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Optimal control problems with multiple characteristic time points in the objective and constraints

AUTOMATICA 2008年第11期44卷 2923-2929页

作者： Loxton, R. C. Teo, K. L. Rehbock, V. Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Control parametrization Optimal control computation non-linear optimal control Constrained optimal control non-linear programming

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To be fair or efficient or a bit of both

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COMPUTERS & OPERATIONS RESEARCH 2008年第12期35卷 3787-3806页

作者： Zukerman, Moshe Mammadov, Musa Tan, Liansheng Ouveysi, Iradj Andrew, Lachlan L. H. Univ Melbourne Dept Elect & Elect Engn ARC Special Res Ctr Ultra Broadband Informat Netw Melbourne Vic 3010 Australia Univ Ballarat Sch Informat Technol & Math Sci Ballarat Vic 3353 Australia Cent China Normal Univ Dept Comp Sci Wuhan 430079 Peoples R China CALTECH Dept Comp Sci Pasadena CA 91125 USA

Introducing a new concept of (alpha, beta)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 = 1, times its fair share, this paper provides a framework ... 详细信息

Introducing a new concept of (alpha, beta)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 <=alpha <= 1, not more than beta >= 1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (alpha, beta)-fairness constraints. This leads to what we call an efficiency-faimess function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well-known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of examples from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.(c) 2007 Elsevier Ltd. All rights reserved.

关键词： non-linear programming utility optimization fairness efficiency-fairness tradeoff bandwidth allocation

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Minimizing the object dimensions in circle and sphere packing problems

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COMPUTERS & OPERATIONS RESEARCH 2008年第7期35卷 2357-2375页

作者： Birgin, E. G. Sobral, F. N. C. Univ Sao Paulo IME Dept Comp Sci BR-05508090 Sao Paulo SP Brazil

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： packing of circles and spheres models algorithms non-linear programming

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Coupled hydrological-economic modelling for optimised irrigated cultivation in a semi-arid catchment of West Africa

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ENVIRONMENTAL MODELLING & SOFTWARE 2008年第4期23卷 385-395页

作者： Ahrends, H. Mast, M. Rodgers, Ch. Kunstmann, H. Inst Meteorol & Climate Res IMK IFU Forschungszentrum Karlsruhe D-82467 Garmisch Partenkirchen Germany Univ Bonn Ctr Res & Dev D-5300 Bonn Germany

A coupled model system, consisting of a distributed hydrological model and an economic optimisation model, communicating via model interfaces, is developed and applied to investigate regional interdependencies between irrigated agriculture and regional water balance and to identify optimised cultivation strategies. The coupled model is employed in the context of a case study in the Atankwidi catchment in the northern Guinea Sudan zone of West Africa. The physically based hydrologic model WaSiM [Schulla, J., Jasper, K., 2001] is used to simulate the water balance of this catchment including a small reservoir-irrigation system complex. The economics of irrigated crop cultivation are optimized under hydrological constraints using the non-linear optimisation model GAMS-ECIM, encoded in GAMS (General Algebraic Modelling System). The coupled model system is utilized for empirical model testing under fictitious scenarios involving variable water availability for irrigation. Interdependencies between irrigation water application quantities and the water balance were identified and maximum agricultural profit was calculated using the coupled model system. The coupled model system is designed as decision-support tool for local authorities and agricultural stakeholders in the Ghanaian Upper East Region (UER). (C) 2007 Elsevier Ltd. All rights reserved.

关键词： model coupling distributed hydrological modelling economic modelling non-linear programming irrigated agriculture decision support West Africa

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On the Algorithm of Determination of Immobile Indices for Convex SIP Problems

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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS 2008年第J08期13卷 13-33页

作者： Kostyukova, Olga I. Tchemisova, Tatiana V. Yermalinskaya, Svetlana A. Natl Acad Sci Belarus Inst Math Dept Math Syst Theory Surganov Str 11 Minsk 220072 BELARUS Univ Aveiro Dept Math P-3810193 Aveiro Portugal Belarussian State Univ Informat & Radioelect Dept Informat Minsk 220013 BELARUS

We consider convex Semi-Infinite programming (SIP) problems with a continuum of constraints. For these problems we introduce new concepts of immobility orders and immobile indices. These concepts are objective and important characteristics of the feasible sets of the convex SIP problems since they make it possible to formulate optimality conditions for these problems in terms of optimality conditions for some NLP problems (with a finite number of constraints). In the paper we describe a finite algorithm (DIO algorithm) of determination of immobile indices together with their immobility orders, study some important properties of this algorithm, and formulate the Implicit Optimality Criterion for convex SIP without any constraint qualification conditions (CQC). An example illustrating the application of the DIO algorithm is provided.

关键词： Convex Semi-Infinite programming non-linear programming optimality criterion constraint qualification condition immobile index immobility order

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Optimization and guidance of very low-thrust transfers to geostationary orbit

Optimization and guidance of very low-thrust transfers to ge...

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57th International Astronautical Congress

作者： Gil-Fernandez, Jesus Tarabini, Lorenzo Graziano, Mariella Gomez-Tierno, M. A. GMV SA Madrid 28760 Spain

A new hybrid direct-indirect optimization algorithm is presented to compute the minimum-time transfer between two orbits, including the phasing with a desired spacecraft. Very-low thrust means several hundred revolutions to perform the large change in orbital elements. The optimal control solution of the fast-evolution problem combined with a direct method for the secular trajectory avoids the numerical instability arising in very long propagations, decreases the computational time, reduces the sensitivity to the initial guess and provides a feasible transfer at every optimization step. Optimization of transfers from GTO to GEO is presented and two types of trajectories are analysed, sub-synchronous (apogee constrained below GEO altitude) and super-synchronous (free apogee altitude). The optimization of a transfer from LEO to a very high orbit (11 ' 23 R E) is presented, showing the applicability of the method to different problems. A guidance algorithm is presented to compensate the deviations of the real trajectory from the optimal one due to off-nominal conditions. The results in closed-loop simulation of the guidance scheme to compensate detenninistic perturbations not considered in the optimization show good performances in both analysed missions.

关键词： trajectory optimization low-thrust optimal control non-linear programming guidance

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Security Constrained Economic Dispatch with Secure Bilateral Transactions in Hybrid Electricity Markets

Security Constrained Economic Dispatch with Secure Bilateral...

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Joint International Conference on Power Systems Technology (POWERCON)/IEEE Power India Conference

作者： Kumar, Ashwani Chanana, Saurabh Natl Inst Technol Kurukshetra Dept Elect Engn Kurukshetra Haryana India

ISBN: (纸本)9781424417636

This paper proposes security constrained economic power dispatch (SCED) of the generators in the presence of secure bilateral transactions for hybrid electricity markets. The proposed non-linear optimization problem considers simultaneous minimization of deviations from scheduled transactions and minimization of fuel cost of the generators. The impact of bilateral transactions on fuel costs of generators and generation pattern has also been studied. The proposed technique has been applied on IEEE 24-bus reliability test system (IRTS).

关键词： non-linear programming secure transaction matrix security constrained economic dispatch transaction matrix pattern

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Optimization based cost comparison between reinforced concrete and steel beams

Optimization based cost comparison between reinforced concre...

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4th International Conference on High Performance Structures and Materials

作者： Merta, I. Kravanja, S. Klansek, U. Vienna Univ Technol Inst Bldg Consturct & Technol A-1060 Vienna Austria Univ Maribor Fac Civil Engn Maribor Slovenia

ISBN: (纸本)9781845641061

This paper presents the optimization based cost comparison between reinforced concrete and doubly-symmetrical welded steel I beams. The task of the research was to define the spans at which each of two different considered structures would show its advantages. The optimization/comparison was performed for simply supported beams for spans between 5 and 30 meters and for a uniformly distributed variable imposed load of 5 kN/m. The structural optimization was performed by the nonlinear programming (NLP) approach. The cost objective function was defined for the optimization and subjected to structural analysis constraints. The structures were designed in accordance with Eurocodes for both the ultimate and serviceability limit states. Beside the optimal self-manufacturing costs, the results also include the optimal masses for the different considered structures.

关键词： structural optimization non-linear programming reinforced concrete beams steel beams

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Real-Coded Genetic Algorithm for Solving Generalized Polynomial programming Problems

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JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2007年第4期11卷 358-364页

作者： Wu, Jui-Yu Chung, Yun-Kung Yuan Univ Dept Ind Engn & Management 135 Yuan Tung Rd Chungli 320 Taiwan

Generalized polynomial programming (GPP) is a non-linear programming (NLP) method based on a non-convex objective function, which is subject to nonconvex inequality constraints. Hence, a GPP problem has multiple local optima in its constrained solution space. General NLP techniques use local optimization, and therefore do not easily solve GPP problems. Some deterministic global optimization approaches have been developed to overcome this drawback of NLP methods. Although these approaches yield a global solution to a GPP problem, they can be mathematically tedious. Therefore, this study presents a real-coded genetic algorithm (RGA), which is a stochastic global optimization method, to find a global solution to a GPP problem. The proposed RGA is used to solve a set of GPP problems. The best solution obtained by the RGA is compared with the known global solution to each test problem. Numerical results show that the proposed RGA converges to a global solution to a GPP problem.

关键词： generalized polynomial programming non-linear programming genetic algorithm

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On retrial queueing model with fuzzy parameters

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2007年第1期374卷 272-280页

作者： Ke, Jau-Chuan Huang, Hsin-I Lin, Chuen-Horng Natl Taichung Inst Technol Dept Informat Management Taichung 404 Taiwan Natl Taichung Inst Technol Dept Stat Taichung 404 Taiwan

This work constructs the membership functions of the system characteristics of a retrial queueing model with fuzzy customer arrival, retrial and service rates. The a-cut approach is used to transform a fuzzy retrial-queue into a family of conventional crisp retrial queues in this context. By means of the membership functions of the system characteristics, a set of parametric non-linear programs is developed to describe the family of crisp retrial queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, more information is provided for use by management. By extending this model to the fuzzy environment, fuzzy retrial-queue is represented more accurately and analytic results are more useful for system designers and practitioners. (c) 2006 Elsevier B.V. All rights reserved.

关键词： fuzzy parameters membership functions non-linear programming retrial queue

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