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The paper describes a general glance to the use of element exchangetechniques for optimization over permutations. A multi-level description ofproblems is proposed which is a fundamental to understand nature and complexityof optimization problems over permutations (e.g., ordering, scheduling,traveling salesman problem). The description is based on permutationneighborhoods of several kinds (e.g., by improvement of an objective function).Our proposed operational digraph and its kinds can be considered as a way tounderstand convexity and polynomial solvability for combinatorial optimizationproblems over permutations. Issues of an analysis of problems and a design ofhierarchical heuristics are discussed. The discussion leads to a multi-leveladaptive algorithm system which analyzes an individual problem andselects/designs a solving strategy (trajectory).

Digraph description of k-interchange technique for optimization over permutations and adaptive algorithm system