Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transport...
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Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand quantities are fuzzy numbers. The idea is based on the extension principle. A pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level alpha. From different values of a, the membership function of the objective value is constructed. Two different types of the fuzzy transportation problem are discussed: one with inequality constraints and the other with equality constraints. It is found that the membership function of the objective value of the equality problem is contained in that of the inequality problem. Since the objective value is expressed by a membership function rather than by a crisp value, more information is provided for making decisions. (C) 2002 Elsevier B.V. All rights reserved.
A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not...
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A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not require a constraint qualification. Weak, strong, strict-converse, and converse duality theorems between primal and dual problems are established. (C) 2001 Elsevier Science Ltd. All rights reserved.
With the continuous improvement of computational performance, vehicle structural design has been addressed using computational methods, resulting in more efficient development of new vehicles. Most simulation-based op...
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With the continuous improvement of computational performance, vehicle structural design has been addressed using computational methods, resulting in more efficient development of new vehicles. Most simulation-based optimization approaches generate deterministic optimal designs without considering variability effects in modeling, simulation, and/or manufacturing. One of the main reasons for this omission is due to the fact that the computing time of a single crash analysis for vehicle structural design still requires significant computing time using a state-of-the-art computer. This calls for the development and implementation of an efficient optimization under uncertainty method. In this paper, a new integrated stochastic optimization method, which combines the advantages of metamodeling techniques and Better Optimization of nonlinear Uncertain Systems (BONUS), is developed for vehicle side impact design. nonlinear metamodels are built by using a stepwise regression method to replace the expensive computational model and BONUS is employed to obtain optimal designs under uncertainty. A benchmark problem for vehicle safety design is used to demonstrate the method. The main goal of this case study is to maintain or enhance the vehicle side impact test performance while minimizing the vehicle weight under various uncertainties.
Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable...
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Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable solution is obtained. We avoid this by formulating and solving the mesh design problem as a mathematical program. Our approach simultaneously modifies both mesh size (h) and local polynomial order (p) to yield an "optimal" mesh for a target error or given computational cost with gradients from local convergence rates. Constraints such as the one irregularity rule during mesh refinement are systematically incorporated in this formulation. The design task leads to a mixed integer nonlinear program (MINLP), that is relaxed to an NLP. To reduce the computations for the NLP, we employ simplified analytical gradients derived from initial mesh calculations. Finally, we apply our method to three model problems showing that complex hp-adaptive grids can be obtained directly from a uniform coarse grid. A commercial optimization software, MINOS [B.A. Murtagh, M.A. Saunders, MINOS 5.4 User's Guide, Technical Report SOL 83-20R, Stanford University, Stanford, 1987, Revised February 1995], was used as the NLP optimizer. (C) 2001 Elsevier Science B.V. All rights reserved.
We show that indefinitely preconditioned symmetric Krylov-subspace methods are very efficient for solving linearized KKT systems arising in equality constrained optimization. We give a numerical comparison of various ...
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We show that indefinitely preconditioned symmetric Krylov-subspace methods are very efficient for solving linearized KKT systems arising in equality constrained optimization. We give a numerical comparison of various Krylov subspace methods in three different forms (original system, null-space transformation, range-space transformation). Furthermore, we give a survey of our previous results concerning indefinite preconditioners and merit functions and prove new propositions.
作者：
Chen, ZWHan, JYXu, DCSuzhou Univ
Dept Math Suzhou 215006 Jingsu Province Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Inst Appl Math Beijing 100080 Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China
In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also p...
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In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient.
Using the so-called aggregate function of the constraints, a new aggregate constraint homotopy (ACH) is constructed and corresponding interior path following method for smooth programming is proposed. It was proved th...
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Using the so-called aggregate function of the constraints, a new aggregate constraint homotopy (ACH) is constructed and corresponding interior path following method for smooth programming is proposed. It was proved that under a weak normal cone condition, the ACH determines a smooth interior path from a given interior point to a K-K-T point. This forms the theoretical base of ACH method.
The optimal control theory can be applied to solve the optimization problems of dynamic system. Two major approaches which are used commonly to solve optimal control problems (OCP) are discussed in this paper. A numer...
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ISBN:
(纸本)0889864241
The optimal control theory can be applied to solve the optimization problems of dynamic system. Two major approaches which are used commonly to solve optimal control problems (OCP) are discussed in this paper. A numerical method based on discretization and nonlinear programming techniques is proposed and implemented an OCP solver. In addition, a systematic procedure for solving optimal control problems by using the OCP solver is suggested. Two various types of OCP, A flight level tracking problem and minimum time problem, are modeled according the proposed NLP formulation and solved by applying the OCP solver. The results reveal that the proposed method constitutes a viable method for solving optimal control problems.
A method for solving optimization problem with continuous parameters using improved ant colony algorithm is presented. In the method, groups of candidate values of the components are constructed, and each value in the...
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ISBN:
(纸本)3540239871
A method for solving optimization problem with continuous parameters using improved ant colony algorithm is presented. In the method, groups of candidate values of the components are constructed, and each value in the group has its trail information. In each iteration of the ant colony algorithm, the method first chooses initial values of the components using the trail information. Then, crossover and mutation can determine the values of the components in the solution. Our experimental results of the problem of nonlinear programming show that our method has much higher convergence speed and stability than that of GA, and the drawback of ant colony algorithm of not being suitable for solving continuous optimization problems is overcome.
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