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Integrated fleet assignment and scheduling for environmentally

TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2022年第0期138卷 103567-103567页

作者： Justin, Cedric Y. Payan, Alexia P. Mavris, Dimitri N. Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA

Regional air mobility refers to the transportation of passengers aboard small aircraft over short distances. These operations are challenging due to low passenger volumes, competing transportation modes, and high operating costs. Nevertheless, the recent convergence of new technologies for electric propulsion and autonomy brings the promise of step-changes in both operating efficiency and sustainability. The next challenge is to define concepts of operations that best use these advanced aircraft. We develop a modeling and optimization environment to address this challenge by first estimating the passenger demand for regional air mobility, and then by concurrently optimizing the fleet assignment and scheduling of these operations. This helps identify the optimum fleet composition and the network of routes that best serve this demand. The contribution of this research is the formulation of the optimization as a half leg half-itinerary mixed-integer linear program using a hierarchical multi-objective approach that provides insights about trade-offs between profitability and emissions. We demonstrate the ability of this environment to solve large fleet assignment and scheduling problems to near optimality by applying it to the United States Northeast Corridor using a fleet of electric and hybrid-electric regional aircraft. Results highlight that the transition to an electrified fleet allows serving twice the number of communities currently served, while reducing the carbon emissions per passenger by fifty percent. With improving battery specific energy density, many more untapped markets can be served profitably and sustainably, and many smaller communities can get connected to the rest of the National Airspace System.

关键词： Scheduling Fleet assignment Demand modeling Sustainability Regional air mobility mixed-integer linear programming Electric aircraft

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A Comparison of Two mixed-integer linear Programs for Piecewise linear Function Fitting

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INFORMS JOURNAL ON COMPUTING 2022年第2期34卷 1042-1047页

作者： Warwicker, John Alasdair Rebennack, Steffen Karlsruhe Inst Technol Inst Operat Res Stochast Optimizat D-76185 Karlsruhe Raden Wurttembe Germany

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many other fields. To find an optimal PWL function, the positioning of the breakpoints connecting adjacent linear segments must not be constrained and should be allowed to be placed freely. Although the univariate PWL fitting problem has often been approached from a global optimisation perspective, recently, two mixed-integer linear programming approaches have been presented that solve for optimal PWL functions. In this paper, we compare the two approaches: the first was presented by Rebennack and Krasko [Rebennack S, Krasko V (2020) Piecewise linear function fitting via mixed-integer linear programming. INFORMS J. Comput. 32(2):507-530] and the second by Kong and Maravelias [Kong L, Maravelias CT (2020) On the derivation of continuous piecewise linear approximating functions. INFORMS J. Comput. 32(3):531-5461 Both formulations are similar in that they use binary variables and logical implications modelled by big-M constructs to ensure the continuity of the PWL function, yet the former model uses fewer binary variables. We present experimental results comparing the time taken to find optimal PWL functions with differing numbers of breakpoints across 10 data sets for three different objective functions. Although neither of the two formulations is superior on all data sets, the presented computational results suggest that the formulation presented by Rebennack and Krasko is faster. This might be explained by the fact that it contains fewer complicating binary variables and sparser constraints. Summary of Contribution: This paper presents a comparison of the mixed-integer linear programming models presented in two recent studies published in the INFORMS Journal on Computing. Because of the similarity of the formulations of the two models, it is not clear which one is preferable. We present a detailed comparison of the two

关键词： piecewise linear function mixed-integer linear programming function fitting

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A new technology implementation via mathematical modeling for the sequence-dependent setup times of industrial problems

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年第PartB期172卷

作者： de Freitas, Miguel Gonsalves Fuchigami, Helio Yochihiro Fed Univ Sao Carlos UFSCar Prod Engn Dept Sao Carlos SP Brazil Fed Univ Goias UFG Fac Sci & Technol FCT Aparecida De Goiania GO Brazil

Scheduling problems with sequence-dependent setup times in industries currently attract the attention of re-searchers and practitioners. This study aims to develop a mathematical model for optimizing a single-machine environment with such times using an analogy with the traveling salesman problem. Employing a technolog-ical and modern modeling language for its computational implementations, firstly, five main formulations of this problem in the literature are evaluated and the best one for addressing the proposed problem is identified. Secondly, an arc-flow completion time and precedence model for a single-machine scheduling problem is assessed. Finally, the proposed model is improved by passing the initial solutions obtained by two heuristics to it. As a result, the mathematical model developed returns lower computational times than state-of-the-art ones (even without improvements to the initial solution) which indicates the success of using an analogy between formulations of the traveling salesman problem and the proposed model.

关键词： Sequence-dependent setup Traveling salesman problem Scheduling Single-machine problem mixed-integer linear programming

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Model and solution method for mean-risk cost-based post-disruption restoration of interdependent critical infrastructure networks

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COMPUTERS & OPERATIONS RESEARCH 2022年 144卷 1页

作者： Alkhaleel, Basem A. Liao, Haitao Sullivan, Kelly M. King Saud Univ Dept Ind Engn Riyadh 11421 Saudi Arabia Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA

Critical infrastructure networks (CINs), such as power grids, water distribution systems, and telecommunication networks, are essential for the functioning of society and the economy. As these infrastructure networks are not isolated from each other, their functions are not independent and may be vulnerable to disruptive events (e.g., component failures, terrorist attacks, natural disasters). For decision makers, how to restore the functions of CINs while accounting for interdependencies and various uncertainties becomes a challenging task. In this work, we study the post-disruption restoration problem for a system of interdependent CINs under uncertainty. We propose a two-stage mean-risk stochastic restoration model using mixed-integer linear programming (MILP) with the goal of minimizing the total cost associated with unsatisfied demands, repair tasks, and flow of interdependent infrastructure networks. The restoration model considers the availability of limited time and resources and provides a prioritized list of components to be restored along with assigning and scheduling them to the available network-specific work crews. Additionally, the model features flexible restoration strategies including multicrew assignment for a single component and a multimodal repair setting along with the consideration of full and partial functioning and dependencies between the multi-network components. The proposed model is illustrated using the power and water networks in Shelby County, Tennessee, United States, under two hypothetical earthquake scenarios.

关键词： Interdependent infrastructure networks Post-disruption restoration mixed-integer linear programming

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On the explicit formulation of reliability assessment of distribution systems with unknown network topology: Incorporation of DG, switching interruptions, and customer-interruption quantification

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APPLIED ENERGY 2022年 324卷

作者： Jooshaki, Mohammad Lehtonen, Matti Fotuhi-Firuzabad, Mahmud Munoz-Delgado, Gregorio Contreras, Javier Arroyo, Jose M. Geologian Tutkimuskeskus GTK Circular Econ Solut Unit Espoo Finland Aalto Univ Dept Elect Engn & Automat Espoo Finland Sharif Univ Technol Elect Engn Dept Tehran Iran Univ Castilla La Mancha Escuela Tecn Super Ingn Ind Ciudad Real Spain

This paper presents an original approach for the evaluation of reliability of active distribution networks with unknown topology. Built upon novel reformulations of conventional definitions for distribution reliability indices, the dependence of system-oriented reliability metrics on network topology is explicitly formulated using a set of mixed-integer linear expressions. Unlike previously reported works also modeling mathemat-ically the relationship between reliability assessment and network topology, the proposed approach allows considering the impact of distributed generation (DG) while accounting for switching interruptions. Moreover, for the first time in the emerging closely related literature, the nonlinearity and nonconvexity of the customer average interruption duration index are precisely characterized. The proposed mixed-integer linear model is suitable for various distribution optimization problems in which the operational topology of the network is not specified a priori. Aiming to exemplify its potential applicability, the proposed formulation is incorporated into a distribution reconfiguration optimization problem. The effectiveness and practicality of the proposed approach are numerically illustrated using various test networks.

关键词： Active distribution networks Customer-interruption quantification Distributed generation mixed-integer linear programming Reliability assessment Switching interruptions Unknown network topology

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Explicit Bounds for Large Gaps Between Cubefree integers 20th

Explicit Bounds for Large Gaps Between Cubefree Integers

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20th Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2022 and 21st Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2023

作者： Kumchev, Angel McCormick, Wade McNew, Nathan Park, Ariana Scherr, Russell Ziehr, Willow Department of Mathematics Towson University Towson MD21252 United States Department of Mathematics Northwestern University EvanstonIL60208 United States School of Mathematics University of Minnesota Twin Cities MinneapolisMN55455 United States Department of Mathematics University of California Berkeley BerkeleyCA94720 United States

ISBN: (纸本)9783031650635

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between cubefree integers. In particular, we show that the interval (Formula presented) contains a cubefree integer for any (Formula presented). The constant 5 can be improved further, if. x is assumed to be larger than a very large constant. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： mixed-integer linear programming

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Hierarchical Optimization for Cross-Regional Planning and Scheduling of Hydrogen Energy Storage Systems Considering Uncertainty

Hierarchical Optimization for Cross-Regional Planning and Sc...

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International Conference of Electrical, Electronic and Networked Energy Systems, EENES 2024

作者： Tang, Zihang Wang, Yingxiao Liu, Yuqian Wu, Jianghua School of Computer Science and Technology Xi’an Jiaotong University Xi’an 710049 China Department of Mathematics Nanjing University Nanjing210023 China Shenzhen Research Institute of Big Data the Chinese University of Hong Kong-Shenzhen Guangdong Shenzhen518172 China

ISBN: (纸本)9789819620418

Cross-regional Hydrogen Energy Storage System (HESS) effectively addresses the uneven spatial and temporal distribution of renewable energy sources by facilitating energy storage, transfer, and scheduling across regions. However, the intermittency of renewable energy sources, dynamic changes in demand, and the high costs pose complex challenges for the planning and scheduling of cross-regional HESSs. Although hierarchical modeling, which is divided into upper-level planning and lower-level scheduling, provides flexibility and robustness in handling uncertainties, the difficulties of high model complexity and low solution efficiency still exist. To this end, this paper improves hierarchical modeling by introducing the concept of dynamic transmission price into HESS, which quantifies the difficulty of transferring stored energy to neighboring cities. This concept then guides the energy trading decisions and the power distribution strategies among HESS, eliminating the need to consider the discrete variable of cross-regional connections in the lower-level scheduling for the significant simplification of the solution process. In addition, this paper synchronously integrates simulated annealing and linear programming algorithms as an efficient optimization approach for this novel hierarchical modeling. A case study considering 50 cities demonstrates the feasibility of the hierarchical model and the effectiveness of the optimization approach, providing strong support for the large-scale consumption and absorption of renewable energy across regions. © Beijing Paike Culture Commu. Co., Ltd. 2025.

关键词： mixed-integer linear programming

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The Use of Artificial Intelligence for the Unit Commitment Problem: State of the Art

The Use of Artificial Intelligence for the Unit Commitment P...

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International Conference of the TC Electrimacs Committee, ELECTRIMACS 2024

作者： Milla, José Pérez-Díaz, Juan I. Department of Hydraulic Energy and Environmental Engineering Universidad Politécnica de Madrid Madrid Spain

ISBN: (纸本)9783031739200

With the increasing complexity of the electricity network, optimizing short-term planning for unit commitment (UC) demands more time and resources. This has prompted many researchers in the field to explore alternative methods, serving as auxiliary accelerators or even replacements for classical mixed integer programming (MIP) algorithms. The core idea behind these alternatives is to leverage the fact that the UC problem is typically solved daily by Independent System Operators (ISOs) with minor changes, resulting in a substantial amount of available data. This characteristic makes the problem particularly suitable for Artificial Intelligence (AI) techniques, such as Machine Learning (ML). This paper aims to delineate the state of the art of AI applied to the UC problem, categorizing articles based on the different AI techniques employed and the characteristics and complexity of the UC problem addressed. Additionally, it seeks to compare the outcomes achieved. As of the author’s knowledge, this systematization task has not yet been accomplished in this emerging research area. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： mixed-integer linear programming

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Applying Instance Space Analysis to Optimize the Construction of Matheuristics 18th

Applying Instance Space Analysis to Optimize the Construct...

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18th International Conference on Learning and Intelligent Optimization, LION 2024

作者： Hildebrandt, Sophie Sand, Guido Pforzheim University of Applied Science Pforzheim Germany University of Twente Enschede Netherlands

ISBN: (纸本)9783031756221

The combination of mathematical programming and heuristics is known as matheuristic. Constructing a matheuristic comprises two steps: First selecting its components, second parameterizing those components. The construction of a matheuristic is often done manually by experts, which leads to expensive engineering processes. To bring matheuristics into practice, their construction should be automated. In this paper a matheuristic construction approach is proposed to close this gap. The approach is based on instance space analysis for the selection and Bayesian optimization for the parametrization of the matheuristic. First computational studies show, how Bayesian optimization can be used to parameterize an original heuristic. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： mixed-integer linear programming

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Forbidden Patterns in mixed linear Layouts 42

Forbidden Patterns in Mixed Linear Layouts

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42nd International Symposium on Theoretical Aspects of Computer Science, STACS 2025

作者： Haun, Deborah Merker, Laura Pupyrev, Sergey Karlsruhe Institute of Technology Germany Menlo Park CA United States

ISBN: (纸本)9783959773652

An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue) number of an ordered graph is the minimum number of required stacks (queues). mixed linear layouts combine these layouts by allowing each set of edges to form either a stack or a queue. The minimum number of stacks plus queues is called the mixed page number. It is well known that ordered graphs with small stack number are characterized, up to a function, by the absence of large twists (that is, pairwise crossing edges). Similarly, ordered graphs with small queue number are characterized by the absence of large rainbows (that is, pairwise nesting edges). However, no such characterization via forbidden patterns is known for mixed linear layouts. We address this gap by introducing patterns similar to twists and rainbows, which we call thick patterns;such patterns allow a characterization, again up to a function, of mixed linear layouts of bounded-degree graphs. That is, we show that a family of ordered graphs with bounded maximum degree has bounded mixed page number if and only if the size of the largest thick pattern is bounded. In addition, we investigate an exact characterization of ordered graphs whose mixed page number equals a fixed integer k via a finite set of forbidden patterns. We show that for k = 2, there is no such characterization, which supports the nature of our first result. © Deborah Haun, Laura Merker, and Sergey Pupyrev.

关键词： mixed-integer linear programming

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