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Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in…
Decision trees are a widely used method for classification, both by themselves and as the building blocks of multiple different ensemble learning methods. The Max-Cut decision tree involves novel modifications to a standard, baseline model…
Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to…
Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version…
In this paper, we develop a new formulation of changeover constraints for mixed integer programming problem (MIP) that emerges in solving a short-term production scheduling problem. The new model requires fewer constraints than the original…
In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible…
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in…
This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process, and develops an efficient search algorithm that is able to solve practical instances of the MIP…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Mixed-integer model predictive control (MI-MPC) can be a powerful tool for modeling hybrid control systems. In case of a linear-quadratic objective in combination with linear or piecewise-linear system dynamics and inequality constraints,…
We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost…