On Scenario Aggregation to Approximate Robust Combinatorial Optimization Problems
نویسندگان
چکیده
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)-approximation for any desired ε > 0. Our method can be applied to minmax as well as min-max regret problems.
منابع مشابه
On Scenario Aggregation to Approximate Robust Optimization Problems
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 wellknown approximation algorithm is the midpoint method, where one takes the average over all scenarios, and solves a problem of nominal type. Despite its simplicity, t...
متن کاملFor Peer Review Two - stage Robust Network Design with Exponential Scenarios
We study two-stage robust variants of combinatorial optimization problems like Steiner tree, Steiner forest, and uncapacitated facility location. The robust optimization problems, previously studied by Dhamdhere et al. [9], Golovin et al. [15], and Feige et al. [13], are two-stage planning problems in which the requirements are revealed after some decisions are taken in stage one. One has to th...
متن کاملRobust Metric Learning by Smooth Optimization
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as users’ implicit feedbacks and citations among articles. As a result, these constraints are usually noisy and contain many mistakes. In this work, we aim to lea...
متن کاملCombinatorial optimization problems with uncertain costs and the OWA criterion
In this paper a class of combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing K distinct cost scenarios. The Ordered Weighted Averaging (OWA for short) aggregation operator is applied to choose a solution. Some well known criteria used in decision making under uncertainty such as the maximum, minimum, ...
متن کاملBottleneck combinatorial optimization problems with uncertain costs and the OWA criterion
In this paper a class of bottleneck combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing a finite number of cost vectors, called scenarios. In order to choose a solution the Ordered Weighted Averaging aggregation operator (shortly OWA) is applied. The OWA operator generalizes traditional criteria in de...
متن کامل