Abstract
This paper presents some theoretical results concerning the effectiveness of an approximate technique, known as local optimization, as applied to a wide class of problems.
First, conditions are described under which the technique ensures exact solutions. Then, in regard to cases in which these conditions cannot be met in practice, a method is presented for estimating the probability that the approximate (locally optimal) solution delivered by such a technique is in fact the exact (globally optimal) solution.
This probability may be viewed as a possible criterion of effectiveness in the design of neighborhoods for specific local optimization algorithms.
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Savage, S.L. Some theoretical implications of local optimization. Mathematical Programming 10, 354–366 (1976). https://doi.org/10.1007/BF01580681
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DOI: https://doi.org/10.1007/BF01580681