Abstract
We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we seek a robust solution that, after the failing elements are revealed, can be augmented in a limited way. However, we commit to preserve the non-failing elements of the initial solution. We settle the computational complexity of such a robust counterpart for various classical polynomial-time solvable combinatorial optimization problems.
We show that for the weighted matroid independent set problem, an optimal solution to the nominal problem is also optimal for its robust counterpart. In fact, matroids are provably the only structures with this strong property. Robust counterparts of other problems are NP-hard, such as the matching problem and the stable set problem, even in bipartite graphs. However, we establish polynomial-time algorithms for the robust counterparts of the unweighted stable set problem in bipartite graphs and the weighted stable set problem in interval graphs, also known as the interval scheduling problem.
Blogger's Review: This research offers a fresh perspective on handling uncertainty in combinatorial optimization problems, particularly under the commitment to retain part of the solution. The findings not only enrich the theoretical framework but also provide new avenues for algorithm design and practical applications.