On Scenario Aggregation to Approximate Robust Optimization Problems

Chassein, André and Goerigk, Marc (2016) On Scenario Aggregation to Approximate Robust Optimization Problems. Working Paper. UNSPECIFIED.

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As most robust combinatorial min-max and min-max regret problems with discrete uncertainty sets are NP-hard, research into approximation algorithm and approximability bounds has been a fruitful area of recent work. A simple and well-known approximation algorithm is the midpoint method, where one takes the average over all scenarios, and solves a problem of nominal type. Despite its simplicity, this method still gives the best-known bound on a wide range of problems, such as robust shortest path, or robust assignment problems. In this paper we present a simple extension of the midpoint method based on scenario aggregation, which improves the current best K-approximation result to an (εK)-approximation for any desired ε>0. Our method can be applied to min-max as well as min-max regret problems.

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27 Apr 2017 12:30
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12 Sep 2023 04:23