Despite the fact that many vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not “under control” from a polyhedral point of view. The equivalence between optimization and separation suggests the existence of integer programming formulations for these problems whose associated polytopes admit elegant characterizations. In this work we … Read more
Given a graph $G=(V,E)$ where $|V|=n$ and $|E|=m$. Graph partitioning problems on $G$ are to find a partition of the vertices in $V$ into clusters satisfying several additional constraints in order to minimize or maximize the number (or the weight) of the edges whose endnodes do not belong to the same cluster. These problems are … 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
The idea of k-adaptability in two-stage robust optimization is to calculate a fixed number k of second-stage policies here-and-now. After the actual scenario is revealed, the best of these policies is selected. This idea leads to a min-max-min problem. In this paper, we consider the case where no first stage variables exist and propose to … Read more
We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either … Read more
The Probabilistic Traveling Salesman Problem, introduced in 1985 by Jaillet, is one of the fundamental stochastic versions of the Traveling Salesman Problem: After the tour is chosen, each vertex is deleted with given probability 1-p. The eliminated vertices are bypassed which leads to shorter tours. The aim is to minimize the expected tour length. The … Read more
In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and … Read more
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is rarely a systematic construction leading to the best possible formulation. We introduce embedding formulations and complexity as a new MIP … Read more
We describe new computer-based search strategies for extreme functions for the Gomory–Johnson infinite group problem. They lead to the discovery of new extreme functions, whose existence settles several open questions. Article Download View New computer-based search strategies for extreme functions of the Gomory–Johnson infinite group problem