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mixed-integer nonlinear and continuous optimization formulations for aircraft conflict avoidance via heading and speed deviations *

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第2期310卷 670-679页

作者： Cafieri, Sonia Conn, Andrew R. Mongeau, Marcel Univ Toulouse ENAC Toulouse France IBM TJ Watson Res Ctr Ossining NY USA

We introduce two new optimization models for the aircraft conflict avoidance problem that aims at issuing decisions on both speed and heading-angle deviations to keep aircraft pairwise separated by a given separation distance. The first model is a new mixed-integer nonlinear formulation. The second model is a continuous optimization formulation, less typical in aircraft conflict avoidance. The advantages of the two models are combined within a three-phase method that we propose to solve the problem to global optimality. Computational experiments on various instances from the literature yield very promising results, and show the effectiveness of the proposed models and of the three-phase solution approach. (c) 2023 Published by Elsevier B.V.

关键词： Global optimization mixed-integer nonlinear optimization Continuous optimization Aircraft conflicts

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mixed integer nonlinear optimization of Coupled Power and Gas Distribution Network Operation 53

Mixed Integer Nonlinear Optimization of Coupled Power and Ga...

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53rd International Universities Power Engineering Conference (UPEC)

作者： Zimmerlin, Martin Mueller, Felicitas Wilferth, Martin Held, Lukas Suriyah, Michael R. Leibfried, Thomas KIT Inst Elect Energy Syst & High Voltage Technol IEH Karlsruhe Germany

ISBN: (纸本)9781538629109

In this contribution a time constrained mixed integer nonlinear optimization is presented aiming at optimal operation of coupled power and gas distribution grids. Optimal scheduling of Power-to-Gas and Combined Heat and Power Systems enables a flexible operation of the resulting multi-carrier energy system. Linear constraints consider static models of the conversion technologies. The distribution grid models of power and gas system are included as nonlinear constraints. In a case study the resulting optimization framework is applied to a small test system based on real data.

关键词： integrated energy system mixed-integer nonlinear optimization MINLP multi-carrier energy system power system natural gas sector coupling

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Optimizing the design and operation of water networks: Two decomposition approaches

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COMPUTERS & CHEMICAL ENGINEERING 2025年 192卷

作者： Li, Yijiang Dey, Santanu S. Sahinidis, Nikolaos, V Susarla, Naresh Zamarripa, Miguel A. Drouven, Markus G. Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Georgia Inst Technol Sch Chem & Biomol Engn Atlanta GA USA Natl Energy Technol Lab Pittsburgh PA 15236 USA

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinear programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.

关键词： mixed-integer nonlinear optimization Time decomposition Network design Produced water

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Gaining or losing perspective for convex multivariate functions on box domains

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MATHEMATICAL PROGRAMMING 2025年第1-2期211卷 319-339页

作者： Xu, Luze Lee, Jon Univ Calif Davis Dept Math Davis CA USA Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

mixed-integer nonlinear optimization formulations of the disjunction between the origin and a polytope via a binary indicator variable is broadly used in nonlinear combinatorial optimization for modeling a fixed cost associated with carrying out a group of activities and a convex cost function associated with the levels of the activities. The perspective relaxation of such models is often used to solve to global optimality in a branch-and-bound context, but it typically requires suitable conic solvers and is not compatible with general-purpose NLP software in the presence of other classes of constraints. This motivates the investigation of when simpler but weaker relaxations may be adequate. Comparing the volume (i.e., Lebesgue measure) of the relaxations as a measure of tightness, we lift some of the results related to the simplex case to the box case. In order to compare the volumes of different relaxations in the box case, it is necessary to find an appropriate concave upper bound that preserves the convexity and is minimal, which is more difficult than in the simplex case. To address the challenge beyond the simplex case, the triangulation approach is used.

关键词： mixed-integer nonlinear optimization Global optimization Convex relaxation Perspective relaxation Polytope Volume Integration

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Cost, resiliency and emissions trade-offs for microgrids in varying socioeconomic settings

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2025年 216卷

作者： Hood, Karoline McMiller, Orlando Nock, Destenie Grymes, James Newman, Alexandra Colorado Sch Mines Mech Engn Dept Golden CO 80401 USA Louisiana State Univ Math Dept Baton Rouge LA 70803 USA Carnegie Mellon Univ Civil & Environm Engn Dept Pittsburgh PA 15213 USA US Mil Acad Math Sci Dept West Point NY 10996 USA

Microgrids offer a decentralized approach to meeting energy and heating demands and can integrate renewable energy technologies, thereby facilitating emissions reductions. This study presents a mixed-integer nonlinear microgrid design and dispatch optimization model that incorporates load shedding. Although existing optimization models examine the trade-offs between meeting demand and the infrastructure and operational cost of doing so, this research contributes by determining the social cost (in terms of health impacts), particularly on vulnerable populations, of failing to supply power during outages, and the extent to which a microgrid can mitigate such outages, albeit at a financial cost. Using case studies across a diverse set of communities, the research examines the ramifications of power outages on healthcare devices. Our findings indicate that a failure to meet at least 20% of energy demand during outages can affect health device functionality, impacting 2%-7% of the population in higher vulnerability communities, compared to having negligible effects in non-vulnerable populations. Conversely, meeting at least 80% of demand during outages impacts less than 2% of the population in the affected community, although with an increase in cost of approximately 25%. Furthermore, the research analyzes changes in pollutant concentrations, attributing them to premature deaths. Employing a model that simulates point-source pollution, our microgrid model, with an emphasis on solid oxide fuel cells, achieves CO2 reductions of up to 5% relative to cases in which no emissions reductions are enforced, with minimal cost increase (typically around 1%). This reduction in emissions corresponds to a 4%-9% decrease in mortality rates.

关键词： mixed-integer nonlinear optimization Microgrid Emissions Particulate matter Resiliency Social vulnerability

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Adjustable robust nonlinear network design without controllable elements under load scenario uncertainties

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MATHEMATICAL PROGRAMMING 2025年 1-35页

作者： Thuerauf, Johannes Gruebel, Julia Schmidt, Martin Univ Technol Nuremberg UTN Dept Liberal Arts & Social Sci Discrete Optimizat Lab Dr Luise Herzberg Str 4 D-90461 Nurnberg Germany Univ Technol Nuremberg UTN Analyt & Optimizat Lab Dr Luise Herzberg Str 4 D-90461 Nurnberg Germany Trier Univ Dept Math Univ Sring 15 D-54296 Trier Germany

We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, load scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all load scenario uncertainties, if and only if a finite number of worst-case load scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future load fluctuations.

关键词： Robust optimization nonlinear flows Potential-based networks Load scenario uncertainties mixed-integer nonlinear optimization

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Clean energy supply chain optimization: Steady-state natural gas transportation

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CLEANER LOGISTICS AND SUPPLY CHAIN 2025年 15卷

作者： Liu, Zhongfu Xu, Shuiying Zhao, Shihao Li, Yuewen Zhou, Meiling Li, Shuosen Meng, Fei PipeChina Engn Technol Innovat Co Ltd Off BldgRonghe RdBinhai New AreaBaoce Bldg Tianjin 300450 Peoples R China Cardinal Operat Beijing 100102 Peoples R China

In the context of the clean energy supply chain, optimizing the natural gas transportation scheme based on steady-state operation can not only enhance the efficiency of pipeline network operation but also facilitate the low-carbon transition of energy. As a crucial component of the clean energy supply chain, natural gas pipeline systems are highly complex, characterized by the intricate topological coupling between pipelines and stations, requiring collaborative optimization decisions for pressure, flow, and the operation of compressor stations. Additionally, the pressure drop and flow in the pipeline must satisfy nonlinear physical equations, which involve hydraulic parameters such as temperature and compressibility factor that vary with flow and pressure. To address these issues, a mixed-integer nonlinear optimization model is developed, and by linearizing the nonlinear equations, a sequential linear programming algorithm is proposed, iteratively updating the hydraulic parameters. The objective is to minimize pipeline transportation costs and energy consumption, achieving optimization of the steady-state operation of the natural gas pipeline system. Experimental results show that the proposed model and algorithm significantly improve the efficiency of the clean energy supply chain, providing theoretical support for the low-carbon and economic aspects of natural gas transportation.

关键词： Steady-state natural gas transport mixed-integer nonlinear optimization Successive linear programming Hydraulic parameters

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THE MULTILINEAR POLYTOPE FOR ACYCLIC HYPERGRAPHS

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SIAM JOURNAL ON optimization 2018年第2期28卷 1049-1076页

作者： Del Pia, Alberto Khajavirad, Aida Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA Univ Wisconsin Wisconsin Inst Discovery Madison WI 53706 USA Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

We consider the multilinear polytope defined as the convex hull of the set of binary points z satisfying a collection of equations of the form z(e) = Pi(zv)(v is an element of e), e is an element of E, where E denotes a family of subsets of {1, . . . , n} of cardinality at least two. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as 0 - 1 polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial structure of the multilinear polytope in conjunction with the acyclicity degree of the underlying hypergraph. We provide explicit characterizations of the multilinear polytopes corresponding to Berge-acylic and gamma-acyclic hypergraphs. As the multilinear polytope for gamma-acyclic hypergraphs may contain exponentially many facets in general, we present a strongly polynomial-time algorithm to solve the separation problem, implying polynomial solvability of the corresponding class of 0 - 1 polynomial optimization problems. As an important byproduct, we present a new class of cutting planes for constructing tighter polyhedral relaxations of mixed-integer nonlinear optimization problems with multilinear subexpressions.

关键词： multilinear polytope cutting planes hypergraph acyclicity separation algorithm mixed-integer nonlinear optimization

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Global optimization in design and control of chemical process systems

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JOURNAL OF PROCESS CONTROL 2000年第2-3期10卷 125-134页

作者： Floudas, CA Princeton Univ Dept Chem Engn Princeton NJ 08544 USA

This paper presents an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of Process Design and Control. The focus is on global optimization methods for (a) twice-differentiable constrained nonlinear optimization problems, Cb) mi?;ed-integer nonlinear optimization problems, and (c) locating all solutions of nonlinear systems of equations. Theoretical advances and computational studies on process design, batch design under uncertainty, phase equilibrium, location of azeotropes, stability margin, process synthesis, and parameter estimation problems are discussed. (C) 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved.

关键词： global optimization twice differentiable NLPs mixed-integer nonlinear optimization locating all solutions alpha BB approach design and control

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An outer-approximation algorithm for maximum-entropy sampling

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DISCRETE APPLIED MATHEMATICS 2024年 347卷 271-284页

作者： Fampa, Marcia Lee, Jon Univ Fed Rio de Janeiro Rio De Janeiro Brazil Univ Michigan Ann Arbor MI 48109 USA

We apply the well-known outer-approximation algorithm (OA) of convex mixed-integer nonlinear optimization to the maximum-entropy sampling problem (MESP), using convex relaxations for MESP from the literature. We discuss possible methodologies to accelerate the convergence of OA, by combining the use of the different relaxations and by selecting additional linearization points using a local-search procedure, disjunctive cuts, a regularization method, and a second-order approximation of the objective of the MESP. We discuss our findings through numerical experiments with a benchmark test problem. (c) 2024 Elsevier B.V. All rights reserved.

关键词： Maximum-entropy sampling mixed-integer nonlinear optimization Outer approximation Disjunctive cuts No-good Local search Regularization Second-order approximation

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