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We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for…
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 programming (MIP) extends linear programming by incorporating both continuous and integer decision variables, making it widely used in production planning, logistics scheduling, and resource allocation. However, MIP remains…
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…
Retrieval-Augmented Generation (RAG) has become a cornerstone technique for enhancing large language models (LLMs) with external knowledge. However, current RAG systems face two critical limitations: (1) they inefficiently retrieve…
Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions…
Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…
Past few years have witnessed a growing recognition of intelligent techniques for the construction of efficient and reliable intrusion detection systems. Due to increasing incidents of cyber attacks, building effective intrusion detection…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
Mixed-integer programming (MIP) research is both mathematically sophisticated and engineering-intensive: testing an algorithmic hypothesis within a branch-and-cut solver requires substantial implementation, debugging, tuning, and…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from…
Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is…
Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…
Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on…
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…
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 consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
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…