We characterize optimal, k-best and sets of k-best solutions for a combinatorial optimization problem via simple exchange properties. We show the relationship of this concept to the concept of adjacency and we extend the concept to discrete optimization problems and problems with objective functions fulfilling the cone-property. We show that those exchange properties play a fundamental role in partitioning strategies for finding sets of k-best solutions. © 1985 Elsevier Science Publishers B.V. (North-Holland).
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