and this helps the system neglect shallow local minima and escape from local minima. In experiments, we have applied our methods to relatively large-scale (N = 80–150) QAPs. Results have shown that our new methods are comparable to the present champion algorithms; for two benchmark problems, they are obtain better solutions than the previous champion algorithms.