A new adaptive multi-start technique for combinatorial global optimizations

Authors:
Kenneth D. Boese;Andrew B. Kahng;Sudhakar Muddu
Affiliations:
UCLA Computer Science Department, Los Angeles, CA 90024-1596, USA;UCLA Computer Science Department, Los Angeles, CA 90024-1596, USA;UCLA Computer Science Department, Los Angeles, CA 90024-1596, USA
Venue:
Operations Research Letters
Year:
1994

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Abstract

We analyze relationships among local minima for the traveling salesman and graph bisection problems under standard neighborhood structures. Our work reveals surprising correlations that suggest a globally convex, or ''big valley'' structure in these optimization cost surfaces. In conjunction with combinatorial results that sharpen previous analyses, our analysis directly motivates a new adaptive multi-start paradigm for heuristic global optimization, wherein starting points for greedy descent are adaptively derived from the best previously found local minima. We test a simple instance of this method for the traveling salesman problem and obtain very significant speedups over previous multi-start implementations.