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Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…
In fields such as autonomous and safety-critical systems, online optimization plays a crucial role in control and decision-making processes, often requiring the integration of continuous and discrete variables. These tasks are frequently…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…
Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to…
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…
In this article, we introduce the concept of discounted pseudocosts, inspired by discounted total reward in reinforcement learning, and explore their application in mixed-integer linear programming (MILP). Traditional pseudocosts estimate…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal…
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…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
Mixed-Integer Programs (MIPs) are NP-hard optimization models that arise in a broad range of decision-making applications, including finance, logistics, energy systems, and network design. Although modern commercial solvers have achieved…
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…
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…
Mixed integer bilinear programs (MIBLPs) offer tools to resolve robotics motion planning problems with orthogonal rotation matrices or static moment balance, but require long solving times. Recent work utilizing data-driven methods has…
Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…
There has been a surge of interest in learning optimal decision trees using mixed-integer programs (MIP) in recent years, as heuristic-based methods do not guarantee optimality and find it challenging to incorporate constraints that are…
We present BackboneLearn: an open-source software package and framework for scaling mixed-integer optimization (MIO) problems with indicator variables to high-dimensional problems. This optimization paradigm can naturally be used to…
Finding a high-quality feasible solution to a combinatorial optimization (CO) problem in a limited time is challenging due to its discrete nature. Recently, there has been an increasing number of machine learning (ML) methods for addressing…