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Granularity for mixed-integer Polynomial Optimization Problems

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第2期205卷 1-24页

作者： Eggen, Carl Stein, Oliver Volkwein, Stefan Univ Konstanz Dept Math & Stat Universitatsstr 10 D-78464 Constance Germany Karlsruhe Inst Technol KIT Inst Operat Res Blucherstr 17 D-76185 Karlsruhe Germany

Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby used to solve those continuous polynomial problems, which generalizes known methods from the literature. Numerical examples from the MINLPLib illustrate our approach.

关键词： mixed-integer nonlinear programming Granularity Rounding Polynomial optimization Semidefinite programming

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Dynamic adjustment strategy of electric bus operations: A spatial branch-and-bound method with acceleration techniques

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2025年 171卷

作者： Yuan, Yin Li, Shukai D'Ariano, Andrea Bosi, Tommaso Yang, Lixing Beijing Jiaotong Univ Sch Syst Sci Beijing 100044 Peoples R China Roma Tre Univ Dept Civil Comp Sci & Aeronaut Technol Engn I-00146 Rome Italy

Electric bus systems frequently encounter operational instability, resulting in delays, bunching and disturbed charging schemes. Advanced technologies like sensoring and wireless connectivity strongly support dynamic adjustments to improve the stability of electric bus systems, fostering flexibility responsiveness to changing operating conditions. This article explores the dynamic adjustment problem of electric bus operations to jointly generate bus charging schemes and timetable adjustments in a real-time decision-making process. We propose a mixed- integer nonlinear programming model for each decision stage, explicitly considering factors such as vehicle overtaking, passenger load, capacity limitations, and charging behaviors. To efficiently solve this problem, we design a spatial branch-and-bound method with multiple acceleration techniques of logical inference for bound contraction, bilinear-specific branching, and parallel computation. Indeed, the original mixed-integer nonlinear programming problem can be split into a series of mixed-integer quadratic programming problems with reduced domains. The acceleration techniques proposed could be easily customized to address other mixed-integer nonlinear programs in such branch-and-bound-based schemes. Computational experiments validate the effectiveness of the proposed adjustment strategy yielding feasible solutions that enhance headway regularity, energy savings and service quality. Additionally, our solution method efficiently tackles real-world scenarios of significant complexity, with up to 12 vehicles running 8 loops on a route comprising 54 stops, with an average of 5.11-seconds computational time, outperforming both the common commercial solver and standard spatial branch-and-bound approaches in computational speed.

关键词： Electric bus system mixed-integer nonlinear programming Acceleration techniques

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Drone-Delivery Network for Opioid Overdose: nonlinear integer Queueing-Optimization Models and Methods

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OPERATIONS RESEARCH 2025年第1期73卷 iii-vii, 1-582, C2-C3页

作者： Lejeune, Miguel A. Ma, Wenbo George Washington Univ Dept Decis Sci Washington DC 20052 USA

We propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naloxone in response to opioid overdoses. The network is represented as a collection of M/G/K / G / K queueing systems in which the capacity K of each system is a decision variable, and the service time is modeled as a decision -dependent random variable. The model is a queuing -based optimization problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions and takes the form of a nonlinear integer problem intractable in its original form. We develop an efficient reformulation and algorithmic framework. Our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed -integer linear programming (MILP) formulation. We demonstrate its generalizability and show that the problem of minimizing the average response time of a collection of M/G/K / G / K queueing systems with unknown capacity K is always MILP-representable. We design an outer approximation branch -and -cut algorithmic framework that is computationally efficient and scales well. The analysis based on real -life data reveals that drones can in Virginia Beach: (1) decrease the response time by 82%, (2) increase the survival chance by more than 273%, (3) save up to 33 additional lives per year, and (4) provide annually up to 279 additional quality -adjusted life years.

关键词： opioid overdose drone delivery optimization-based queueing model survival chance mixed-integer nonlinear programming stochastic network design

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Outer Approximation Method for Discrete AC Optimal Power Flow

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IEEE TRANSACTIONS ON POWER SYSTEMS 2025年第2期40卷 1943-1954页

作者： Jabr, Rabih A. Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

This paper introduces an Outer Approximation (OA) method for solving discrete AC Optimal Power Flow (OPF) problems that account for switching decisions. The OPF problem is formulated via the extended conic quadratic format. It includes selecting generators for dispatch and controlling switched-type capacitor/inductor banks. The OA method is based on relaxing nonlinear equality constraints into conic and linear inequalities with penalty slack variables. The resulting mixed-integer Second-Order Cone programming (MISOCP) solution is iterated with a continuous variable nonlinear programming (NLP) solver that holds the discrete decisions constant at their most recent MISOCP values. The OA method can utilize polyhedral approximations and is scalable to test instances with more than 3000 nodes. Comparisons are reported with globally optimal discrete AC OPF results from the recent literature and a commercial solver for nonconvex mixed-integer nonlinear programming (MINLP) utilizing dynamic outer approximation and piecewise linear approximation with spatial branching. Comparative analysis shows that the proposed OA method provides global solutions for previously studied test instances while offering significant speed-up. It also applies to larger test networks where the other methods fail to calculate a feasible solution.

关键词： Switches Reactive power programming Load flow Renewable energy sources Mathematical models Generators Convex optimization iterative algorithms mixed-integer nonlinear programming optimization methods power system analysis computing power system management

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A Unified Framework for Integrated Energy Systems Optimization With Day-Ahead and Real-Time Coordination

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IEEE ACCESS 2024年 12卷 140628-140642页

作者： Masoumi, Amin Korkali, Mert Marzband, Mousa Univ Missouri Dept Elect Engn & Comp Sci Columbia MO 65211 USA King Abdulaziz Univ Ctr Res Excellence Renewable Energy & Power Syst Jeddah 21589 Saudi Arabia

The operational phase of integrated energy systems (IESs), installed in distribution systems, is increasingly confronted with uncertainties in electrical consumption and output power of variable energy resource (VRE) (e.g., solar photovoltaics). One common approach to mitigate this challenge is to implement day-ahead (DA) scheduling based on cleared prices and purchased power. While this method is effective to some extent, it may not always provide the level of accuracy required. Another viable option is the application of incentive-based demand-response program (I-DRP), where adjustments to energy usage are made in return for a fixed tariff. Nonetheless, this method could result in monopolistic decision-making within an expanding energy industry, albeit assisting in alleviating the barrier. The complexity doubles as the nonlinear formulation of economic objective function is considered in the optimization stage. Hence, the optimality of the solution is a matter of concern. To address these challenges, this research introduces a two-stage coordinated strategy (TSCS) that combines accurate short-term forecasting of uncertainties and I-DRP with regulations of DA and real-time markets to identify the best possible offers and improves the operational efficiency of the IES. By conducting simulations on the IEEE 85-bus test system and comparing the results of the proposed algorithm with those of stochastic programming with fixed reward and penalty rates, our study demonstrates the reliability and accuracy of TSCS, highlighting the flexibility of offers in terms of customer's participation in the optimal operation of the IES.

关键词： Costs Optimization Batteries programming Accuracy Uncertainty Real-time systems Energy management Intserv networks Demand response Machine learning nonlinear systems Integrated energy systems (IESs) incentive-based demand-response programs machine learning mixed-integer nonlinear programming two-stage programming

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A mixed-integer nonlinear Model to Support the Operation of Distribution Systems With Hidden DERs

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IEEE TRANSACTIONS ON POWER DELIVERY 2025年第1期40卷 484-496页

作者： Vasconcelos, Pedro N. Trindade, Fernanda C. L. Venkatesh, Bala Freitas, Walmir de Souza, Antonio C. Zambroni Taranto, Glauco N. Univ Fed Itajuba BR-37500903 Itajuba Brazil Univ Estadual Campinas BR-13083970 Campinas Brazil Toronto Metropolitan Univ Toronto ON M5B 2K3 Canada Univ Fed Rio de Janeiro BR-21945970 Rio De Janeiro RJ Brazil

With impending deep electrification powered by innumerable Distributed Energy Resources (DERs), modeling each DER individually is becoming a critical challenge to the Distribution System Operators (DSOs). Even though the DSOs know the total DER installed capacity at the feeder level, the exact individual type, location, and size of such generators may remain unknown. This paper proposes a mixed-integer nonlinear programming formulation to support the operation of distribution systems under massive DER integration. The proposal accurately estimates distribution system power flows, relying on a limited set of measurements. It aims to establish equivalent DER models representing hidden resources and improve the representation of limited-visibility networks. The only DER information required is the total solar and wind installed capacity at the feeder level. The performance is assessed by comparing estimated and measured values of bus voltage magnitudes and branch power flows. Results demonstrate the efficacy of the proposed formulation in accurately replicating measurements, achieving an accuracy of over 90% when estimating active power flows in unmetered branches.

关键词： Voltage measurement Load flow Distributed power generation Power measurement Accuracy Reactive power Wind speed Aggregates State estimation Sparse matrices Deep electrification distributed generation hidden DERs mixed-integer nonlinear programming radial distribution systems

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Transitioning to electrification: Optimal strategies for ship fleet replacement

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2025年 174卷

作者： Cui, Ziyu Fu, Xiaowen Jin, Huan Chen, Anthony Wang, Kun Hong Kong Polytech Univ Dept Ind & Syst Engn Kowloon Hong Kong Peoples R China Univ Nottingham Dept Comp Sci Ningbo Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China

To reduce carbon emissions, some shipping companies are strategically transitioning their fleets from diesel-powered ships to electric ones. However, the question of how to cost-effectively design this fleet conversion and the construction of charging stations for electric ships remains a critical issue. In this paper, we present a mixed-integer nonlinear programming (MINLP) model to minimize the total cost of designing the ship fleet replacement plan within a given planning horizon. At the planning level, the yearly strategic transition schedules for purchasing and salvaging ships are obtained, while the optimal strategy for charging station construction is also determined to satisfy annual cargo demand and charging demand. Then, our model integrates the operational level to determine optimal fleet deployment strategies and operational decisions. Meanwhile, the impact of real-world factors such as waterway depth and emission cost are discussed, respectively. Moreover, we introduce two subsidy schemes and compare their effectiveness on the fleet electrification process. Finally, the proposed model is applied to the Yangtze River shipping network in China using real data. The results show that the shipping company will initially invest in lower-cost electric ships with a limited budget, followed by the acquisition of larger ships. The charging stations are strategically established in the downstream areas, coinciding with the initial deployment of electric ships. Moreover, the impacts of fuel prices and emission cost of diesel-powered ships on the electrification process are compared, with the results indicating that the increase in emission cost has a more pronounced effect on the total cost compared to the rise in fuel prices. Additionally, the subsidy schemes' effect is explored, revealing that financial incentives markedly accelerate the fleet electrification process.

关键词： Electrification Electric ships Fleet replacement Charging stations mixed-integer nonlinear programming

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Superstructure-based optimization of membrane network systems for multicomponent liquid mixture separation

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JOURNAL OF MEMBRANE SCIENCE 2025年 717卷

作者： Verma, Harshit Jassby, David Maravelias, Christos T. Princeton Univ Dept Chem & Biol Engn 50 Olden St Princeton NJ 08540 USA Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA 90095 USA Princeton Univ Andlinger Ctr Energy & Environm Princeton NJ 08540 USA

The design of membrane networks to recover chemical components from liquid mixtures is intricate due to the large number of potential network configurations. Additionally, nonidealities present in liquid mixtures pose difficulties in describing membrane permeators. In this work, we present a framework for membrane network synthesis to recover valuable components from liquid mixtures using mixed-integer nonlinear programming (MINLP). First, to model membrane permeation, we develop a physics-based nonlinear surrogate model for crossflow membranes. Second, we construct a richly connected superstructure to account for all potential membrane network configurations. Third, we demonstrate how the two aforementioned elements can be integrated into a MINLP model to obtain the optimal membrane network configuration. Finally, through various applications, we illustrate how the proposed approach can achieve globally optimal solutions.

关键词： Separation network synthesis mixed-integer nonlinear programming Global optimization

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Optimal design of hydrogen-blended natural gas pipeline network considering separation systems

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AICHE JOURNAL 2025年第2期71卷

作者： Gu, Shiya Bai, Yunhai Dong, Yachao Du, Jian Dalian Univ Technol Inst Chem Proc Syst Engn Sch Chem Engn Dalian 116024 Liaoning Peoples R China CNPC Chuanqing Drilling Engn Co Ltd Drilling & Prod Technol Res Inst Xian Shaanxi Peoples R China Natl Engn Lab Explorat & Dev Low Permeabil Oil & G Xian Shaanxi Peoples R China

Blending hydrogen into existing natural gas pipelines is considered the most feasible choice for long-distance, large-scale hydrogen transportation in the early stage of hydrogen economy development. To integrate the optimization of hydrogen-blended natural gas pipeline network and subsequent hydrogen/natural gas separation process, this article presents a mixed-integer nonlinear programming model, aiming to minimize the total annual project net cost. To tackle the computational complexity resulting from the large-scale and nonlinear nature of practical design problems, a decomposition algorithm is tailored to the proposed model. Two case studies demonstrate that compared to stepwise model, the proposed pipeline-separation integrated model offers economic benefits and practical value, incorporating separation processes and satisfying constraints of hydrogen demand, pressure and blending ratio requirements, which achieves an economically optimal design for both pipeline transportation and separation systems, and provides a viable solution for the broader application of hydrogen-blended natural gas networks.

关键词： hydrogen infrastructure design methane-hydrogen separation mixed-integer nonlinear programming pipeline network superstructure-based optimization

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An Enhanced Logic-Based Bender's Decomposition Algorithm with Proximity Principle for Simulator-Based Distillation Process Optimization

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PROCESSES 2025年第4期13卷 977-977页

作者： Tian, Chenshan Zhang, Xiaodong Lan, Yang Sun, Jinsheng Tianjin Univ Technol Sch Chem Engn & Technol Tianjin 300072 Peoples R China Shanghai Jiao Tong Univ Coll Smart Energy Shanghai 200240 Peoples R China

The optimization of distillation processes is particularly challenging due to the presence of nonlinear equations and integer variables, resulting in complex mixed-integer nonlinear programming (MINLP) problems. This work introduces an enhanced optimization algorithm, the logic-based proximity principle Bender's decomposition (LB-PBD), to address non-convex MINLP issues in simulator-based distillation optimization. The key innovation, the proximity principle, improves lower bound predictions by prioritizing information from the closest known integer solutions. Additionally, the integration of a multi-start points strategy and a delayed convergence strategy ensures the algorithm achieves global optimality while avoiding premature convergence. The effectiveness if the proposed LB-PBD is validated through three case studies. Numerical experiments demonstrate so-called proximity principle superior ability of original algorithm to navigate local optima, making LB-PBD more versatile than traditional deterministic algorithm (logic-based outer approximation algorithm) and stochastic algorithm (adaptive superstructure-differential evolution algorithm). In a single-column distillation case, LB-PBD achieves high accuracy. In an extractive distillation case, the algorithm successfully optimizes the separation of a near-azeotropic mixture, reducing energy consumption and improving product recovery compared to previous solutions. These results highlight LB-PBD as a robust and effective tool for solving non-convex MINLLP problems, particularly in simulator-based distillation process optimization.

关键词： distillation optimization mixed-integer nonlinear programming proximity principle Bender's decomposition simulator-based optimization

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