Elsevier

Operations Research Letters

Volume 16, Issue 2, September 1994, Pages 101-113
Operations Research Letters

A new adaptive multi-start technique for combinatorial global optimizations

https://doi.org/10.1016/0167-6377(94)90065-5Get rights and content

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.

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    Partial support for this work was provided by ARO DAAK-70-92-K-0001, ARO DAAL-03-92-G-0050, NSF MIP-9110696, and NSF Young Investigator Award MIP-9257982.

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