Margin Optimal Classification Trees
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mixed-integer programming
Evaluating Mixed-Integer Programming Models over Multiple Right-hand Sides
A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is not known exactly; however, there is no consensus metric for evaluating a MIP model when considering multiple right-hand sides. In … Read more
Dynamic Rebalancing Optimization for Bike-sharing Systems: A Modeling Framework and Empirical Comparison
Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more
Revisiting local branching with a machine learning lens
Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution … Read more
Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump
The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate … Read more
Learning to Use Local Cuts
An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more
PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming
In deterministic optimization, it is typically assumed that all parameters of the problem are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this … Read more
Logic-based Benders decomposition with a partial assignment acceleration technique for avionics scheduling
Pre-runtime scheduling of large-scale electronic systems, as those in modern aircraft, can be computationally challenging. In this paper, we study a distributed integrated modular avionic system of practical relevance where the scheduling includes to assign communication messages to time slots and to sequence tasks on modules. For this problem, the challenge is the huge number … Read more
Continuous Covering on Networks: Strong Mixed Integer Programming Formulations
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
Ensemble Methods for Robust Support Vector Machines using Integer Programming
In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to develop models which are robust against small perturbations in the training data. We … Read more