Multiparametric robust solutions for combinatorial problems with parameterized locally budgeted uncertainty

TL;DR

This paper introduces a novel multiparametric algorithm for finding robust solutions in combinatorial problems under locally budgeted uncertainty, ensuring near-optimal robustness across parameter variations.

Contribution

It presents the first algorithm capable of generating a solution set that guarantees near-optimal robustness for all parameter values in combinatorial problems.

Findings

Effective for shortest path problems

Applicable to p-median problems

Demonstrates computational efficiency

Abstract

In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The algorithm consists of applying a multiparametric algorithm to obtain a near optimal multiparametric solution relative to the objective function for a combinatorial problem defined to find a robust solution for parameters fixed. As far as we know this is the first algorithm presented to do that task. Computational experience is presented to shortest path and $p$-medians problems