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The Distribution of Vaccine among Countries in the Case of a Pandemic

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arXiv 2024年

作者： Vizvári, Béla Kovács, Gergely Dept. of Industrial Engineering Eastern Mediterranean University Cyprus Edutus University Tatabánya Hungary

Purpose: Only few companies were able to produce vaccine again COVID-19. Thus, one producer supplied it to many countries. The distribution was not effective. Some countries overstocked the vaccine while other countries were not able to buy enough. The purpose of the present paper is to provide with a frame such that one producer distributes the vaccine to a set of countries in a way that the shortage is minimized. Methodology: The consumption of the countries are approximated by regression functions taking into account the saturation of the process. The distribution of the vaccine is determined by MIP models of operations research. Findings: Effective distribution of vaccine can be obtained for even a large number of countries. Both the level of the shortage and the number of the consecutive shortage days in a country can be controlled. Practical implications: A group of countries can act as a single partner of a pharmaceutical company. They can get a steady supply. The company gets a well-organized delivery plan. Social implications: More people can be saved because of the steady supply of the vaccine. Originality: The paper develops a new concept for the fair distribution of vaccines between countries. This concept and the method derived from it can be applied in the event of future pandemics on a global scale. © 2024, CC BY.

关键词： mixed-integer linear programming

Fair Minimum Representation Clustering via integer programming

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arXiv 2024年

作者： Lawless, Connor Günlük, Oktay Stanford University United States Georgia Institute of Technology United States

Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV channels) whose benefit can only be attained by groups when they reach a minimum level of representation (e.g., 50% to elect their desired candidate). In this paper, we study the k-means and k-medians clustering problems with the additional constraint that each group (e.g., demographic group) must have a minimum level of representation in at least a given number of clusters. We formulate the problem through a mixed-integer optimization framework and present an alternating minimization algorithm, called MiniReL, that directly incorporates the fairness constraints. While incorporating the fairness criteria leads to an NP-Hard assignment problem within the algorithm, we provide computational approaches that make the algorithm practical even for large datasets. Numerical results show that the approach is able to create fairer clusters with practically no increase in the clustering cost across standard benchmark datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Confirming the Chen-Raspaud Conjecture for k = 3 and k = 4 Using Enhanced Discharging Methods

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arXiv 2024年

作者： Fiedorowicz, Michal Department of Physics University of Warsaw Poland

The Chen-Raspaud Conjecture posits that for every integer k ≥ 2, any graph G with maximum average degree mad(G) k1 and odd girth at least 2k + 1 admits a homomorphism to the Kneser graph KG2k+1,k. While this conjecture has been confirmed for k = 2 and k = 3, it remains open for larger values of k. In this paper, I present comprehensive and rigorous proofs confirming the conjecture for k = 3 and k = 4. By employing enhanced discharging methods, introducing new structural lemmas, and conducting a thorough analysis of the graphs in question, I not only confirm the conjecture for these cases but also strengthen the theoretical framework, laying the groundwork for potential extensions to higher values of k. © 2024, CC BY.

关键词： mixed-integer linear programming

Feature selection in linear Support Vector Machines via a hard cardinality constraint: a scalable conic decomposition approach

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arXiv 2024年

作者： Bomze, Immanuel D’Onofrio, Federico Palagi, Laura Peng, Bo Faculty of Mathematics and Research Network Data Science University of Vienna Oskar-Morgenstern-Platz 1 Wien1090 Austria Department of Computer Control and Management Engineering Sapienza University of Rome Via Ariosto 25 Rome00185 Italy VGSCO University of Vienna Oskar-Morgenstern-Platz 1 Wien1090 Austria

In this paper, we study the embedded feature selection problem in linear Support Vector Machines (SVMs), in which a cardinality constraint is employed, leading to an interpretable classification model. The problem is NP-hard due to the presence of the cardinality constraint, even though the original linear SVM amounts to a problem solvable in polynomial time. To handle the hard problem, we first introduce two mixed-integer formulations for which novel semidefinite relaxations are proposed. Exploiting the sparsity pattern of the relaxations, we decompose the problems and obtain equivalent relaxations in a much smaller cone, making the conic approaches scalable. To make the best usage of the decomposed relaxations, we propose heuristics using the information of its optimal solution. Moreover, an exact procedure is proposed by solving a sequence of mixed-integer decomposed semidefinite optimization problems. Numerical results on classical benchmarking datasets are reported, showing the efficiency and effectiveness of our *** Codes 90C22, 90C11 © 2024, CC BY-NC-ND.

关键词： mixed-integer linear programming

Evaluation of Prosumer Networks for Peak Load Management in Iran: A Distributed Contextual Stochastic Optimization Approach

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arXiv 2024年

作者： Noori, Amir Tavassoli, Babak Fereidunian, Alireza The Faculty of Electrical Engineering KN Toosi of Technology Tehran Iran

Renewable prosumers face the complex challenge of balancing self-sufficiency with seamless grid and market integration. This paper introduces a novel prosumers network framework aimed at mitigating peak loads in Iran, particularly under the uncertainties inherent in renewable energy generation and demand. A cost-oriented integrated prediction and optimization approach is proposed, empowering prosumers to make informed decisions within a distributed contextual stochastic optimization (DCSO) framework. The problem is formulated as a bi-level two-stage multi-time scale optimization to determine optimal operation and interaction strategies under various scenarios, considering flexible resources. To facilitate grid integration, a novel consensus-based contextual information sharing mechanism is proposed. This approach enables coordinated collective behaviors and leverages contextual data more effectively. The overall problem is recast as a mixed-integer linear program (MILP) by incorporating optimality conditions and linearizing complementarity constraints. Additionally, a distributed algorithm using the consensus alternating direction method of multipliers (ADMM) is presented for computational tractability and privacy preservation. Numerical results highlights that integrating prediction with optimization and implementing a contextual information-sharing network among prosumers significantly reduces peak loads as well as total costs. © 2024, CC BY.

关键词： mixed-integer linear programming

Best-subset instrumental variable selection method using mixed integer optimization with applications to health-related quality of life and education–wage analyses

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Research Square

Research Square 2024年 rs3rs-5550004页

作者： Qasim, Muhammad Månsson, Kristofer Balakrishnan, Narayanaswamy Department of Economics Finance and Statistics Jönköping International Business School Jönköping University Sweden Department of Mathematics and Statistics McMaster University HamiltonON Canada

The classical best-subset selection method has been demonstrated to be nondeterministic polynomial-time hard and thus presents computational challenges. This problem can now be solved via advanced mixed integer optimization (MIO) algorithms for linear regression. We extend this methodology to linear instrumental variable (IV) regression and propose the best-subset instrumental variable (BSIV) method incorporating the MIO procedure. Classical IV estimation methods assume that IVs must not directly impact the outcome variable and should remain uncorrelated with nonmeasured variables. However, in practice, IVs are likely to be invalid, and existing methods can lead to a large bias relative to standard errors in certain situations. The proposed BSIV estimator is robust in estimating causal effects in the presence of unknown IV validity. We demonstrate that the BSIV using MIO algorithms outperforms two-stage least squares, Lasso-type IVs, and two-sample analysis (median and mode estimators) through Monte Carlo simulations in terms of bias and relative efficiency. We analyze two datasets involving the health-related quality of life index and proximity and the education–wage relationship to demonstrate the utility of the proposed method. © 2024, CC BY.

关键词： mixed-integer linear programming

A Production Routing Problem with Mobile Inventories

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arXiv 2025年

作者： Lefgoum, Raian Afsar, Sezin Carpentier, Pierre Chancelier, Jean-Philippe De Lara, Michel Cermics École Nationale des Ponts et Chaussées IP Paris 6 et 8 avenue Blaise Pascal Marne la Vallée77455 Cedex 2 France Universidad de Oviedo Principality of Asturias Gijón Spain UMA ENSTA Paris IP Paris France

Hydrogen is an energy vector, and one possible way to reduce CO2 emissions. This paper focuses on a hydrogen transport problem where mobile storage units are moved by trucks between sources to be refilled and destinations to meet demands, involving swap operations upon arrival. This contrasts with existing literature where inventories remain stationary. The objective is to optimize daily routing and refilling schedules of the mobile storages. We model the problem as a flow problem on a time-expanded graph, where each node of the graph is indexed by a time-interval and a location and then, we give an equivalent mixed integer linear programming (MILP) formulation of the problem. For small to medium-sized instances, this formulation can be efficiently solved using standard MILP solvers. However, for larger instances, the computational complexity increases significantly due to the highly combinatorial nature of the refilling process at the sources. To address this challenge, we propose a two-step heuristic that enhances solution quality while providing good lower bounds. Computational experiments demonstrate the effectiveness of the proposed approach. When executed over the large-sized instances of the problem, the median (resp. the mean) obtained by this two-step heuristic outperforms the median (resp. the mean) obtained by the direct use of the MILP solver by 12.7 % (resp. 9 %), while also producing tighter lower bounds. These results validate the efficiency of the method for optimizing hydrogen transport systems with mobile storages and swap operations. Copyright © 2025, The Authors. All rights reserved.

关键词： mixed-integer linear programming

An ANN-Enhanced Approach for Flatness-Based Constrained Control of Nonlinear Systems

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arXiv 2025年

作者： Do, Huu-Thinh Prodan, Ionela Stoican, Florin Univ. Grenoble Alpes Grenoble INP LCIS ValenceF-26000 France Institute of Engineering and Management University Grenoble Alpes France Department of Automatic Control and Systems Engineering UPB Romania

Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat systems. Specifically, the class of flat systems enjoys the benefit of feedback linearizability, i.e., the systems can be linearized by means of a proper variable transformation. However, the price for linearizing the dynamics is that the constraint descriptions are distorted geometrically. Our results show that, by using neural networks, these constraints can be represented as a union of polytopes, enabling the use of mixed-integer programming tools to guarantee constraint satisfaction. We further analyze the integration of the characterization into efficient settings such as control Lyapunov function-based and model predictive control (MPC). Interestingly, this description also allows us to explicitly compute the solution of the MPC problem for the nonlinear system. Several examples are provided to illustrate the effectiveness of our framework. © 2025, CC BY-NC-ND.

关键词： mixed-integer linear programming

Bias Detection via Maximum Subgroup Discrepancy

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arXiv 2025年

作者： Němeček, Jiří Kozdoba, Mark Kryvoviaz, Illia Pevný, Tomáš Mareček, Jakub

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study a distance of a given dataset, viewed as a distribution, to a given ground-truth reference dataset. However, classical metrics, such as the Total Variation and the Wasserstein distances, are known to have high sample complexities and, therefore, may fail to provide meaningful distinction in many practical scenarios. In this paper, we propose a new notion of distance, the Maximum Subgroup Discrepancy (MSD). In this metric, two distributions are close if, roughly, discrepancies are low for all feature subgroups. While the number of subgroups may be exponential, we show that the sample complexity is linear in the number of features, thus making it feasible for practical applications. Moreover, we provide a practical algorithm for the evaluation of the distance, based on mixed-integer optimization (MIO). We also note that the proposed distance is easily interpretable, thus providing clearer paths to fixing the biases once they have been identified. It also provides guarantees for all subgroups. Finally, we empirically evaluate, compare with other metrics, and demonstrate the above properties of MSD on real-world datasets. © 2025, CC BY.

关键词： mixed-integer linear programming