In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more
A large number of the real world planning problems which are today solved using Operations Research methods are actually multi-objective planning problems, but most of them are solved using single-objective methods. The reason for converting, i.e. simplifying, multi- objective problems to single-objective problems is that no standard multi-objective solvers exist and specialized algorithms need to … Read more
The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig-Wolfe decomposition and Quadratic Convex Reformulation principles. As a representative case study, we apply them to a cardinality constrained quadratic knapsack problem, providing extensive experimental insights. We show that … Read more
Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIP), we address a fundamental research question, that is to assess if good decomposition patterns can be consistently found by looking only at static properties of MIP input instances, or not. We adopt a data driven approach, devising a … Read more
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite non-convexities in the feasible region. As a side result, we present a new characterization of the conflict separation condition in the form of … Read more
We consider the problem of packing congruent circles with the maximum radius in a unit square. As a mathematical program, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem which possesses a large number of local optima. We study several convexification techniques for the circle packing problem, including polyhedral and semi-definite relaxations and … Read more
We present a novel formulation for startup cost computation in the unit commitment problem (UC). Both the proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. The proposed formulation is tested empirically against existing formulations on large-scale unit commitment instances drawn … Read more
The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving … Read more
An important problem in the breeding of livestock, crops, and forest trees is the optimum of selection of genotypes that maximizes genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures genetic diversity, therefore, the optimal selection can be cast as a second-order cone programming (SOCP) problem. Yamashita et … Read more
The generalized intersection cut (GIC) paradigm is a recent framework for generating cutting planes in mixed integer programming with attractive theoretical properties. We investigate this computationally unexplored paradigm and observe that a key hyperplane activation procedure embedded in it is not computationally viable. To overcome this issue, we develop a novel replacement to this procedure … Read more