We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0-1 variables x_j indicating whether faclility j is used or not and y_{ij} variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, … Read more
We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more
We investigate the optimal piecewise linear interpolation of the bivariate product xy over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the interpolation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using these as … Read more
Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be discrete sets. In this work, we study the set-covering location problem when … Read more
In this paper, we establish a polynomial equivalence between tree ensemble optimization and optimization of multilinear functions over the Cartesian product of simplices. We use this insight to derive new formulations for tree ensemble optimization problems and to obtain new convex hull results for multilinear polytopes. A computational experiment on multi-commodity transportation problems with costs … Read more
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
The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality in practice. In this paper, we develop … 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
In this paper, we study the sparse integer least squares problem (SILS), an NP-hard variant of least squares with sparse {0, 1, -1}-vectors. We propose an l1-based SDP relaxation, and a randomized algorithm for SILS, which computes feasible solutions with high probability with an asymptotic approximation ratio 1/T^2 as long as the sparsity constant σ … Read more
The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on propagation techniques for cyclic groups. Our algorithms come with the guarantee to find all possible variable fixings that can be derived from … Read more