Cost distributions in large combinatorial optimisation problems

We have examined the cost distribution of locally optimal solutions in certain combinatorial optimisation problems. This distribution is found to be peaked about a value characteristic of the algorithm involved, with a width that decreases with the system size N . I t is shown that the distribution of costs E is of the form exp(Ng(E)) and that g(E) is self-averaging. Consequently, estimation of the optimal cost is best achieved by curve fitting to g(E) . Possible forms for g ( e ) are proposed.