On scenario aggregation to approximate robust combinatorial optimization problems

Chassein, André and Goerigk, Marc (2018) On scenario aggregation to approximate robust combinatorial optimization problems. Optimization Letters, 12 (7). pp. 1523-1533. ISSN 1862-4472

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Abstract

As most robust combinatorial min–max and min–max regret problems with discrete uncertainty sets are NP-hard, research in 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)(εK) -approximation for any desired ε>0ε>0 . Our method can be applied to min–max as well as min–max regret problems.

Item Type:
Journal Article
Journal or Publication Title:
Optimization Letters
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-017-1206-x
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2606
Subjects:
ID Code:
88308
Deposited By:
Deposited On:
18 Oct 2017 09:30
Refereed?:
Yes
Published?:
Published
Last Modified:
05 Apr 2020 04:41