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An overview of exact algorithms for the Euclidean Steiner tree problem in n-space

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2016年第5期23卷 861-874页

作者： Fampa, Marcia Lee, Jon Maculan, Nelson Univ Fed Rio de Janeiro Inst Matemat Dept Ciencia Comp Rio De Janeiro RJ Brazil Univ Fed Rio de Janeiro COPPE PESC Rio De Janeiro RJ Brazil Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

The Euclidean Steiner tree problem (ESTP) in R-n is to find a shortest network interconnecting p given points in n-dimensional Euclidean space. The problem was first described in the plane and an algorithm with very good practical efficiency has been proposed to solve this particular case. The generalization for higher dimensions was proposed in the 19th century, however the numerical solution of the problem remains very challenging when n >= 3. We give an overview of the exact algorithms presented in the literature for the ESTP when n >= 3 and discuss their common and distinguished features, their advantages and drawbacks, and some possible directions for improvement toward the numerical solution of large instances of the problem.

关键词： Euclidean Steiner tree problem n-dimensional Euclidean space exact algorithm mixed-integer nonlinear programming global optimization

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Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes

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OPTIMIZATION METHODS & SOFTWARE 2020年第1期35卷 37-64页

作者： Burlacu, Robert Geissler, Bjoern Schewe, Lars Friedrich Alexander Univ Erlangen Nurnberg FAU Erlangen Germany

We propose a method for solving mixed-integer nonlinear programmes (MINLPs) to global optimality by discretization of occurring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear programme (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP, we develop an iterative algorithm which solves MIP relaxations that are adaptively refined. We are able to give convergence results for a wide range of MINLPs requiring only continuous nonlinearities with bounded domains and an oracle computing maxima of the nonlinearities on their domain. Moreover, the practicalness of our approach is shown numerically by an application from the field of gas network optimization.

关键词： mixed-integer nonlinear programming piecewise linear approximation gas transport optimization global optimization adaptivity

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Liner ship route schedule design with port time windows

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2014年 41卷 1-17页

作者： Wang, Shuaian Alharbi, Abdurahim Davy, Pam Univ Wollongong Sch Math & Appl Stat Wollongong NSW 2522 Australia

This paper examines a practical tactical liner ship route schedule design problem, which is the determination of the arrival and departure time at each port of call on the ship route. When designing the schedule, the availability of each port in a week, i.e., port time window, is incorporated. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear nonconvex optimization model. In view of the problem structure, an efficient holistic solution approach is proposed to obtain global optimal solution. The proposed solution method is applied to a trans-Atlantic ship route. The results demonstrate that the port time windows, port handling efficiency, bunker price and unit inventory cost all affect the total cost of a ship route, the optimal number of ships to deploy, and the optimal schedule. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Container liner shipping Schedule design Containership scheduling Port time windows mixed-integer nonlinear programming

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Fuzzy decision-making design of chemical plant using mixed-integer hybrid differential evolution

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COMPUTERS & CHEMICAL ENGINEERING 2002年第12期26卷 1649-1660页

作者： Huang, HJ Wang, FS Natl Chung Cheng Univ Dept Chem Engn Chiayi 62102 Taiwan

In this study, we have introduced a fuzzy decision-making approach to design a multi-objective optimal design problem of a multiproduct batch chemical plant. In the crisp decision-making approach, the designer is first to solve the multi-objective optimization problem, and then to check whether each optimal objective function value satisfies the rigid preference goal. In real world application, the preference goal for each objective function is an interval bound not a rigid value so that the problem becomes a fuzzy goal optimization problem. A monotonic increasing or decreasing membership function is used to define the degree of satisfaction for each objective function so that the fuzzy goal optimization problem is then represented as an augmented minimax problem formulated as mixed-integer nonlinear programming (MINLP) models. To obtain a unique solution, we have introduced the mixed-integer hybrid differential evolution (MIHDE) to solve the MINLP problems. The MIHDE can straightforwardly solve the problem without any mathematical model transformation. Two examples were used to illustrate the applicability of the proposed interactive algorithm. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： mixed-integer nonlinear programming fuzzy decision-making multi-objective optimization batch design differential evolution

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Optimal design of an isotope separation system

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FUSION TECHNOLOGY 1996年第3期30卷 337-348页

作者： Boisset, L Latge, C Pibouleau, L Guittard, P Domenech, S ECOLE NATL SUPER INGENIEURS GENIE CHIM CNRSUMR 5503F-31078 TOULOUSEFRANCE PROSIM SA F-31078 TOULOUSEFRANCE

Cryogenic distillation cascades are proposed to be used today to separate hydrogen isotopes in the fuel cycle of a fusion reactor, It is necessary to design these cascades so that their tritium inventory, is minimal. We have thus developed optimization tools in order to simultaneously optimize the structure and the operating parameters of these distillation sequences. This leads to the implementation of a mixed-integer nonlinear programming procedure in a process simulator The application concerns the International Thermonuclear Experimental Reactor (ITER) isotope separation system. Successive simulation and optimization studies have been carried out which show the accuracy of the simulation and lead to the suggestion of a new arrangement of units for the cascade, with a higher number of columns.

关键词： isotope separation mixed-integer nonlinear programming superstructure

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Validation of nominations in gas network optimization: models, methods, and solutions

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OPTIMIZATION METHODS & SOFTWARE 2015年第1期30卷 15-53页

作者： Pfetsch, Marc E. Fuegenschuh, Armin Geissler, Bjoern Geissler, Nina Gollmer, Ralf Hiller, Benjamin Humpola, Jesco Koch, Thorsten Lehmann, Thomas Martin, Alexander Morsi, Antonio Roevekamp, Jessica Schewe, Lars Schmidt, Martin Schultz, Ruediger Schwarz, Robert Schweiger, Jonas Stangl, Claudia Steinbach, Marc C. Vigerske, Stefan Willert, Bernhard M. Tech Univ Darmstadt Dept Math Darmstadt Germany Helmut Schmidt Univ Dept Mech Engn Hamburg Germany Zuse Inst Berlin Berlin Germany Univ Erlangen Nurnberg Dept Math D-91054 Erlangen Germany Open Grid Europe GmbH Essen Germany Univ Duisburg Essen Dept Math Duisburg Germany Leibniz Univ Hannover Inst Appl Math D-30167 Hannover Germany

In this article, we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult nonconvex mixedinteger nonlinear feasibility problem. The first phase consists of four distinct algorithms applying mixedinteger linear, mixedinteger nonlinear, nonlinear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high-quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.

关键词： gas network optimization nomination mixed-integer nonlinear programming gas transport optimization

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Optimal acquisition policy with quantity discounts and uncertain demands

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2009年第9期47卷 2409-2425页

作者： Zhang, Guoqing Ma, Liping Univ Windsor Dept Ind & Mfg Syst Engn Windsor ON N9B 3P4 Canada Aspen Technol Canada Ltd Calgary AB Canada

We study the acquisition policy decision problem for a supply network involving one manufacturer and multiple suppliers. The manufacturer produces multiple products under uncertain demands and each supplier provides price discounts. The problem is to determine the manufacturer's acquisition policy and production levels so as to maximise the manufacturer's expected profit, subject to both the manufacturer's and suppliers' capacities. We present a mixed integer nonlinear programming (MINLP) formulation of the problem, for both single- and multiple-sourcing procurement policies. General algebraic modeling system (GAMS) and its solvers, combining external integration functions, are employed to solve the complex MINLP problem. The preliminary computation results and managerial analysis are reported.

关键词： supplier selection uncertainty quantity discount mixed-integer nonlinear programming

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Real-time train regulation in the metro system with energy storage devices: An efficient decomposition algorithm with bound contraction

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2024年 159卷

作者： Li, Shukai Yuan, Yin Chen, Zebin Yang, Lixing Yu, Chengpu Beijing Jiaotong Univ Sch Syst Sci Beijing 100044 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

Focusing on the energy -conservation train operation issues, this paper proposes an effective real-time train regulation scheme for metro systems with energy storage devices. Specifically, to minimize train timetable deviation, passenger waiting and energy consumption, we formulate a mixed -integer nonlinear programming model to generate energy -efficient train regulation strategies. This model explicitly considers the train traffic, passenger load and storage, immediate and delayed uses of regenerative energy. Carefully tailored to the proposed model, we devise an efficient decomposition algorithm to split the original problem into small-scale subproblems. In the algorithm, specific values of binary variables, passenger -flow estimates and logic -based cuts are consecutively identified and updated. Besides, bound contraction and bilinear -specific warming start procedures are particularly designed for further acceleration. Numerical experiments are conducted to validate the proposed model and method. Our energyefficient train regulation strategies can improve train departure punctuality, headway regularity, reduce passenger waiting times, and achieve energy savings. Furthermore, the solution algorithm exhibits promising computational efficiency in real -world experiments, thereby facilitating an online implementation.

关键词： Metro system Real-time train regulation Energy storage devices Decomposition algorithm mixed-integer nonlinear programming

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A Multi-Objective Optimization Approach to Polygeneration Energy Systems Design

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AICHE JOURNAL 2010年第5期56卷 1218-1234页

作者： Liu, Pei Pistikopoulos, Efstratios N. Li, Zheng Univ London Imperial Coll Sci Technol & Med CPSE Dept Chem Engn London SW7 2AZ England Tsinghua Univ Dept Thermal Engn Beijing 100084 Peoples R China

Polygeneration, typically involving co-production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large-scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity poly generation plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non-convex mixed-integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 1218-1234, 2010

关键词： polygeneration process design mixed-integer nonlinear programming global multiobjective optimization parallel computation

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Price optimization with reference price effects: A generalized Benders' decomposition method and a myopic heuristic approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期280卷 555-567页

作者： Shams-Shoaaee, Seyed Shervin Hassini, Elkafi McMaster Univ Sch Computat Sci & Engn Hamilton ON Canada McMaster Univ DeGroote Sch Business Hamilton ON Canada

We consider a multi-period revenue maximization and pricing optimization problem in the presence of reference prices. We formulate the problem as a mixed integer nonlinear program and develop a generalized Benders' decomposition algorithm to solve it. In addition, we propose a myopic heuristic and discuss the conditions under which it produces efficient solutions. We provide analytical results as well as numerical computations to illustrate the efficiency of the solution approaches as well as some managerial pricing insights. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Pricing Reference pricing mixed-integer nonlinear programming Generalized Benders' decomposition

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