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Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…
We address the challenge of efficiently solving parameterized sequences of convex Mixed-Integer Nonlinear Programming (MINLP) problems through warm-starting techniques. We focus on an outer approximation (OA) approach, for which we develop…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource…
A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming…
A common challenge in real-time operations is deciding whether to re-solve an optimization problem or continue using an existing solution. While modern data platforms may collect information at high frequencies, many real-time operations…
Solving large-scale Mixed Integer Programs (MIP) can be difficult without advanced algorithms such as decomposition based techniques. Even if a decomposition technique might be appropriate, there are still many possible decompositions for…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
Modern Mixed Integer Linear Programming (MILP) solvers use the Branch-and-Bound algorithm together with a plethora of auxiliary components that speed up the search. In recent years, there has been an explosive development in the use of…
With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate…
The p-center problem consists in selecting p centers among M to cover N clients, such that the maximal distance between a client and its closest selected center is minimized. For this problem we propose two new and compact integer…
This paper introduces $\Delta$-MILP, a powerful variant of the mixed-integer linear programming (MILP) optimization framework to solve NASA's Deep Space Network (DSN) scheduling problem. This work is an extension of our original MILP…
Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is…
In many operational contexts, solutions to NP-hard combinatorial optimization problems, modeled by means of Mixed-Integer Linear Programming (MILP), may become infeasible due to unpredictable disruptions. Typically, reoptimizing by solving…
The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to…
Autonomous systems must solve motion planning problems subject to increasingly complex, time-sensitive, and uncertain missions. These problems often involve high-level task specifications, such as temporal logic or chance constraints, which…
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that…
In this paper, we develop a unified machine learning (ML) approach to predict high-quality solutions for single-machine scheduling problems with a non-decreasing min-sum objective function with or without release times. Our ML approach is…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…