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In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications.…
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…
Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear…
Decision trees are a popular machine learning model which are traditionally trained by heuristic methods. Massive improvements in computing power and optimisation techniques has led to renewed interest in learning globally optimal decision…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn…
Risk assessment tools in healthcare commonly employ point-based scoring systems that map patients to ordinal risk categories via thresholds. While electronic health record (EHR) data presents opportunities for data-driven optimization of…
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We…
Mixed Integer Programming (MIP) is NP-hard, and yet modern solvers often solve large real-world problems within minutes. This success can partially be attributed to heuristics. Since their behavior is highly instance-dependent, relying on…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of…
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…
In hybrid Model Predictive Control (MPC), a Mixed-Integer Quadratic Program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect…
Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from…
We introduce a mixed integer program (MIP) for assigning importance scores to each neuron in deep neural network architectures which is guided by the impact of their simultaneous pruning on the main learning task of the network. By…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on…
Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…