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A common strategy for improving optimization algorithms is to restart thealgorithm when it is believed to be trapped in an inferior part of the searchspace. However, while specific restart strategies have been developed forspecific problems (and specific algorithms), restarts are typically notregarded as a general tool to speed up an optimization algorithm. In fact, manyoptimization algorithms do not employ restarts at all.  Recently, "bet-and-run" was introduced in the context of mixed-integerprogramming, where first a number of short runs with randomized initialconditions is made, and then the most promising run of these is continued. Inthis article, we consider two classical NP-complete combinatorial optimizationproblems, traveling salesperson and minimum vertex cover, and study theeffectiveness of different bet-and-run strategies. In particular, our restartstrategies do not take any problem knowledge into account, nor are tailored tothe optimization algorithm. Therefore, they can be used off-the-shelf. Weobserve that state-of-the-art solvers for these problems can benefitsignificantly from restarts on standard benchmark instances.

A Generic Bet-and-run Strategy for Speeding Up Traveling Salesperson and Minimum Vertex Cover