Abstract
We investigate the behavior of local improvement algorithms applied to combinatorial optimization problems with multiple local optima. In general, these algorithms display two characteristics: speed and inaccuracy. This behavior is correctly predicted by our model: we show that the expected number of iterations is linear for a wide range of randomness assumptions, and that the number of local optima tends to be exponentially large. We also give some results and constructions that suggest that known NP-complete problems cannot be solved even probabilistically by any “reasonable” local improvement method.
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