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Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
Multi-product pipelines are a highly efficient means of transporting liquids. Traditionally used to transport petroleum, its products and derivatives, they are now being repurposed to transport liquified natural gas admixed with hydrogen of…
Following the recent push for trustworthy AI, there has been an increasing interest in developing contrastive explanation techniques for optimisation, especially concerning the solution of specific decision-making processes formalised as…
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
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…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
Oil products are the main source of energy in the world today. Distribution of these products is one of the main issues in the industry. The main tools for this work are pipelines, and along with it, railways, shipping and roads are also…
Today, it is more important than ever before for users to have trust in the models they use. As Machine Learning models fall under increased regulatory scrutiny and begin to see more applications in high-stakes situations, it becomes…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…
Maximizing oil production from gas-lifted oil wells entails solving Mixed-Integer Linear Programs (MILPs). As the parameters of the wells, such as the basic-sediment-to-water ratio and the gas-oil ratio, are updated, the problems must be…
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…
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…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
We compute the closest convex piecewise linear-quadratic (PLQ) function with minimal number of pieces to a given univariate piecewise linear-quadratic function. The Euclidean norm is used to measure the distance between functions. First, we…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
Given a piecewise linear (PL) function $p$ defined on an open subset of $\R^n$, one may construct by elementary means a unique polyhedron with multiplicities $\D(p)$ in the cotangent bundle $\R^n\times \R^{n*}$ representing the graph of the…
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…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Governments across the world are planning to increase the share of renewables in their energy systems. The siting of new wind and solar power plants requires close coordination with grid planning, and hence co-optimization of investment in…
Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…