Fabio Furini We consider a generalization of the knapsack problem in which items are partitioned into classes, each characterized by a fixed cost and capacity. We study three alternative Integer Linear Programming formulations. For each formulation, we design an efficient algorithm to compute the linear programming relaxation (one of which is based on Column Generation techniques). We … Read more
Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR based Branch and Bound (DSATUR) is an effective exact algorithm for the … Read more
The integration of Unmanned Aircraft Systems (UAS) into civil airspace is one of the most challenging problems for the automation of the Controlled Airspace, and the optimization of the UAS route is a key step for this process. In this paper, we optimize the planning phase of a UAS mission that consists of departing from … Read more
In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set … Read more
We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within … Read more
We consider the Train Timetabling Problem (TTP) in a railway node (i.e. a set of stations in an urban area interconnected by tracks), which calls for determining the best schedule for a given set of trains during a given time horizon, while satisfying several track operational constraints. In particular, we consider the context of a … Read more
Two dimensional cutting problems are about obtaining a set of rectangular items from a set of rectangular stock pieces and are of great relevance in industry, whenever a sheet of wood, metal or other material has to be cut. In this paper, we consider the 2-stage two-dimensional knapsack (2TDK) problem which requires finding the maximum … Read more
In this work we propose and test a new linearisation technique for Binary Quadratic Problems (BQP). We computationally prove that the new formulation, called Extended Linear Formulation, performs much better than the standard one in practice, despite not being stronger in terms of Linear Programming relaxation (LP). We empirically prove that this behaviour is due … Read more
The principal idea of this paper is to exploit Semidefinite Programming (SDP) relaxation within the framework provided by Mixed Integer Nonlinear Programming (MINLP) solvers when tackling Binary Quadratic Problems (BQP). SDP relaxation is well-known to provide strong bounds for BQP in practice. However, the method is not typically implemented in many state-of-the-art MINLP solvers based … Read more
Dantzig-Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computational proof-of-concept that the reformulation can be automated. That … Read more