Constructing Representative Scenarios to Approximate Robust Combinatorial Optimization Problems
Marc Goerigk

TL;DR
This paper introduces a linear programming method to construct representative scenarios in robust combinatorial optimization, improving approximation guarantees over traditional methods and demonstrating practical benefits through numerical experiments.
Contribution
It presents a novel linear program for scenario construction that enhances approximation guarantees in robust combinatorial optimization.
Findings
The new method guarantees at least as good an approximation as existing methods.
Element-wise worst-case can outperform the midpoint approach with many scenarios.
Numerical experiments show a 20% improvement in approximation guarantee.
Abstract
In robust combinatorial optimization with discrete uncertainty, two general approximation algorithms are frequently used, which are both based on constructing a single scenario representing the whole uncertainty set. In the midpoint method, one optimizes for the average case scenario. In the element-wise worst-case approach, one constructs a scenario by taking the worst case in each component over all scenarios. Both methods are known to be -approximations, where is the number of scenarios. In this paper, these results are refined by reconsidering their respective proofs as optimization problems. We present a linear program to construct a representative scenario for the uncertainty set, which guarantees an approximation guarantee that is at least as good as for the previous methods. Incidentally, we show that the element-wise worst-case approach can have an advantage over the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRisk and Portfolio Optimization · Probabilistic and Robust Engineering Design · Advanced Multi-Objective Optimization Algorithms
