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Evaluating mixed-integer programming models over multiple right-hand sides

OPERATIONS RESEARCH LETTERS 2023年第4期51卷 414-420页

作者： Alfant, Rachael M. Ajayi, Temitayo Schaefer, Andrew J. Rice Univ Dept Computat Appl Math & Operat Res Houston TX 77005 USA Nat Source Improved Plants Ithaca NY 14850 USA

A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is not known exactly;however, there is no consensus metric for evaluating a MIP model when considering multiple right-hand sides. In this paper, we provide model formulations for the expectation and extrema of absolute and relative MIP gap functions over finite discrete sets. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： mixed-integer programming Superadditive duality Value function

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A mixed-integer programming approach to strategic planning of chemical centres: A case study in the UK

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COMPUTERS & CHEMICAL ENGINEERING 2011年第8期35卷 1359-1373页

作者： Liu, Pei Whitaker, Alan Pistikopoulos, Efstratios N. Li, Zheng Univ London Imperial Coll Sci Technol & Med CPSE Dept Chem Engn London SW7 2AZ England Tsinghua Univ State Key Lab Power Syst Dept Thermal Engn Beijing 100084 Peoples R China

Chemical centres provide great potential to tackle the worldwide energy and environmental issues via integrated chemical synthesis and heat and power generation. However, planning of chemical centres still involves many formidable challenges, including locating production sites, arrangement of transportation, and selection of appropriate technologies. These problems become further complicated when considering the geographic situation of a region under study. In this paper, we propose a multi-period mixed-integer programming (MIP) approach to the optimal planning of chemical centres. The planning horizon is firstly divided into several time intervals, and the planning region is represented by a grid. Then a superstructure representation is developed to capture all available logistic and technical options. Based on the superstructure representation, an MIP problem is developed, and by solving it an optimal planning strategy can be obtained. A real-life case study for the UK follows, where the UK is divided into a grid of 34 cells. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Strategic planning Process integration Chemical synthesis Emissions reduction Superstructure mixed-integer programming

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Electric vehicle routing optimization for sustainable kitchen waste reverse logistics network using robust mixed-integer programming ☆

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2024年 128卷

作者： Shi, Yi Vanhaverbeke, Lieselot Xu, Jiuping Sichuan Univ Business Sch Chengdu 610064 Peoples R China Vrije Univ Brussel Dept Business Technol & Operat Res Grp MOBI Pl Laan 2 B-1050 Brussels Belgium

This paper proposes an innovative reverse logistics network (RLN) to manage kitchen waste (KW) transportation and resource treatment. The network employs battery electric (BE) trucks for transportation, and the challenge lies in determining the distribution of various KW treatment centers and establishing the optimal transportation routes for KW and its residues. The proposed RLN is self-sufficient, because the electricity produced by the centers within the network is adequate to power the BE trucks. We develop a matched mixedinteger programming model to optimize the entire process, with the goal of minimizing the total potential economic and environmental costs. Notably, the model considers comprehensive cost components and employs a carbon trading policy to translate carbon emissions into carbon costs. We use robust optimization to generate optimal solutions that remain viable even under the worst -case scenario concerning uncertain parameters. We then test the feasibility of the proposed methodology in a real -world case. We conduct specific scenario analyses on capacity and mode of trucks to offer practical KW transportation strategies and recommendations. We found that the larger the capacity of a BE truck, the greater the economic and environmental benefits for the KW RLN. The self-sufficient KW RLN using BE trucks proved to be the least costly, followed by the ordinary KW RLN using BE trucks, while the KW RLN using diesel trucks was the most expensive and environmentally detrimental.

关键词： Kitchen waste mixed-integer programming Reverse logistics network Transportation capacity Transportation mode Vehicle routing problem

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A nonlinear mixed-integer programming approach for variable selection in linear regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第11期52卷 5434-5445页

作者： Roozbeh, Mahdi Babaie-Kafaki, Saman Aminifard, Zohre Semnan Univ Fac Math Stat & Comp Sci POB 35195-363 Semnan Iran

Modern statistical studies often encounter regression models with high dimensions in which the number of features p is greater than the sample size n. Although the theory of linear models is well-established for the traditional assumption p < n, making valid statistical inference in high dimensional cases is a considerable challenge. With recent advances in technologies, the problem appears in many biological, medical, social, industrial, and economic studies. As known, the LASSO method is a popular technique for variable selection/estimation in high dimensional sparse linear models. Here, we show that the prediction performance of the LASSO method can be improved by eliminating the structured noises through a mixed-integer programming approach. As a result of our analysis, a modified variable selection/estimation scheme is proposed for a high dimensional regression model which can be considered as an alternative of the LASSO method. Some numerical experiments are made on the classical riboflavin production and some simulated data sets to shed light on the practical performance of the suggested method.

关键词： Linear regression model LASSO method mixed-integer programming Sparsity Variable selection

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Using mixed-integer programming to solve power grid blackout problems

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DISCRETE OPTIMIZATION 2007年第1期4卷 115-141页

作者： Bienstock, Daniel Mattia, Sara Columbia Univ Dept IEOR New York NY 10027 USA Univ Roma La Sapienza DIS Rome Italy

We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks Subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. (c) 2006 Elsevier B.V. All rights reserved.

关键词： power flows mixed-integer programming blackouts

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Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年第3期41卷 1501-1534页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

关键词： Data-driven computing mixed-integer programming Global optimization Order statistics Reliability with unknown distribution

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A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期313卷 602-615页

作者： Ketkov, Sergey S. HSE Univ Lab Algorithms & Technol Networks Anal Rodionova St 136 Nizhnii Novgorod 603093 Russia Univ Zurich Dept Business Adm CH-8032 Zurich Switzerland

This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.

关键词： Uncertainty modeling Distributionally robust optimization mixed-integer programming Wasserstein metric Incomplete data

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A new mixed-integer programming model for spatial forest planning

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CANADIAN JOURNAL OF FOREST RESEARCH 2019年第12期49卷 1493-1503页

作者： Gharbi, Chourouk Ronnqvist, Mikael Beaudoin, Daniel Carle, Marc-Andre Univ Laval Fac Sci & Genie Dept Genie Mecan Quebec City PQ G1V 0A6 Canada Univ Laval Fac Foresterie Geog & Geomat Dept Sci Bois & Foret Quebec City PQ G1V 0A6 Canada Univ TELUQ Ecole Sci Adm Quebec City PQ G1K 9H6 Canada

The unit restriction model and the area restriction model are the two main approaches to dealing with adjacency in forest harvest planning. In this paper, we present a new mixed-integer programming (MIP) formulation that can be classified as both a unit restriction approach and an area restriction approach. Weneed to generate a feasible cluster to formulate the model. However, unlike other approaches, there is no need to generate specific model constraints representing computationally burdensome clusters for large cases. We describe and analyze our approach by comparing it with the most efficient approaches presented in the literature. Comparisons are made from modeling and computational points of view. Results showed that the proposed model was competitive with regard to modeling complexity and size of formulation. Furthermore, it is easy to implement in standard modeling software.

关键词： mixed-integer programming forest management adjacency area restriction model unit restriction model

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Power Reduction in FM Networks by mixed-integer programming: A Case Study

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IEEE ACCESS 2024年 12卷 23725-23732页

作者： Avella, Pasquale Nobili, Paolo Sassano, Antonio Univ Sannio Dipartimento Ingn I-82100 Benevento Italy Univ Tuscia DAFNE I-01100 Viterbo Italy Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gestionale DI I-00185 Rome Italy

The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by uniformly cutting the radiated power at every transmitter can potentially impair the quality of service. A careful evaluation and optimization study are in order. In this paper, by analyzing the Italian frequency modulation analog broadcasting service, we show that it is indeed possible to significantly reduce the energy consumption of the broadcasters without sacrificing the quality of the service, rather, even getting improvements.

关键词： Climate change Energy consumption mixed integer linear programming Power system management Energy conservation Optimization methods Power system reliability Power system measurements Human factors Quality of service Broadcasting Broadcast networks FM power reduction mixed-integer programming

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Cloud manufacturing service selection optimization and scheduling with transportation considerations: mixed-integer programming models

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2018年第1-4期95卷 43-70页

作者： Akbaripour, Hossein Houshmand, Mahmoud van Woensel, Tom Mutlu, Nevin Sharif Univ Technol Dept Ind Engn Tehran Iran Eindhoven Univ Technol Sch Ind Engn Eindhoven Netherlands

Cloud manufacturing is an emerging service-oriented manufacturing paradigm that integrates and manages distributed manufacturing resources through which complex manufacturing demands with a high degree of customization can be fulfilled. The process of service selection optimization and scheduling (SSOS) is an important issue for practical implementation of cloud manufacturing. In this paper, we propose new mixed-integer programming (MIP) models for solving the SSOS problem with basic composition structures (i.e., sequential, parallel, loop, and selective). Through incorporation of the proposed MIP models, the SSOS with a mixed composition structure can be tackled. As transportation is indispensable in cloud manufacturing environment, the models also optimize routing decisions within a given hybrid hub-and-spoke transportation network in which the central decision is to optimally determine whether a shipment between a pair of distributed manufacturing resources is routed directly or using hub facilities. Unlike the majority of previous research undertaken in cloud manufacturing, it is assumed that manufacturing resources are not continuously available for processing but the start time and end time of their occupancy interval are known in advance. The performance of the proposed models is evaluated through solving different scenarios in the SSOS. Moreover, in order to examine the robustness of the results, a series of sensitivity analysis are conducted on key parameters. The outcomes of this study demonstrate that the consideration of transportation and availability not only can change the results of the SSOS significantly, but also is necessary for obtaining more realistic solutions. The results also show that routing within a hybrid hub-and-spoke transportation network, compared with a pure hub-and-spoke network or a pure direct network, leads to more flexibility and has advantage of cost and time saving. The level of saving depends on the value of discount factor f

关键词： Cloud manufacturing Service selection and scheduling Service occupancy Hub-and-spoke transportation network mixed-integer programming

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