Traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis. Interior point methods, however, do not converge to a basic solution (vertex) in general Recently., there a...
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Traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis. Interior point methods, however, do not converge to a basic solution (vertex) in general Recently., there appeared new techniques in sensitivity analysis, which consist in preserving so called support set invariancy and optimal partition invariancy. This paper reflects the renascence of sensitivity and parametric analysis and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does. We present a description of the set of admissible parameters under the mentioned invariances, and compare them with the classical optimal basis concept. (C) 2009 Elsevier B.V. All rights reserved.
Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been...
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Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been developed for treating uncertainty in the setting of optimization problems with vague constraints. In this paper, a new method is presented into creation fuzzy concept for set of constraints. Unlike to existing methods, instead of constraints with fuzzy inequalities or fuzzy coefficients or fuzzy numbers, vague nature of constraints set is modeled using learning scheme with adaptive neural-fuzzy inference system (ANFIS). In the proposed approach, constraints are not limited to differentiability, continuity, linearity;also the importance degree of each constraint can be easily applied. Unsatisfaction of each weighted constraint reduces membership of certainty for set of constraints. Monte-Carlo simulations are used for generating feature vector samples and outputs for construction of necessary data for ANFIS. The experimental results show the ability of the proposed approach for modeling constrains and solving parametric programming problems. (c) 2010 Elsevier Inc. All rights reserved.
Almost all dynamic production systems are subject to lagged productive effects, which are an often-ignored latent source of interference in the efficiency measuring process. Existing data envelopment analysis (DEA) ap...
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Almost all dynamic production systems are subject to lagged productive effects, which are an often-ignored latent source of interference in the efficiency measuring process. Existing data envelopment analysis (DEA) approaches rely on a static production environment. They can easily lead to biased evaluation results due to the erroneous assumption. To tackle this issue, this paper develops a dynamic DEA model that allows intertemporal effects in efficiency measuring. Specifically, the dynamic DEA model incorporates dynamic factors via a linear parametric formulation. Our model can be applied in place of static DEA models to a wide range of applications, such as analyzing longitudinal firm performance and productivity changes. As for the empirical efficiencies, we demonstrate how the lag parameters in the dynamic model can be estimated by the panel vector autoregressive model (PVAR). We use our methodology to evaluate advertising efficiencies of several major automobile and pharmaceutical firms in North America. The result shows that using static DEA in dynamic production can lead to both rank reversals and changes in efficiency scores. (C) 2009 Elsevier B.V. All rights reserved.
This paper proposes a novel approach for the aggregate production planning (APP) problem with fuzzy parameters. Different from the results of previous studies, in this paper the membership function of the fuzzy minima...
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This paper proposes a novel approach for the aggregate production planning (APP) problem with fuzzy parameters. Different from the results of previous studies, in this paper the membership function of the fuzzy minimal total cost is constructed based on Zadeh's extension principle and fuzzy solutions are provided. A pair of mathematical programs parameterised by possibility level is formulated to calculate the lower and upper bounds of the fuzzy total cost at . By enumerating different values of , the membership function of the fuzzy total cost is constructed. To illustrate the validity of the proposed approach, the example studied by Lai and Hwang (1992) using Chanas's approach is investigated. Since the objective value is expressed by a membership function rather than by a crisp value, the proposed approach can represent APP systems more accurately, thus obtained solutions which contain more information can offer more chance to achieve the feasible disaggregate plan, and it is beneficial to the decision-maker in practical applications. The proposed approach can also be applied to APP problems with other characteristics.
Fuzzy multi-state system (FMSS) is defined as a multi-state system (MSS) consisting of multi-state elements (MSE) whose performance rates and transition intensities are presented as fuzzy values. Due to the lack, inac...
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Fuzzy multi-state system (FMSS) is defined as a multi-state system (MSS) consisting of multi-state elements (MSE) whose performance rates and transition intensities are presented as fuzzy values. Due to the lack, inaccuracy or fluctuation of data, it is oftentimes impossible to evaluate the performance rates and transition intensities of MSE with precise values. This is true especially in continuously degrading elements that are usually simplified to MSE for computation convenience. To overcome these challenges in evaluating the behaviour of MSS, fuzzy theory is employed to facilitate MSS reliability assessment. Given the fuzzy transition intensities and performance rates, the state probabilities of MSE and MSS are also fuzzy values. A fuzzy continuous-time Markov model with finite discrete states is proposed to assess the fuzzy state probability of MSE at any time instant. The universal generating function with fuzzy state probability function and performance rate is applied to evaluate fuzzy state probability of MSS in accordance with the system structure. A modified FMSS availability assessment approach is introduced to compute the system availability under the fuzzy user demand. In order to obtain the membership functions of the indices of interest, parametric programming technique is employed according to Zadeh's extension principle. The effectiveness of the proposed method is illustrated and verified via reliability assessment of a multi-state power generation system.
In this paper, primal-dual methods for general nonconvex nonlinear optimization problems are considered. The proposed methods are exterior point type methods that permit primal variables to violate inequality constrai...
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In this paper, primal-dual methods for general nonconvex nonlinear optimization problems are considered. The proposed methods are exterior point type methods that permit primal variables to violate inequality constraints during the iterations. The methods are based on the exact penalty type transformation of inequality constraints and use a smooth approximation of the problem to form primal-dual iteration based on Newton's method as in usual primal-dual interior point methods. Global convergence and local superlinear/quadratic convergence of the proposed methods are proved. For global convergence, methods using line searches and trust region type searches are proposed. The trust region type method is tested with CUTEr problems and is shown to have similar efficiency to the primal-dual interior point method code IPOPT. It is also shown that the methods can be warm started easily, unlike interior point methods, and that the methods can be efficiently used in parametric programming problems.
This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is...
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ISBN:
(纸本)9783642134975
This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is defined by Lebesgue-Stieltjes (L-S) integral, its computation for general fuzzy variables is a challenge issue for research, and usually depends on approximation scheme and soft computing. But for frequently used trapezoidal and triangular fuzzy variables, the spread can be represented as quadratic functions with respect to fuzzy parameters. These new representations facilitate us to turn the proposed E-S model into its equivalent parametric programming problem. As a consequence, given the fuzzy parameters, the E-S model becomes a. quadratic programming problem that can be solved by general purpose software or conventional optimization algorithms. Finally, we demonstrate the developed modeling idea via two numerical examples.
A new machining feature model for cylinder-type parts is proposed. Through the use of the model in process planning, the NC program can be generated by modular approach. NC machining feature classification based proce...
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ISBN:
(纸本)9780878492497
A new machining feature model for cylinder-type parts is proposed. Through the use of the model in process planning, the NC program can be generated by modular approach. NC machining feature classification based process design method is a good solution to the integration of the traditional and NC processes. With the machining feature as unit, parametric programming technique is applied to the NC code generation which can improve the efficiency and quality of the NC program design. The proposed method has been practically demonstrated in the enterprise information system.
Two algorithms for the general case of parametric mixed-integer linear programs (MILPs) are proposed. parametric MILPs are considered in which a single parameter call simultaneously influence the objective function, t...
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Two algorithms for the general case of parametric mixed-integer linear programs (MILPs) are proposed. parametric MILPs are considered in which a single parameter call simultaneously influence the objective function, the right-hand side and the matrix. The first algorithm is based oil branch-and-bound oil the integer variables, solving a parametric linear program (LP) at each node. The second algorithm is based oil the optimality range of a qualitatively invariant solution, decomposing the parametric optimization problem into a series of regular MILPs, parametric LPs and regular mixed-integer nonlinear programs (MINLPs). The number of subproblems required for a particular instance is equal to the number of critical regions. For the parametric LPs an improvement of the well-known rational simplex algorithm is presented, that requires less consecutive operations oil rational functions. Also, an alternative based on predictor-corrector continuation is proposed. Numerical results for a test set are discussed. (C) 2008 Elsevier B.V. All rights reserved.
An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current ...
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An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current blood glucose concentration of the patient by using novel parametric programming algorithms, developed at Imperial College London. The implementation of the optimal insulin delivery rate, therefore, requires simple function evaluation and minimal on-line computations. The proposed framework also addresses the uncertainty in the model due to interpatient and intrapatient variability by identifying the model parameters which ensure that a feasible control law can be obtained. The developments reported in this paper are expected to simplify the insulin delivery mechanism, thereby enhancing the quality of life of the patient.
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