Recoverable robust representatives selection problem under interval continuous budgeted uncertainty

2026-08-16

AI Summary

This study addresses the computational challenges inherent in the recoverable robust representative selection problem under continuous budgeted uncertainty. By rigorously analyzing the structural properties of the problem, this work elucidates the fundamental impact of continuous budget constraints on computational complexity. Building upon these theoretical insights, strongly polynomial-time algorithms are developed for both the general case and significant special instances. These contributions effectively overcome the computational bottlenecks associated with traditional approaches, enabling efficient and exact solutions. Consequently, this research provides novel theoretical foundations and algorithmic frameworks for robust optimization in uncertain environments, significantly advancing the state of the art in this domain.

Abstract

In this paper, the recoverable robust representative selection problem is considered, where uncertain second-stage costs are modeled using interval uncertainty with a continuous budget. While the variant under a discrete uncertainty budget is known to be NP-hard, we show that transitioning to a continuous budget fundamentally alters the computational complexity landscape. Specifically, by exploiting the structural properties of the problem under the continuous budget model, we design a strongly polynomial-time algorithm for the general case. Furthermore, we propose an even more efficient strongly polynomial-time algorithm for an important special case.

Problem

• Recoverable robust optimization
• Representative selection problem
• Continuous budgeted uncertainty
• Interval uncertainty

Innovation

• Recoverable Robust Optimization
• Continuous Budgeted Uncertainty
• Strongly Polynomial-time Algorithm
• Computational Complexity
• Representative Selection Problem