We propose two new classes of valid inequalities (VIs) for the binary knapsack polytope, based on non-minimal covers. We also show that these VIs can be obtained through neither sequential nor simultaneous lifting of well-known cover inequalities. We further provide conditions under which they are facet-defining. The usefulness of these VIs is demonstrated using computational … Read more
We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick linearization (Operations Research Letters 51 (2023) 146-152). In this paper we extend the result to more general linearizations, and present a simpler proof. Moreover, … 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 consists in selecting one point from \(k\) given sets, each set consisting of \(n\) points, with the aim of minimizing the sum of distances to the barycenter of the \(k\) points chosen. This problem is known to be NP-hard. We compute the Wasserstein barycenter by exploiting the Euclidean distance … 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 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 … Read more
Bike Sharing Systems (BSSs) offer a sustainable and efficient urban transportation solution, bringing flexible and eco-friendly alternatives to city logistics. During their operation, BSSs may suffer from unbalanced bike distribution among stations, requiring rebalancing operations throughout the system. The inherent uncertain demand at the stations further complicates these rebalancing operations, even when performed during downtime. … Read more
We study a class of bi-objective integer programs known as bi-objective knapsack problems (BOKPs). Our research focuses on the development of innovative exact and approximate solution methods for BOKPs by synergizing algorithmic concepts from two distinct domains: multi-objective integer programming and (deep) reinforcement learning. While novel reinforcement learning techniques have been applied successfully to single-objective … Read more