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arXiv 2024年

作者： Fina, Luke Petersen, Christopher Hale, Matthew Department of Mechanical and Aerospace Engineering University of Florida GainesvilleFL United States School of Electrical and Computer Engineering Georgia Institute of Technology AtlantaGA United States

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. To solve a MILP, we relax it with a linear program approximation. We first show that if the linear program relaxation satisfies Slater’s condition, then relaxing the problem, solving it, and rounding the relaxed solution produces a point that is guaranteed to satisfy the constraints of the original MILP. Next, we form a Lagrangian saddle point problem that is equivalent to the linear program relaxation, and then we regularize the Lagrangian in both the primal and dual spaces. We then develop a parallelized algorithm to compute saddle points of the regularized Lagrangian, and we show that it is tolerant to asynchrony in the computations and communications of primal and dual variables. Suboptimality bounds and convergence rates are presented for convergence to a saddle point. Simulation results illustrate these theoretical developments in practice, and show that relaxation and regularization combined typically have only a mild impact on the suboptimality of the solution obtained. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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A Study of TMA Aircraft Conflict-Free Routing and Operation: With mixed integer linear programming, Multi-Agent Path Finding, and Metaheuristic-Based Neighborhood Search

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2024年第10期25卷 13976-13990页

作者： Zhang, Yi Zhang, Sheng Zhang, Yicheng Yin, Yifang ASTAR Inst Infocomm Res I2R Singapore 138632 Singapore

In this paper, we proposed a conflict-free routing strategy combined with scheduling for Terminal Manoeuvring Area (TMA) multi-aircraft to guarantee a safe separation. By incorporating Standard Terminal Arrival Routes (STARs) as route constraints, a mixed-logic model is designed to maximize the runway throughput while ensuring minimum separation between aircraft and avoiding overtaking on each STARs segment. Control techniques such as speed recommendation and holding operations are employed to the model to address potential conflicts. Three different algorithms are developed to solve the model: branch and bound with mixed-integer linear programming, multi-agent pathfinding with constraint programming, and meta-heuristics with evolutionary neighborhood search. These algorithms are tested on multiple cases of varying scales. Finally, we demonstrate the advantages of the proposed three algorithms by simulating realistic scenarios and comparing the results with Singapore ADS-B (Automatic dependent Surveillance-Broadcast) historical dataset. In one hour testing, results show that our method could reduce the last aircraft landing time nearly 10 minutes and save more than 80 minutes for total flight travel times for all aircraft, as well as non-vectoring flight trajectories, which indicates its potential to be used as an auxiliary decision-making tool for Air Traffic Controllers (ATCOs).

关键词： Aircraft Atmospheric modeling Routing Stars Sequential analysis Air traffic control Safety Air traffic management trajectory based operation mixed-integer linear programming constraint programming meta-heuristics harmony search priority-based multiagent path finding

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A mixed integer linear programming approach for the design of chemical process families

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COMPUTERS & CHEMICAL ENGINEERING 2024年 183卷

作者： Stinchfield, Georgia Morgan, Joshua C. Naik, Sakshi Biegler, Lorenz T. Eslick, John C. Jacobson, Clas Miller, David C. Siirola, John D. Zamarripa, Miguel Zhang, Chen Zhang, Qi Laird, Carl D. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Natl Energy Technol Lab NETL Pittsburgh PA 15236 USA NETL Support Contractor Pittsburgh PA 15236 USA Carrier Global Corp Palm Beach Gardens FL 33418 USA Sandia Natl Labs Albuquerque NM 87123 USA Univ Minnesota Dept Chem Engn & Mat Sci Minneapolis MN 55455 USA

The need for rapid and widespread deployment of new technologies to address climate change goals (e.g., deep, economy -wide decarbonization) presents new opportunities for advancing modular design strategies. Conventional engineering approaches focus on unique designs for each installation, while missing opportunities for manufacturing standardization. Extending insights from the automotive industry, we optimize a platform of common unit module designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed -integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus (R) as part of CCSI2.

关键词： Process Family Design Manufacturing Optimization mixed-integer linear programming Carbon capture

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A mixed-integer linear programming model for sustainable blood supply chain problems with shelf-life time and multiple blood types

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Decision Analytics Journal 2023年 8卷

作者： Mansur, Agus Handayani, Dwi Iryaning Wangsa, Ivan Darma Utama, Dana Marsetiya Jauhari, Wakhid Ahmad Department of Industrial Engineering Faculty of Industrial Technology Universitas Islam Indonesia Yogyakarta 55584 Indonesia Department of Industrial Engineering Universitas Panca Marga Jl. Raya Dringu Krajan Mayangan Probolinggo Indonesia Department of Industrial and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya Kampus ITS Sukolilo 60111 Indonesia Department of Industrial Engineering University of Muhammadiyah Malang Malang Indonesia Department of Industrial Engineering Universitas Sebelas Maret Jl. Ir Sutami 36 A Surakarta 57126 Indonesia

The blood supply chain (BSC) is a complex system with optimization challenges, whose activities impact carbon emissions and the environment, especially with regard to the disposal of expired blood bag waste. This study proposes a new mixed-integer linear programming (MILP) model that considers multiple echelons, multiple blood types, transportation and production emissions, and blood bag shelf life to maximize profit in the blood supply chain system. The model is applied to a real-world case study. The research results confirmed that the model could mitigate the BSC challenges. We also conducted sensitivity analysis of patient demand parameters, blood production capacity, selling price, and shelf life to investigate the impact of the key factors affecting the total profit, costs, carbon emissions, and number of obsolete products. © 2023 The Author(s)

关键词： Blood supply chain Blood type Carbon emission mixed-integer linear programming Shelf-life time Sustainability

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A mixed-integer linear programming model for multiechelon and multimodal supply chain system considering carbon emission

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COGENT ENGINEERING 2022年第1期9卷 Article: 2044589页

作者： Ardliana, Thina Pujawan, I. Nyoman Siswanto, Nurhadi Shipbldg Inst Polthechn Dept Design & Manufacture Surabaya Indonesia Sepuluh Nopember Inst Technol Dept Ind Engn Surabaya Indonesia

Considering carbon emissions when making supply chain decisions has been an essential contributor for keeping this world more sustainable. This paper presents a mixed-integer linear programming (MILP) model to optimize production and transportation decision where the transportation activities involve a multimodal combination. The proposed mathematical model was aimed at minimizing the total costs incurred from supply chain activities as well as the emissions generated. Carbon cap is used to ensure that the emissions produced in the whole activities do not exceed the allowable limit. In this research, we address a multi-product, multi-plant, multi-departure, and arrival stations where multiple customers are to be served for multiple periods. The numerical tests show that the demand, carbon tax, and distance significantly affected the total emissions and the total costs. Interestingly, we observed that the decisions are much more affected by the logistical costs rather than the emission costs. The model presented in this paper can assist the decision makers to make production, delivery, and inventory decisions when multi-modal transportation is involved.

关键词： Supply chain system multimodal mixed-integer linear programming carbon emission

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A mixed-integer linear programming approach for collateral management

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Decision Analytics Journal 2024年 10卷

作者： Goblet, Jordan Willame, Fabien Grauls, Jan Euroclear Koning Albert II Laan 1 Brussels 1210 Belgium

Collateral management involves the efficient monitoring and allocation of assets to mitigate credit risk in financial transactions and is crucial for institutions such as commercial banks, investments banks, and central counterparties. It helps to ensure financial stability and compliance with regulatory requirements. This study is centered on a fundamental objective of collateral management, namely to collateralize as much as possible a set of transactions given a limited asset portfolio. In practice, an allocation is dynamic, necessitating periodic adjustments due to fluctuations over time in the asset pool, the transactions set, and asset value. Consequently, the objective is not merely the identification of an optimal allocation from zero but the optimization of an obsolete allocation in response to these fluctuations. The size and complexity of real-world problems often preclude direct resolution through conventional MILP solvers. In addition, each collateral adjustment movement incurs associated costs. In this research, a two-step method based on linear and mixed-integer linear programming formulations with ℓ₁ penalties is devised, with the principal aim of minimizing under-allocation while simultaneously controlling the number of adjustment movements required. The method is tested on 20 real-world collateral givers and invariably reaches a good trade-off between solution quality, computational time, and the number of movements. © 2024 The Authors

关键词： Collateral management Collateral optimization linear programming mixed-integer linear programming ℓ1 regularization

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A mixed integer linear programming approach for a new form of facility layout problem

A mixed integer linear programming approach for a new form o...

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2nd International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Zhang, Yipei Che, Ada Northwestern Polytech Univ Sch Management Xian 710072 Peoples R China

ISBN: (纸本)9781479967735

This paper aims to study a new form of facility layout problem, in which the building has already been constructed and the specific room layout inside has been determined. Unlike the traditional facility layout problem, what we take into account is how to assign a certain number of rooms to a given number of departments with the purpose of maximizing the utilization rate of the rooms. This is equivalent to minimizing the total difference value between the extra area of different departments after satisfying their required area, thus reducing the space waste. To solve this special combinatorial optimization problem, we develop a mixed-integer linear programming (MILP) model. The model is solved using commercial software CPLEX12.6. Computational results on several randomly generated instances demonstrate the effectiveness of the proposed approach.

关键词： Facility layout Combinatorial optimization problem mixed-integer linear programming

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mixed integer linear programming for new trends in wind farm cable routing

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Electronic Notes in Discrete Mathematics 2018年 64卷 115-124页

作者： Fischetti, Martina Pisinger, David Vattenfall BA Wind Technical University of Denmark Operations Research DTU Management Produktionstorvet 426 B Lyngby DK-2800 Kgs. Denmark Technical University of Denmark Operations Research DTU Management Produktionstorvet 426 B Lyngby DK-2800 Kgs. Denmark

The efficient production of green energy plays an import role in modern economies. In this paper we address the optimization of cable connections between turbines in an offshore wind park. Different versions of this problem have been studied recently. In a previous joint project with Vattenfall BA Wind (a global leader in energy production) we have studied and modeled the main constraints arising in practical cases. Building on that model, in the present paper we address new features that have been recently proposed by Vattenfall's experts. Turbines are becoming still more customized, therefore it is important to be able to evaluate the impact of new technologies with a flexible optimization tool. We here show how some new features can effectively be modeled and solved using a mixed-integer linear programming paradigm. Computational results on a real-world case are briefly presented. © 2018 Elsevier B.V.

关键词： computational analysis mixed-integer linear programming Network models wind farm optimization

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PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via mixed integer linear programming

PAAMP: Polytopic Action-Set And Motion Planning for Long Hor...

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2024 International Conference on Intelligent Robots and Systems

作者： Jaitly, Akshay Farzan, Siavash Worcester Polytech Inst Robot Engn Dept Worcester MA 01609 USA Calif Polytech State Univ San Luis Obispo Elect Engn Dept San Luis Obispo CA 93407 USA

ISBN: (纸本)9798350377712;9798350377705

Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging non-convex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a linear Program. This reformulation enables us to address motion planning as a mixed integer linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

关键词： mixed-integer linear programming

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Stochastic Optimization Model for Energy Management of a Hybrid Microgrid using mixed integer linear programming 21st

Stochastic Optimization Model for Energy Management of a Hyb...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Franke, G. Schneider, M. Weitzel, T. Rinderknecht, S. Tech Univ Darmstadt Inst Mechatron Syst Mech Engn Darmstadt Germany Tech Univ Darmstadt Inst Prod & Supply Chain Management Darmstadt Germany

In the context of increasing decentralization of the energy supply system, the concepts of microgrids are well suited to realise a reduction of CO2-emissions and create opportunities for new business models. For this the operation of the microgrid has a significant impact. In real systems, however, the consideration of uncertainties in generation and consumption data is essential for the operating strategy. Therefore, in this paper we propose an optimization model based on mixed-integer linear programming for the hybrid microgrid of a residential building district and include stochastic optimization in a computationally efficient way. For this, a two-stage approach is used. In a first step, we do a day-ahead optimization to determine a schedule for the combined heat and power plant and the power exchanged with the grid. In a second step, based on the results of the day-ahead optimization and the observed values for the uncertain parameters the intraday optimization is carried out. Using a numerical example, we demonstrate the advantages of this stochastic optimization over conventional optimization based on point forecasts. The data used originates from a real project district in Darmstadt, Germany. Copyright (C) 2020 The Authors.

关键词： Residential micro grid battery energy storage system optimal operating strategy mixed-integer linear programming stochastic optimization

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