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Min-max and min-max regret versions of combinatorial optimization problems: A survey

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  • Aissi, Hassene
  • Bazgan, Cristina
  • Vanderpooten, Daniel

Abstract

Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min s-t cut, knapsack. Since most of these problems are NP-hard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.

Suggested Citation

  • Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:427-438
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