Related papers: Machine Learning Augmented Branch and Bound for Mi…
With the accelerated development of Industry 4.0, intelligent manufacturing systems increasingly require efficient task allocation and scheduling in multi-robot systems. However, existing methods rely on domain expertise and face challenges…
Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot…
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…
Optimal planning with respect to learned neural network (NN) models in continuous action and state spaces using mixed-integer linear programming (MILP) is a challenging task for branch-and-bound solvers due to the poor linear relaxation of…
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer…
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…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
Resource allocation in wireless networks, such as device-to-device (D2D) communications, is usually formulated as mixed integer nonlinear programming (MINLP) problems, which are generally NP-hard and difficult to get the optimal solutions.…
Mixed Integer Programming (MIP) has been extensively applied in areas requiring mathematical solvers to address complex instances within tight time constraints. However, as the problem scale increases, the complexity of model formulation…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…
Planning the maintenance of nuclear power plants is a complex optimization problem, involving a joint optimization of maintenance dates, fuel constraints and power production decisions. This paper investigates Mixed Integer Linear…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…
In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization.…
In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…