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A continuous strategy to solve a class of mixed optimization problems

DISCRETE APPLIED MATHEMATICS 2014年第Part1期164卷 264-275页

作者： do Nascimento, Roberto Quirino Lima, Edson Figueiredo, Jr. de Oliveira Santos, Rubia Mara Univ Fed Paraiba Dept Stat BR-58059900 Joao Pessoa Paraiba Brazil Univ Fed Paraiba Dept Math BR-58059900 Joao Pessoa Paraiba Brazil Univ Fed Mato Grosso do Sul Dept Math Campo Grande MS Brazil

This work presents a method to solve a class of discrete optimization problems, including linear, quadratic, convex, and discrete geometric programming problems. The methodology consists of inserting, in the original problem, additional geometric constraints where any viable solution is also discrete. Moreover, a strategy to solve signomial geometric programming problems is developed. Computational results are shown through some examples of facility location, machining economics and economic order quantity problems. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Global optimization Discrete optimization generalized geometric programming Facility location problems

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A continuous strategy to solve a class of mixed optimization problems

A continuous strategy to solve a class of mixed optimization...

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1st International Symposium on Combinatorial Optimization (ISCO)

关键词： Global optimization Discrete optimization generalized geometric programming Facility location problems

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A global optimization using linear relaxation for generalized geometric programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第2期190卷 345-356页

作者： Qu, Shaojian Zhang, Kecun Wang, Fusheng Xian Jiaotong Univ Fac Sci Xian 710049 Peoples R China

Many local optimal solution methods have been developed for solving generalized geometric programming (GGP). But up to now, less work has been devoted to solving global optimization of (GGP) problem due to the inherent difficulty. This paper considers the global minimum of (GGP) problems. By utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex (GGP) problem is reduced to a sequence of linear programming problems. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of (GGP) on a microcomputer. (C) 2007 Elsevier B.V. All rights reserved.

关键词： generalized geometric programming global optimization linear relaxation branch and bound

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A robust algorithm for generalized geometric programming

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JOURNAL OF GLOBAL OPTIMIZATION 2008年第4期41卷 593-612页

作者： Shen, Peiping Ma, Yuan Chen, YongQiang Henan Normal Univ Coll Mat & Informat Sci Xinxiang 453007 Peoples R China

Most existing methods of global optimization for generalized geometric programming (GGP) actually compute an approximate optimal solution of a linear or convex relaxation of the original problem. However, these approaches may sometimes provide an infeasible solution, or far from the true optimum. To overcome these limitations, a robust solution algorithm is proposed for global optimization of (GGP) problem. This algorithm guarantees adequately to obtain a robust optimal solution, which is feasible and close to the actual optimal solution, and is also stable under small perturbations of the constraints.

关键词： generalized geometric programming robust solution global optimization essential optimal solution monotonic optimization

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Global Optimization of Robot Control System Via generalized geometric programming

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1st International Conference Intelligent Robotics and Applications

作者： Gong, Jing Jia, Ruiqing NE Dianli Univ Sch Civil Engn Jilin 132012 Peoples R China

ISBN: (纸本)9783540885160

A model of the robot control system can be described as a generalized geometric programming problem. The objection is to minimize the error subject to stability and torque constraints. A global optimization approach of generalized geometric programming has been used for solving the model. The relationships of sampling tithe versus the proportional gain (K-p), integral gain K-i, and the derivative gain K-v are studied. It is showed that the values of the control parameters (K-p, K-i, K-v) decrease as the sampling time increases before becoming flat. It is also concluded that generalized geometric programming is an efficient mathematical technique for the nonlinear control of robotic system.

关键词： global optimization robot control generalized geometric programming

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On generalized geometric programming problems with non-positive variables

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期178卷 10-19页

作者： Tsai, Jung-Fa Lin, Ming-Hua Hu, Yi-Chung Natl Taipei Univ Technol Dept Business Management Taipei 10608 Taiwan Shih Chien Univ Dept Informat Management Taipei 10462 Taiwan Chung Yuan Christian Univ Dept Business Adm Chungli 32023 Taiwan

generalized geometric programming (GGP) problems occur ' frequently in engineering design and management. Some exponential-based decomposition methods have been developed for solving global optimization of GGP problems. However, the use of logarithmic/exponential transformations restricts these methods to handle the problems with strictly positive variables. This paper proposes a technique for treating non-positive variables with integer powers in GGP problems. By means of variable transformation, the GGP problem with non-positive variables can be equivalently solved with another one having positive variables. In addition, we present some computationally efficient convexification rules for signornial terms to enhance the efficiency of the optimization approach. Numerical examples are presented to demonstrate the usefulness of the proposed method in GGP problems with non-positive variables. (c) 2006 Elsevier B.V. All rights reserved.

关键词： global optimization generalized geometric programming non-positive variables convexification

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A GGP Approach to Solve Non Convex Min-max Predictive Controller for a Class of Constrained MIMO Systems Described by State-space Models

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2011年第3期9卷 452-460页

作者： Kheriji, Amira Bouani, Faouzi Ksouri, Mekki Natl Engn Sch Tunis Lab Anal & Control Syst ACS Tunis 1002 Tunisia

This paper proposes a new method to solve non convex min-max predictive controller for a class of constrained linear Multi Input Multi Output (MIMO) systems. A parametric uncertainty state space model is adopted to describe the dynamic behavior of the real process. Moreover, the output deviation method is used to design the j-step ahead output predictor. The control law is obtained by the resolution of a non convex min-max optimization problem under input constraints. The key idea is to transform the initial non convex optimization problem to a convex one by means of variable transformations. To this end, the generalized geometric programming (GGP) which is a global deterministic optimization method is used. An efficient implementation of this approach will lead to an algorithm with a low computational burden. Simulation results performed on Multi Input Multi Output (MIMO) system show successful set point tracking, constraints satisfaction and good non-zero disturbance rejection.

关键词： Constrained control disturbance rejection generalized geometric programming MIMO systems parametric uncertainty predictive control set point tracking state space model

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A new rectangle branch-and-pruning approach for generalized geometric programming

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期183卷 1027-1038页

作者： Shen, Peiping Jiao, Hongwei Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Peoples R China Henan Inst Sci & Technol Dept Math Xinxiang 453003 Peoples R China

generalized geometric programming (GGP) problem occurs frequently in engineering design and management. In this paper, a branch-and-pruning global optimization algorithm is proposed for GGP. By utilizing some transformations, a linear relaxation of the problem (GGP) is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region. Then a new pruning technique is given to accelerate the convergence of the given algorithm, and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution. The proposed algorithm which connects branch-and-bound method with the pruning technique successfully is convergent to the global minimum, according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm. (c) 2006 Elsevier Inc. All rights reserved.

关键词： generalized geometric programming global optimization pruning technique linear relaxation branch-and-bound

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Coverage-Time Optimization for Clustered Wireless Sensor Networks: A Power-Balancing Approach

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IEEE-ACM TRANSACTIONS ON NETWORKING 2010年第1期18卷 202-215页

作者： Shu, Tao Krunz, Marwan Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA

In this paper, we investigate the maximization of the coverage time for a clustered wireless sensor network by optimal balancing of power consumption among cluster heads (CHs). Clustering significantly reduces the energy consumption of individual sensors, but it also increases the communication burden on CHs. To investigate this tradeoff, our analytical model incorporates both intra- and intercluster traffic. Depending on whether location information is available or not, we consider optimization formulations under both deterministic and stochastic setups, using a Rayleigh fading model for intercluster communications. For the deterministic setup, sensor nodes and CHs are arbitrarily placed, but their locations are known. Each CH routes its traffic directly to the sink or relays it through other CHs. We present a coverage-time-optimal joint clustering/routing algorithm, in which the optimal clustering and routing parameters are computed using a linear program. For the stochastic setup, we consider a cone-like sensing region with uniformly distributed sensors and provide optimal power allocation strategies that guarantee (in a probabilistic sense) an upper bound on the end-to-end (inter-CH) path reliability. Two mechanisms are proposed for achieving balanced power consumption in the stochastic case: a routing-aware optimal cluster planning and a clustering-aware optimal random relay. For the first mechanism, the problem is formulated as a signomial optimization, which is efficiently solved using generalized geometric programming. For the second mechanism, we show that the problem is solvable in linear time. Numerical examples and simulations are used to validate our analysis and study the performance of the proposed schemes.

关键词： Clustering coverage time generalized geometric programming linear programming sensor networks signomial optimization topology control

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A continuous strategy to solve a class of discrete optimization problems

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Electronic Notes in Discrete Mathematics 2010年第C期36卷 279-286页

作者： Quirino do Nascimento, Roberto Figueiredo Lima, Edson de Oliveira Santos, Rubia Mara Department of Statistics Universidade Federal da Paraíba (UFPB) Paraíba Brazil Department of Mathematics Universidade Federal da Paraíba (UFPB) Paraíba Brazil Department of Mathematics Universidade Federal do Mato Grossso do Sul (UFMS) Mato Grosso do Sul Brazil

In this work we develop a method to solve a class of discrete optimization problems. This class covers linear, quadratic, convex, and discrete geometric programming problems. The methodology consists in inserting additional geometric constraints where any viable solution is also discrete. Moreover, we also adopt a methodology for solution of signomial geometric programming problems and solve the problem. We present some examples of facility location problems and the results obtained. © 2010 Elsevier B.V.

关键词： Discrete Optimization Facility Location Problems generalized geometric programming Global Optimization

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