Result: K-adaptability in stochastic combinatorial optimization under objective uncertainty.

• Introduced a new paradigm for stochastic combinatorial optimization under objective uncertainty. • Investigated computational complexity of the resulting problem. • Developed different exact and heuristic solution methods and compared them experimentally. We address combinatorial optimization problems with uncertain objective functions, given by discrete probability distributions. Within this setting, we investigate the so-called K -adaptability approach: the aim is to calculate a set of K feasible solutions such that the objective value of the best of these solutions, calculated in each scenario independently, is optimal in expectation. Interpreted as a stochastic optimization problem, we only consider second-stage variables, however, the corresponding candidate solutions are selected in the first stage, i.e., before the scenario is known. We show that this problem is NP-hard even if the underlying certain problem is trivial, and present further complexity results concerning approximability and fixed-parameter tractability with respect to K. Moreover, we present exact solution methods as well as a heuristic for this problem and compare them in an extensive experimental evaluation, where the underlying problem is the Unconstrained Binary Optimization Problem, the Shortest Path Problem or the Spanning Tree Problem. It turns out that the performance and the ranking of these approaches strongly depends on the parameter K and on the number of scenarios. [ABSTRACT FROM AUTHOR]

Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)