A new adaptive multi-start technique for combinatorial global optimizations

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 signi cant speedups over previous multi-start implementations.