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Solving mixed integer nonlinear chemical engineering problems via simulated annealing approach

CHEMICAL AND BIOCHEMICAL ENGINEERING QUARTERLY 2004年第4期18卷 329-335页

作者： Özçelik, Y Özçelik, Z Ege Univ Fac Engn Dept Chem Engn Bornova Turkey

The optimization models of chemical engineering processes are generally nonlinear and mixed integer, nonlinear in structure, and contain several equality and inequality constraints and bounds on variables. mixed integer nonlinear programming problems (MINLP) can be solved using either gradient methods or stochastic methods. Gradient methods need to separate the problem to mixed integer Linear programming (MILP) and nonlinear programming (NLP) problems and some special formulations where the continuity or convexity has to be imposed. In this work, an algorithm (SARAN) that was based on a simulated annealing algorithm of Corana(1) was developed to solve MINLP problems. Then the algorithm and some alternatives for the basic steps of a simulated annealing were tested for 100 sequences of pseudo random numbers using 11 MINLP test problems. Finally the results were compared with the results of the M-SIMPSA(2) for small and medium scaled problems.

关键词： mixed integer nonlinear programming nonlinear optimization simulated annealing

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Modeling the Multicommodity Multimodal Routing Problem with Schedule-Based Services and Carbon Dioxide Emission Costs

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MATHEMATICAL PROBLEMS IN ENGINEERING 2015年第1期2015卷 1-21页

作者： Sun, Yan Lang, Maoxiang Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ MOE Key Lab Urban Transportat Complex Syst Theory Beijing 100044 Peoples R China

We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1) multicommodity flow routing;(2) a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services;(3) carbon dioxide emissions consideration;and (4) a generalized costs optimum oriented to customer demands. The specific planning of freight routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.

关键词： multi-modal routing multi-commodity flow schedule-based service time-flexible service mixed integer nonlinear programming linearization method

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A new mathematical model for the Weber location problem with a probabilistic polyhedral barrier

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第20期51卷 6110-6128页

作者： Amiri-Aref, Mehdi Javadian, Nikbakhsh Tavakkoli-Moghaddam, Reza Baboli, Armand Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Univ Tehran Coll Engn Dept Ind Engn Tehran Iran Inst Natl Sci Appl DISP Lab F-69621 Villeurbanne France

With the wide application of location theory in a variety of industries, the presence of barriers merits the attention of managers and engineers. In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for the starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. In addition, a modification of the polyhedral barrier is presented which is equivalent to the original problem. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space into a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported.

关键词： Weber location problem polyhedral barrier mixed integer nonlinear programming optimisation

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Solving a dynamic separation problem using MINLP techniques

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APPLIED NUMERICAL MATHEMATICS 2008年第4期58卷 395-406页

作者： Emet, Stefan Westerlund, Tapio Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland Univ Turku Dept Math FIN-20014 Turku Finland

In the present paper a dynamic separation problem is modeled and solved using mixed integer nonlinear programming (MINLP) techniques. The objective is to maximize the profit for continuous cyclic operation, and at the same time, to find the optimal configuration for the separation column system. The dynamics of the chromatographic separation process are modeled as a boundary value problem which is solved, within the optimization, using an iterative finite difference method. The separation of a fructose-glucose mixture is solved using the Extended Cutting Plane (ECP) method. It is shown that the production planning can be done efficiently for different purity requirements, such that all the output of a system can be utilized. Using a process design that is optimized it is thus possible to use existing complex systems, or to design new systems, more efficiently and also to reduce the energy costs or the costs in general. The presented problem is a challenging application involving time-consuming calculations that, though the high capacity of todays computers, underlines the role of robust and fast numerical tools within optimization. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： mixed integer nonlinear programming chromatographic separation extended cutting plane method

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A multi-scenario and multi-objective scheduling optimization model for liquefied light hydrocarbon pipeline system

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2019年 141卷 566-579页

作者： Qiu, Rui Zhang, Haoran Gao, Xiaoyong Zhou, Xingyuan Guo, Zhichao Liao, Qi Liang, Yongtu China Univ Petr Beijing Key Lab Urban Oil & Gas Distribut Technol Fuxue Rd 18 Beijing 102249 Peoples R China Univ Tokyo Ctr Spatial Informat Sci 5-1-5 Kashiwanoha Kashiwa Chiba 2778568 Japan China Univ Petr Inst Ocean Engn Fuxue Rd 18 Beijing 102249 Peoples R China

The mixed transportation mode based pipeline system plays a significant role in the supply chain of liquefied light hydrocarbon. Inefficient scheduling may lead to problems of frequent pump stoppage/restart, high energy consumption, and frequent pressure fluctuation. To avoid these problems, this paper implements the discrete-time representation to develop a multi-scenario and multi-objective mixed integer nonlinear programming model to minimize the pump operation cost and the number of the switching operation. In the model, several factors, such as transportation mode, inventory limits of injection stations, flow rate and pressure limits of pipeline segments, are taken into consideration. Additionally, the uncertainty of the liquefied light hydrocarbon production is described by scenarios. The improved augmented epsilon-constraint method is implemented to solve this model. Finally, the model is successfully applied to a multi-source single-sink liquefied light hydrocarbon pipeline system in Daqing oilfield in China. The experimental results show that the proposed model outperforms another two available models in profit, safety, and robustness aspects. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Liquefied light hydrocarbon Pipeline system Scheduling Multi-scenario Multi-objective mixed integer nonlinear programming

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Reduced superstructure solution of MINLP problem in refinery hydrogen management

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2009年第22期34卷 9233-9238页

作者： Khajehpour, M. Farhadi, F. Pishvaie, M. R. Sharif Univ Technol Dept Chem & Petr Engn Tehran Iran

Minimizing Hydrogen waste into fuel gas within the H-2 network in a refinery is the objective function of an optimization problem in this paper. The superstructure obtained for a refinery wide concept, is first solved and validated for literature cases, then is reduced by heuristic rules, based on engineering judgment. The reduced superstructure contains all simulation procedures of pseudo-components definitions, fine tunings of all unit operations to reach actual operating conditions, reactions characterization, linear and nonlinear equalities and inequalities as system constraints. The set of governing equations are solved with Genetic Algorithm. Based on this optimization, in an Iranian refinery 22.6% reduction of H-2 production and a saving of 1.19 million $/year could be achieved. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

关键词： Optimization Hydrogen management Refinery Superstructure Reduced superstructure mixed integer nonlinear programming Genetic algorithm

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A bulk arrival queueing model with fuzzy parameters and varying batch sizes

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APPLIED MATHEMATICAL MODELLING 2006年第9期30卷 920-929页

作者： Chen, Shih-Pin Natl Chung Cheng Univ Dept Business Adm Chiayi 621 Taiwan

This paper develops a nonlinear programming approach to derive the membership functions of the steady-state performance measures in bulk arrival queueing systems with varying batch sizes, in that the arrival rate and service rate are fuzzy numbers. The basic idea is based on Zadeh's extension principle. Two pairs of mixed integer nonlinear programs (MINLP) with binary variables are formulated to calculate the upper and lower bounds of the system performance measure at possibility level alpha. From different values of alpha, the membership function of the system performance measure is constructed. For practice use, the defuzzification of performance measures is also provided via Yager ranking index. To demonstrate the validity of the proposed method, a numerical example is solved successfully. (c) 2005 Elsevier Inc. All rights reserved.

关键词： bulk arrival queue fuzzy sets mixed integer nonlinear programming

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Bus schedule coordination for the last train service in an intermodal bus-and-train transport network

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2015年 60卷 360-376页

作者： Dou, Xueping Meng, Qiang Guo, Xiucheng Southeast Univ Sch Transportat Nanjing 210096 Jiangsu Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

Only when a designated bus arrives at a particular bus stop (that connects to a rail station) earlier than the departure time of the associated last train by at least the necessary transfer walking time can passengers on the designated bus successfully access the rail network and finish the remainder of their trips by train. This paper first proposes an optimal bus schedule coordination problem for last train service in an intermodal bus-and-train transport network by offsetting and perturbing the original bus schedules to reduce transfer failures from bus service to train service based on the given last train schedules. The proposed problem is then formulated as a mixed integer nonlinear programming (MINLP) model. The MINLP model is equivalently transformed into a mixed integer linear programming (MILP) model that can be exactly solved by any optimization solvers, such as CPLEX. A case study based on eight real bus lines and the mass rapid transit (MRT) system in Singapore is conducted, and it shows that the bus schedule coordinated by the developed model is able to improve operational intermodal connectivity substantially. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Intermodal bus-and-train network Bus schedule coordination Last train Bus blockage mixed integer nonlinear programming mixed integer linear programming

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Optimization of an orbital long-duration rendezvous mission

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AEROSPACE SCIENCE AND TECHNOLOGY 2016年 58卷 482-489页

作者： Zhang, Jin Tang, Guo-jin Luo, Ya-zhong Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Hunan Peoples R China

The phasing segment of the rendezvous mission between a cargo spacecraft and a space station usually lasts for several weeks, and actually presents an orbital long-duration problem. In this study, this orbital long-duration problem is formulated as a mixed integer nonlinear programming (MINLP) problem in which the maneuver revolution numbers (integers), maneuver arguments of latitude and impulse magnitude are used as design variables at the same time. A hybrid approach is then proposed to solve this MINLP problem. First, a linear dynamics model considering the J(2) term of the Earth non-spherical gravity is employed to formulate an approximate phasing problem, which is optimized using a genetic algorithm. Second, a shooting iteration process considering the coupling effect between the in-plane and out-of-plane maneuvers is proposed to improve the approximate solution to satisfy the terminal conditions of the high-precision problem. The proposed approach is demonstrated for a typical two-week rendezvous phasing mission. The results show that the proposed approach can stably obtain the near optimal high-precision solution by integrating the perturbed trajectory only a few times. Furthermore, a long-duration rendezvous phasing plan is compatible with any initial phase angles that the in-plane velocity increment remains almost unchanged when the initial phase angle changes. However, under the same conditions, the out-of-plane velocity increment has considerable variations. Compared with a two-day rendezvous phasing plan, a two-week plan could have several successive coplanar launch opportunities for the chaser by aiming different terminal revolution numbers. (C) 2016 Elsevier Masson SAS. All rights reserved.

关键词： Orbital rendezvous Long-duration maneuvers mixed integer nonlinear programming Engineering optimization

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A reformulation framework for global optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第1期57卷 115-141页

作者： Lundell, Andreas Skjal, Anders Westerlund, Tapio Abo Akad Univ Ctr Excellence Optimizat & Syst Engn SF-20500 Turku Finland

In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are used to obtain the convex underestimators. For more general nonconvex functions two versions of the so-called alpha BB-underestimator, valid for twice-differentiable functions, are integrated in the actual reformulation framework. However, in contrast to what is done in branch-and-bound type algorithms, no direct branching is performed in the actual algorithm. Instead a piecewise convex reformulation is used to convexify the entire problem in an extended variable-space, and the reformulated problem is then solved by a convex MINLP solver. As the piecewise linear approximations are made finer, the solution to the convexified and overestimated problem will form a converging sequence towards a global optimal solution. The result is an easily-implementable algorithm for solving a very general class of optimization problems.

关键词： Global optimization Reformulation technique Convex underestimators mixed integer nonlinear programming Twice-differentiable functions Signomial functions Piecewise linear functions alpha BB-underestimator SGO-algorithm

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