In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD is to cluster the vectors according to their subspace membership and recover the underlying basis, which can … Read more
\(\) We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision-maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which … Read more
Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in … Read more
We consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on … Read more
\(\) In this note, we study the size of the support of solutions to linear Diophantine equations $Ax=b, ~x\in\Z^n$ where $A\in\Z^{m\times n}, b\in\Z^n$. We give an asymptotically tight upper bound on the smallest support size, parameterized by $\|A\|_\infty$ and $m$, and taken as a worst case over all $b$ such that the above system has … Read more
Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more
Electric vehicles (EV) pave a promising way towards low-carbon transportation, but the transition to all EV fleets creates new challenges for the public transportation sector. Despite increasing adoption of electric buses, the main challenges presented by the battery electric bus technology include the lack of charging facilities, the reduced operating capacity per battery charge compared … Read more
\(\) We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator \( \text{LS}_+\), with a particular focus on a search for relatively small graphs with high \( \text{LS}_+\)-rank (the least number of iterations of the \( \text{LS}_+\) operator on the fractional stable set polytope to compute … Read more
Supervalid inequalities are a specific type of constraints often used within the branch-and-cut framework to strengthen the linear relaxation of mixed-integer programs. These inequalities share the particular characteristic of potentially removing feasible integer solutions as long as they are already dominated by an incumbent solution. This paper focuses on supervalid inequalities for solving binary interdiction … Read more
Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. More precisely, we generate one cut … Read more