Abstract
We postulate that real world data are almost always noisy, and an exact solution to a noisy input instance of a combinatorial optimization problem is not what we really want. Noise, or input data uncertainty, has a variety of reasons, such as for instance the need to estimate data based on imprecise measurements or on predictions (drawn from historical data and expected modifications). There is a variety of popular ways to deal with this uncertainty problem. In lucky cases in which the input data distribution is known, one might aim at obtaining a solution that is good in expectation. A different, promising way to handle uncertainty is based on the availability of a discrete set of possible problem instances (sometimes reflecting a distribution), so-called scenarios. A solution must be proposed for a set of scenarios as input, and thereafter a single scenario reveals itself as the actual one. The goal here is to achieve a high quality of the proposed solution with respect to the revealed scenario. Stochastic programming can be used to aim at a good solution in expectation that is feasible for most scenarios. In contrast, robust optimization most often aims at a solution that is feasible in all scenarios and has smallest worst case cost. In any case, uncertainty is considered a curse, a burden, a difficult problem that needs to be dealt with at extra computational cost.
Keywords
- Problem Instance
- Minimum Span Tree
- Stochastic Programming
- Combinatorial Optimization Problem
- Robust Optimization
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2012 Springer-Verlag Berlin Heidelberg
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Widmayer, P. (2012). Combinatorial Optimization with Noisy Inputs: How Can We Separate the Wheat from the Chaff?. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_1
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DOI: https://doi.org/10.1007/978-3-642-28076-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28075-7
Online ISBN: 978-3-642-28076-4
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