In this paper, the goal is to incorporate qualitative criteria in addition to quantitative criteria to facility layout design (FLD) problem. To this end, we present an integrated methodology based on the synthetic val...
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In this paper, the goal is to incorporate qualitative criteria in addition to quantitative criteria to facility layout design (FLD) problem. To this end, we present an integrated methodology based on the synthetic value of fuzzy judgments and nonlinear programming (SVFJ-NLP). The facility layout patterns (FLPs) together with their performance measures of total cost of material handling are generated by a computer-aided layout-design tool, CRAFT. Also, the performance measures of second quantitative criterion (construction cost of width walls) are calculated by appraising these FLPs. The SVFJ is then applied to collect the performance measures related to qualitative criteria and finally, a non-linear programming (NLP) model is proposed to solve the FLD. Results obtained from a real case study validate the effectiveness of the proposed model. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(...
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In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (eta(i))(i) assumption. The equivalence between saddle points and optima, and a characterization of optimal solutions are established under suitable generalized invexity requirements. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual. It is shown in this study, with examples, that the introduced generalized Fritz John condition combining with the invexity with respect to different (eta(i))(i) are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is t...
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In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques: (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown;(c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems. (C) 2003 Elsevier Science Ltd. All rights reserved.
In this paper, a mixed integer nonlinear programming model is proposed to concurrently design two segments (i.e., upstream and midstream) of crudel oil supply chain. The network includes all entities and their connect...
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In this paper, a mixed integer nonlinear programming model is proposed to concurrently design two segments (i.e., upstream and midstream) of crudel oil supply chain. The network includes all entities and their connections from oil wells to product depots. Furthermore, a real world example is applied to show the improved model application. Furthermore, a sensitivity analysis in which +/- 20% deviations at a time were placed on two parameters is presented. Also, model performance is analyzed with GAMS 22.6. The proposed multiperiod and multiproduct model consists of several decisions (i.e., oil field development, transformation, transportation, and distribution). The main contributions of this work are inclusion of all entities related to upstream and midstream segments and both oil field development and transformation planning, simultaneously. Finally, it is shown that a decrease in production cost of refinery products will lead to more net profit given all refinery production capacity are used. Also, increase in refinery production capacity will improve network net profit given new fixed cost investment is not applied (e.g., refineries and transportation modes). This is the first study that simultaneously considers and optimizes upstream and midstream of crude oil supply chain. Second, it presents a unique mathematical model. Third, all features and parameters are included. Fourth, it is practical and may be used for other crude oil supply chain.
CNC lathes often use hydraulic systems or motors to lock the turret, which causes the turret to have a high temperature rise and a large thermal deformation. The traditional measuring method couples the thermal distor...
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CNC lathes often use hydraulic systems or motors to lock the turret, which causes the turret to have a high temperature rise and a large thermal deformation. The traditional measuring method couples the thermal distortions of the spindle and the turret together, which is not conducive to establishing the thermal error model. To solve this problem, a new measuring method was used in this research to decouple the thermal linear and angular distortions of the spindle and the turret. In addition, constraints on the model coefficients were proposed by studying the effects of long-term and short-term variations in ambient temperature on the thermal deformation of machine tools, thus transforming the thermal deformation modeling of the spindle and turret into nonlinear programming problems. After building the thermal deformation models of the spindle and the turret, the thermal distortion model of the whole machine tool was obtained by combining them. Finally, three experiments were designed to verify the validity of the established models, and the models were compared with those established using conventional methods. The experimental results showed that the models built based on thermal distortion decoupling and nonlinear programming had higher accuracy and robustness.
A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus...
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A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear programming problem, which is solved numerically. This paper identifies this method as being of a general class of direct transcription methods and proceeds to investigate the relationship between the original optimal control problem and the approximating nonlinear programming problem, by comparing the optimal control necessary conditions with the optimality conditions for the discretized problem. Attention is focused on the Lagrange multipliers of the nonlinear programming problem, which are shown to be discrete approximations to the adjoint variables of the optimal control problem. This relationship is exploited to test the adequacy of the discretization and to verify optimality of assumed control structures. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme that discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-bum rendezvous, and a low-thrust transfer to the moon.
In this paper, a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming, limit analysis and the conventional disp...
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In this paper, a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming, limit analysis and the conventional displacement-based finite element method. The analysis is based on a general yield function which can take the form of the Mohr Coulomb or Drucker-Prager criterion. By using an associated flow rule, a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization. The plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained. The nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation. The calculation is based entirely on kinematically admissible velocities without calculation of the stress field. The finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint. The objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load. An effective, direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem. The effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples. (c) 2005 Elsevier Ltd. All rights reserved.
Moving horizon estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has bee...
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Moving horizon estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this bottleneck is proposed. The strategy exploits recent advances in nonlinear programming algorithms and sensitivity concepts. A detailed analysis of the optimality conditions of MHE problems is presented. As a result, strategies for fast covariance information extraction from general nonlinear programming algorithms are derived. It is shown that highly accurate state estimates can be obtained in large-scale MHE applications with negligible on-line computational costs.. (C) 2008 Elsevier Ltd. All rights reserved.
The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior-point methods for linear and quadratic programming. Major modifications include a merit funct...
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The paper describes an interior-point algorithm for nonconvex nonlinear programming which is a direct extension of interior-point methods for linear and quadratic programming. Major modifications include a merit function and an altered search direction to ensure that a descent direction for the merit function is obtained. Preliminary numerical testing indicates that the method is robust. Further, numerical comparisons with MINOS and LANCELOT show that the method is efficient, and has the promise of greatly reducing solution times on at least some classes of models.
One of the main objectives in tolerance charting is to determine the working dimensions and tolerances at the lowest cost without violating the blueprint specifications. In view of this, this paper presents a simple d...
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One of the main objectives in tolerance charting is to determine the working dimensions and tolerances at the lowest cost without violating the blueprint specifications. In view of this, this paper presents a simple dimensional chains identification method. After establishing all necessary equations and constraints, a nonlinear objective function is formulated. Subsequently, all these relationships are submitted to an optimisation software, OPTIVAR written in FORTRAN for the determination of the unknown variables. In addition, an example is incorporated to demonstrate the effectiveness of this proposed methodology.
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