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The robust selection problem with information discovery
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AI
DOI：10.1016/j.dam.2025.12.012.png)
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Abstract
En 中文
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this information, one can then choose the set of items to be selected, still facing uncertainty on the unobserved parameters. In this paper, we study two specific variants of this problem. The first variant considers objective uncertainty and focuses on selecting a single item. The second variant considers constraint uncertainty instead, which means that some selected items may fail. We show that both problems are NP-hard in general. We also propose polynomial-time algorithms for special cases where the sets of items that can be simultaneously queried are defined by a cardinality or a knapsack constraint. For the problem with constraint uncertainty, we also show how the objective function can be expressed as a linear program, leading to a mixed-integer linear programming reformulation for the general case. We illustrate the performance of this formulation using numerical experiments. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
Selection
Robust optimization
Decision-dependent uncertainty
Combinatorial optimization
NP-hardness
Journal
D
IF:
1.1
Papers:
336
Citations:
7.7K