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arXiv 2021年

作者： Hertrich, Christoph Basu, Amitabh Di Summa, Marco Skutella, Martin London School of Economics and Political Science London United Kingdom Johns Hopkins University Baltimore United States Università degli Studi di Padova Padua Italy Technische Universität Berlin Berlin Germany

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical geometry, we provide a mathematical counterbalance to the universal approximation theorems which suggest that a single hidden layer is sufficient for learning any function. In particular, we investigate whether the class of exactly representable functions strictly increases by adding more layers (with no restrictions on size). As a by-product of our investigations, we settle an old conjecture about piecewise linear functions by Wang and Sun [74] in the affirmative. We also present upper bounds on the sizes of neural networks required to represent functions with logarithmic depth. Copyright © 2021, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Improving a Production-Inventory Model in the Multi-Machine, Hybrid MTO-MTS Chemical Industry

Improving a Production-Inventory Model in the Multi-Machine,...

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作者： T. M. P. Vranken Eindhoven University of Technology

学位级别：硕士

In this research, a redesign is proposed for a production-inventory model in the hybrid MTO-MTS chemical industry. The project, conducted at SABIC, converges from a higher decision making level to a lower decision making level, i. e. from the tactical level to the operational level. First, a general MTO- MTS decision framework is adapted from literature to fit to the problem context at hand. Thereafter, inventory control systems are evaluated and an applicable design for the context is presented. At last, a production planning model integrating a block planning approach is presented for a non-identical parallel machine production environment. The proposed MILP formulation extents current literature on block planning by introducing different types, timings and lengths of blocks, allowing for backorders, and introducing service level constraints. In a case study, the products are partitioned based on the proposed MTO-MTS decision framework and inventory policy parameters are determined for MTS items. A simulation study validated that the new design generated significant cost reductions and increased performance on service levels. Moreover, the planning model is able to decrease the production costs significantly by allocating production orders cost optimal to the different machines.

关键词： make-to-order make-to-stock MTO-MTS partitioning sequence-dependent setups block planning production planning mixed-integer linear programming non-identical parallel machines

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A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

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Frontiers of Chemical Science and Engineering 2019年第4期13卷 784-802页

作者： Nikolaos Rakovitis Nan Zhang Jie Li Liping Zhang Centre for Process Integration School of Chemical Engineering and Analytical ScienceThe University of ManchesterManchesterM139PLUK Department of Industrial Engineering School of Machinery and AutomationWuhan University of Science and TechnologyWuhan 430081China

The increasing demand of goods,the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing *** scheduling of their processes can lead facilities towards this *** a great number of mathematical models have been developed for such scheduling,they may still lead to large model sizes and computational *** this work,we develop two novel mathematical models using the unit-specific eventbased modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event *** computational results demonstrate that both proposed mathematical models reduce the number of event points *** proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

关键词： scheduling multipurpose batch processes simultaneous transfer mixed-integer linear programming

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A two-stage flow-shop scheme for the multi-satellite observation and data downlink scheduling problem considering weather uncertainties

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2019年第Aug.期188卷 263-275页

作者： Xiao, Yiyong Zhang, Siyue Yang, Pei You, Meng Huang, Jiaoying Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China

An Earth observation satellite (EOS) is a sort of low earth orbit (LEO) satellite that is equipped with high resolution cameras for observing various types of target objects scattered across the surface of the Earth. The available time windows of multiple EOSs for observing a given target object and for downloading the acquired image/video data from satellites to ground receiver stations are scarce resources that should to be utilized efficiently. This problem is hereby named as the multi-satellite observation and data-downlink scheduling problem (MSODSP). We developed a two-stage flow shop scheme for the MSODSP in order to optimize the observation scheduling (at stage 1) and data-downlink scheduling (at stage 2) concurrently and get truly optimized results. A mixed-integer linear programming (MILP) model is developed for the MSODSP with three objective functions. The effects of weather uncertainties on the tasks' success are considered in the MILP model, which allow us to conduct a reliability-maximized task arrangement of EOSs. Computational experiments were conducted on the simulated data of a real LEO satellite to verify the proposed MILP model. The results showed that it was able to solve real-world instances of the MSODSP for up to 20 tasks over 8 days.

关键词： Satellite earth observation Scheduling mixed-integer linear programming Optimization

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A bi-objective model for design and analysis of sustainable intermodal transportation systems: a case study of Turkey

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2019年第19期57卷 6146-6161页

作者： Resat, Hamdi Giray Turkay, Metin Izmir Univ Econ Dept Ind Engn TR-35330 Izmir Turkey Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey

This paper presents a mixed-integer linear optimisation model to analyse the intermodal transportation systems in the Turkish transportation industry. The solution approach includes mathematical modelling, data analysis from real-life cases and solving the resulting mathematical programming problem to minimise total transportation cost and carbon dioxide emissions by using two different exact solution methods in order to find the optimal solutions. The novel approach of this paper generates Pareto solutions quickly and allows the decision makers to identify sustainable solutions by using a newly developed solution methodology for bi-objective mixed-integer linear problems in real-life cases.

关键词： Logistics sustainability mixed-integer linear programming bi-objective optimisation

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Optimal design and dispatch of a hybrid microgrid system capturing battery fade

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OPTIMIZATION AND ENGINEERING 2019年第1期20卷 179-213页

作者： Goodall, Gavin Scioletti, Michael Zolan, Alex Suthar, Bharatkumar Newman, Alexandra Kohl, Paul Colorado Sch Mines Dept Mech Engn Golden CO 80401 USA Univ Texas Austin Dept Mech Engn Austin TX 78712 USA Georgia Inst Technol Sch Chem & Biomol Engn Atlanta GA 30332 USA

Microgrids provide power to remote communities and at operational sites that are not connected to a grid. We consider such a microgrid that consists of batteries, photovoltaics, and diesel generators, and optimize the components it comprises and a corresponding dispatch strategy at hourly fidelity so as to minimize procurement, operations and maintenance, and fuel costs. The system is governed by constraints such as meeting demand and adhering to component interoperability and capability. Our contribution lies in the introduction to this optimization model of a set of constraints that incorporates capacity fade of a battery and temperature effects. We show, using data from a forward operating base and solving the corresponding instances for a time horizon of 8760h, that higher temperatures decrease resistance, leading to better round-trip energy efficiency, but at the same time increase capacity fade of the battery, resulting in a higher overall operating cost. In some cases, the procurement strategy is robust to the fade of the battery, but fade can influence battery state of charge and power output as the available battery capacity degrades over time and with use.

关键词： Design optimization Dispatch optimization Microgrids Batteries mixed-integer linear programming Systems analysis

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Application of critical path method to stochastic processes with historical operation data

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2019年 149卷 195-208页

作者： Takakura, Yuya Yajima, Tomoyuki Kawajiri, Yoshiaki Hashizume, Susumu Nagoya Univ Dept Mat Proc Engn Nagoya Aichi Japan Georgia Inst Technol Dept Chem & Biomol Engn Atlanta GA 30332 USA Nara Coll Natl Inst Technol Dept Control Engn Nara Japan

The CPM (Critical Path Method) is a network-based approach for project management. This method identifies the longest path, which allows us to find the critical path that must be shortened so that the completion time of the whole project can be shortened. However, considering uncertainty in CPM is not straightforward. In this paper, we consider an optimization problem for stochastic CPM problems, where task durations are expressed as discrete histograms obtained from historical operation data, that maximizes the probability that all tasks are completed within a given completion time by improving the task durations on the critical path. We propose two reformulations of the problem as a mixed-integer linear programming problem: one based on tasks, and the other based on paths. In addition, we propose an iterative method to solve the problem efficiently by reducing the number of binary variables. Finally, we demonstrate efficiency of our proposed methods in some case studies. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Critical path method Project scheduling Time-cost trade off problem Uncertain durations mixed-integer linear programming Historical operation data

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A hybrid time MILP model for the pump scheduling of multi-product pipelines based on the rigorous description of the pipeline hydraulic loss changes

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COMPUTERS & CHEMICAL ENGINEERING 2019年 121卷 174-199页

作者： Zhou, Xingyuan Zhang, Haoran Qiu, Rui Liang, Yongtu Wu, Guangming Xiang, Chengcheng Yan, Xiaohan China Univ Petr Natl Engn Lab Pipeline Safety Beijing Key Lab Urban Oil & Gas Distribut Technol Fuxue Rd 18 Beijing 102249 Peoples R China Univ Tokyo Ctr Spatial Informat Sci 5-1-5 Kashiwanoha Kashiwa Chiba 2778568 Japan Univ Southern Calif Viterbi Sch Engn 3650 McClintockAve Los Angeles CA 90089 USA Res Inst China Natl Offshore Oil Corp Sun Palace South St 6 Beijing 100027 Peoples R China

As the primary means of transporting refined products, multi-product pipelines play a significant role in ensuring downstream energy supply. The pump scheduling optimization of multi-product pipeline can significantly lower the energy consumption of the pipeline. With the input parameters of pipeline flowrates and batch interface locations, which are determined by a specific detailed schedule, this paper first proposes an innovative method for a rigorous description of pipeline hydraulic loss changes during the multi-batch sequential transportation process. Based on the hybrid time representation, the scheduling horizon is divided into two levels of time windows and a mixed-integer linear programming (MILP) model for the pump scheduling of multi-product pipelines is established according to the proposed method. Various technical and operational constraints are considered. Finally, the established model is successfully applied to a real-world multi-product pipeline, with three operation modes, in China. The superiority, accuracy, and applicability of this model are validated in detail through comparison with a previous model. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Pump scheduling Multi-product pipeline mixed-integer linear programming Hydraulic loss Time continuity

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Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2019年 127卷 237-278页

作者： Zhang, Yongxiang D'Ariano, Andrea He, Bisheng Peng, Qiyuan Southwest Jiaotong Univ Sch Transportat & Logist POB 610031 Chengdu Sichuan Peoples R China Roma Tre Univ Dept Engn Via Vasca Navale 79 I-00146 Rome Italy

This paper addresses the problem of improving the integration between passenger timetabling and track maintenance scheduling. We propose a microscopic optimization model and an iterative algorithm for solving this problem efficiently. Block sections are considered as the basic microscopic elements for train movements in a railway network. A mixed-integer linear programming formulation is proposed for the integrated optimization problem in which train timing, sequencing and routing are the timetabling variables, while timing and sequencing of maintenance tasks are the track maintenance variables. The objective function is to minimize the total train travel time and the maintenance tardiness cost. The constraints proposed in this work address the practical specifications of the INFORMS RAS 2016 Problem Solving Competition (2016 PSC). In this context, the main decision variables are the entrance and exit times of the trains on each block section plus the start and end times of each maintenance task. Since the integrated optimization problem is strongly NP-hard, an iterative algorithm is proposed to compute near-optimal solutions in a short computation time. The algorithm is based on a decomposition of the overall problem into sub-problems related to train scheduling and/or routing with or without track maintenance task scheduling. The connecting information between the two sub-problems concerns the selected train routes plus the start and end times of the maintenance tasks. Computational experiments are performed on a set of realistic railway instances, which were introduced during the 2016 PSC. The iterative algorithm outperforms a standard MILP solver and the first-place team of this competition in terms of both solution quality and time to deliver the new best-known solutions. The scalability of the iterative algorithm is investigated when increasing the number of trains and track maintenance tasks. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Railway scheduling Infrastructure maintenance Integrated optimization mixed-integer linear programming

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Flexibility Scheduling for Large Customers

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IEEE TRANSACTIONS ON SMART GRID 2019年第1期10卷 371-379页

作者： Angizeh, Farhad Parvania, Masood Fotuhi-Firuzabad, Mahmud Rajabi-Ghahnavieh, Abbas Univ Utah Dept Elect & Comp Engn Salt Lake City UT 84112 USA Sharif Univ Technol Ctr Excellence Power Syst Control & Management Elect Engn Dept Tehran 11369363 Iran Sharif Univ Technol Dept Energy Engn Tehran 11369363 Iran

Large customers are considered as major flexible electricity demands which can reduce their electricity casts by choosing appropriate strategies to participate in demand response programs. However, practical methods to aid the large customers for handling the complex decision making process for participating in the programs have remained scarce. This paper proposes a novel decision-making tool for enabling large customers to determine how they adjust their electricity usage from normal consumption patterns in expectation of gaining profit in response to changes in prices and incentive payments offered by the system operators. The proposed model, formulated as a mixed-integer linear programming problem, simultaneously determines the optimal integration of the flexibility options including flexible load rescheduling and utilizing onsite generation and energy storage systems, along with energy procurement from the grid that allows the large customers to optimize their energy portfolio from different sources including bilateral contracts and the market. The characteristics of the proposed integrated flexibility scheduling and energy procurement model and its benefits are investigated through several case studies conducted on a test large industrial load.

关键词： Demand response flexible load energy storage systems onsite generation energy procurement large customers mixed-integer linear programming

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