We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and Nordström (2022) for binary programs to handle any additional difficulties arising from unbounded and continuous variables, and covers a broad range of … Read more
Congestion games allow to model competitive resource sharing in various distributed systems. Pure Nash equilibria, that are stable outcomes of a game, could be far from being socially optimal. Our goal is to identify combinatorial structures that limit the inefficiency of equilibria. This question has been mainly investigated for congestion games defined over networks. Instead, … Read more
The simplified Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of \(k\) given sets, each set consisting of \(n\) points, with the aim of minimizing the sum of distances to the barycenter of the \(k\) chosen points. This problem is also known as the cheapest hub … Read more
In this paper, we propose ROBIST, a simple, yet effective, data-driven algorithm for optimization under parametric uncertainty. The algorithm first generates solutions in an iterative manner by sampling and optimizing over a relatively small set of scenarios. Then, using statistical testing, the robustness of the solutions is evaluated, which can be done with a much … Read more
In this paper, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis of streamlining the definition of branch-and-bound. We introduce “skewed $k$-trees” which give a hierarchy of relaxations that is incomparable to that of Sherali-Adams, and we show that it is much better for some instances. We also … Read more
The maximum independent set (MIS) seeks to find a subset of vertices with the maximum size such that no pair of its vertices are adjacent. This paper develops a recursive fixing procedure that generalizes the existing polytime algorithm to solve the maximum independent set problem on chordal graphs, which admit simplicial orderings. We prove that … Read more
The vehicle routing problem with stochastic demands (VRPSD) generalizes the classic vehicle routing problem by considering customer demands as random variables. Similarly to other vehicle routing variants, state-of-the-art algorithms for the VRPSD are often based on set-partitioning formulations, which require efficient routines for the associated pricing problems. However, all these set-partitioning-based approaches have strong assumptions … Read more
We propose an extension of matrix games where the row player may select rows and remove columns, subject to a budget constraint. We present an exact mixed-integer linear programming (MILP) formulation for the problem, provide analytical results concerning its solution, and discuss applications in the security domain. Our computational experiments show heuristic approaches on average … Read more
We address the Green Vehicle Routing Problem with Two-Dimensional Loading Constraints and Split Delivery (G2L-SDVRP), which extends the split delivery vehicle routing problem to include customer demands represented by two-dimensional, rectangular items. We aim to minimize carbon dioxide (CO\(_2\)) emissions instead of travel distance, a critical issue in contemporary logistics activities. The CO\(_2\) emission rate … Read more
We study the continuous-time service network design problem (CTSNDP) under travel time uncertainty, aiming to design a transportation service network along a continuous-time planning horizon, with robust operational efficiency even in the presence of travel time deviations. Incorporating travel time uncertainty holds a great practical value. However, it poses a significant challenge in both problem … Read more