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Adaptive stability: general approach and examples

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Abstract

In this article we study the situation, where an optimal solution of a combinatorial optimization problem is known and we are equipped with the simple algorithms allowing to adapt our solution to different distortions of the initial data set. We wish to describe the distortions which allow the adaptation of the given optimal solution by the given simple algorithm preserving the optimality of the first. This approach, lying between common stability and reoptimization, is called adaptive stability. In the article we construct the conditions of adaptive stability for a range of combinatorial optimization problems having a particular structure. The obtained conditions allow to build efficiently the corresponding adaptive stability areas. The stability areas may be used for postoptimal preferring among different optimal solutions whether these are multiple solutions belonging to a single mathematical model or a set of optimal solutions corresponding to different models. The abstract concept is illustrated by two examples of combinatorial optimization problems: traveling salesman problem and task distribution problem.

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Acknowledgments

The work was supported by Russian Science Foundation 14-11-00109.

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Correspondence to Evgeny Ivanko.

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Ivanko, E. Adaptive stability: general approach and examples. Oper Res Int J 15, 437–452 (2015). https://doi.org/10.1007/s12351-015-0180-2

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  • DOI: https://doi.org/10.1007/s12351-015-0180-2

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