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A covering problem may be stated as follows: Formula: see text An algorithm has been programmed on the IBM 7094 for solving such problems. For a given problem, it generates a set of independent “locally-optimum” solutions. If p is the probability that any one solution is actually an optimum, then for n independently generated solutions we have a prob-babiiity of 1−(1 − p) n that an optimal solution appears in the set generated. Computational experience indicates that this approach yields good results for large problems (up to m · n ≦ 0.5 × 10 6 ).
Richard H. Roth (1969) studied this question.