The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance in integer programming, this concept has interpretations in aspects of social choice, symmetric cryptanalysis, and machine learning. We … Read more
Large-neighbourhood search (LNS) heuristics are important mathematical programming techniques that search for primal feasible solutions by solving an auxiliary problem with a restricted feasible region. Extending such powerful generic LNS heuristics to the branch- and-price context is inherently challenging. The most prominent challenges arise from the fact that in branch-and-price algorithms, columns are generated with … Read more
To realize the benefits of network connectivity in transfer-based transit networks, it is critical to minimize transfer disutility for passengers by synchronizing timetables of intersecting routes. We propose a mixed-integer linear programming timetable synchronization model that incorporates new features, such as dwell time determination and vehicle capacity limit consideration, which have been largely overlooked in … Read more
The temporal bin packing problem with fire-ups (TBPP-FU) is a two-dimensional packing problem where one geometric dimension is replaced by a time horizon. The given items (jobs) are characterized by a resource consumption, that occurs exclusively during an activity interval, and they have to be placed on servers so that the capacity constraint is respected … Read more
Airlines solve many different optimization problems and combine the resulting solutions to ensure smooth, minimum-cost operations. Crucial problems are the Fleet Assignment, which assigns aircraft types to flights of a given schedule, and the Tail Assignment, which determines individual flight sequences to be performed by single aircraft. In order to find a cost-optimal solution, many … Read more
The One-Dimensional Cutting Stock Problem with Setup Cost (CSP-S) is a cutting problem that seeks a cutting plan with a minimum number of objects and a minimum number of different patterns. This problem gains relevance in manufacturing settings, where time consuming operations to set up the knives of the cutting machine for the new patterns … Read more
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from slow runtimes, due to weak linear programming (LP) relaxations. In this paper, we first propose a … Read more
Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances … Read more
We study a delivery strategy for last-mile deliveries in urban areas which combines freight transportation with mass mobility systems with the goal of creating synergies contrasting negative externalities caused by transportation. The idea is to use the residual capacity on public transport means for moving freights within the city. In particular, the system is such … Read more
We propose a new method for separating valid inequalities for the epigraph of a function of binary variables. The proposed inequalities are disjunctive cuts defined by disjunctive terms obtained by enumerating a subset $I$ of the binary variables. We show that by restricting the support of the cut to the same set of variables $I$, … Read more