We tackle the network design problem for centralized traffic assignment, which can be cast as a mixed-integer convex optimization (MICO) problem. For this task, we propose different formulations and solution methods i...
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With the increasing popularity of deep learning techniques, there has been a growing interest in combining learning methods with mixed-integer linear programming (MILP) solving processes. A promising approach is to in...
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With the increasing popularity of deep learning techniques, there has been a growing interest in combining learning methods with mixed-integer linear programming (MILP) solving processes. A promising approach is to incorporate the learning model as a module in traditional methods. Cut selection is a fundamental subroutine in modern MILP solvers used to select a subset of generated cuts and enhance solver performance. In this work, we present a supervised learning framework to improve the effectiveness of cut selection. Cut selection scoring rules are typically weighted sums of different metrics, and we have developed weighted cut selection metrics based on Machine Learning (ML) techniques for different problems. We propose a novel Neural Network (NN) architecture that incorporates a Graph Convolutional Neural Network (GCN) with a self-attention mechanism to determine appropriate weights. The resulting model serves as a component of the solver and is evaluated through controlled experiments on real-world MILPs. The numerical results demonstrate that our approach outperforms the standard SCIP cut selection strategy, especially on datasets containing the same class of problems.
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverag...
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Community engagement plays a critical role in anti-poaching efforts, yet existing mathematical models aimed at enhancing this engagement often overlook direct participation by community members as alternative patrolle...
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Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of thi...
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Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Cur...
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We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for o...
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Large Language Models (LLMs) have demonstrated strong performance across various natural language processing tasks, yet their proficiency in mathematical reasoning remains a key challenge. Addressing the gap between n...
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In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is...
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In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of mixedintegerprogramming (MIP) problems. Distinct substantially from existing learning-to-optimize methods,...
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