A novel sequential approach for solving dynamic optimization problems containing path constraints on state variables is presented and its performance analyzed. As in the simultaneous approach, we discretize both state...
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A novel sequential approach for solving dynamic optimization problems containing path constraints on state variables is presented and its performance analyzed. As in the simultaneous approach, we discretize both state and control variables using collocation on finite elements, so that path constraints can be guaranteed inside each element. The state variables are solved in a manner similar to that in the sequential approach;this eliminates the discretized differential-algebraic equations and state variables, so that the problem is reduced to a smaller problem only with inequality constraints and control variables. Therefore, it possesses advantages of both the simultaneous and the sequential approach. Furthermore, the elimination of the equality constraints substantially simplifies the line search problem and thus larger steps can be taken by successive quadratic programming (SQP) toward the optimum. We call this dynamic optimization method a quasi-sequential approach. We compare this new approach with the simultaneous approach in terms of computational cost and by analyzing the solution path. A highly nonlinear reactor control and the optimal operation of a heat-integrated column system are used to demonstrate the effectiveness of this approach. As a result, it can be concluded that this quasi-sequential approach is well suited for solving highly nonlinear large-scale optimal control problems. (c) 2005 American Institute of Chemical Engineers.
Hierarchical structures have been introduced in the literature to deal with the dimensionality problem, which is the main drawback to the application of neural networks and fuzzy models to modeling and control of larg...
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Hierarchical structures have been introduced in the literature to deal with the dimensionality problem, which is the main drawback to the application of neural networks and fuzzy models to modeling and control of large-scale systems. In the present work, hierarchical neural fuzzy (HNF) models are reviewed, focusing on the model-based control of a biotechnological process. The model considered here consists of a set of neural fuzzy systems connected in cascade and is used in the modeling of an industrial plant for ethyl alcohol ( ethanol) production. Based on the HNF model of the process, a nonlinear model predictive controller (HNF-MPC) is designed and applied to control the process. The performance of the HNF-MPC is illustrated within servo and regulatory scenarios.
We consider a supply chain, which consists of several retailers and one supplier. The retailers, who possibly differ in their cost and demand parameters, may be coordinated through replenishment strategies and transsh...
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We consider a supply chain, which consists of several retailers and one supplier. The retailers, who possibly differ in their cost and demand parameters, may be coordinated through replenishment strategies and transshipments, that is, movement of a product among the locations at the same echelon level. We prove that in order to minimize the expected long-run average cost for this system, an optimal replenishment policy is for each retailer to follow an order-up-to S policy. Furthermore, we demonstrate how the values of the order-up-to quantities can be calculated using a sample-path-based optimization procedure. Given an order-up-to S policy, we show how to determine an optimal transshipment policy, using a linear programming/network flow framework. Such a combined numerical approach allows us to study complex and large systems.
Case-series analysis is used to estimate relative incidences of clinical events in defined time intervals after vaccination compared to a control period. It has advantages, in terms of both a reduction in data collect...
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Case-series analysis is used to estimate relative incidences of clinical events in defined time intervals after vaccination compared to a control period. It has advantages, in terms of both a reduction in data collection effort, because it uses only data on cases, and a reduction in the resultant variances of estimates, due to individuals being self-controlled. The existence and uniqueness of relative incidence estimates in case-series analysis are investigated. For the relative incidence of a clinical event, a simple condition for existence and uniqueness of the estimate of the parameter vector in a case-series model is established. An algorithm is developed to examine the established condition, which provides a clue for remedy when the condition for existence and uniqueness is not satisfied. (C) 2005 Elsevier B.V. All rights reserved.
We study optimal age-replacement policies for machines in series with non-instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost-rate subject to a steady-state throughput requi...
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We study optimal age-replacement policies for machines in series with non-instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost-rate subject to a steady-state throughput requirement and another that maximizes steady-state throughput subject to a cost-rate budget constraint. Under reasonable assumptions, the single-machine cost-optimal and throughput-optimal solutions are unique and orderable, and the multi-machine optimal solutions have appealing structure. Furthermore, we establish equivalence between the two formulations and provide an illustrative numerical example. (C) 2006 Wiley Periodicals, Inc.
Genetic algorithms are nature-inspired heuristics for search and optimization. The key to success lies in focusing the search space on a feasible region where a global optimum is located. This study investigates an ap...
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Genetic algorithms are nature-inspired heuristics for search and optimization. The key to success lies in focusing the search space on a feasible region where a global optimum is located. This study investigates an approach that adaptively shifts and shrinks the size of the search space of the feasible region by employing feasible and infeasible solutions in the population to reach the global optimum. Several test cases demonstrate the ability of this approach to improve significantly the speed of convergence to the global optimum with reasonable precision. (c) 2005 Elsevier B.V. All rights reserved.
In this paper an algorithm based on simulated annealing is developed to solve time optimal control problems (t-OCPs). In the beginning, a procedure that a t-OCP is converted into a nonlinear programming problem by par...
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In this paper an algorithm based on simulated annealing is developed to solve time optimal control problems (t-OCPs). In the beginning, a procedure that a t-OCP is converted into a nonlinear programming problem by parametrizing the control input and the time horizon is demonstrated. Then, all the unspecified parameters embedded in the converted problem, including the discretized control inputs and the associated time grids, are optimized by the proposed algorithm. For demonstrating the efficiency of our algorithm in the optimization, four typical examples are provided.
The time-optimal control problem of a hovering quad-rotor helicopter is addressed in this paper. Instead of utilizing the Pontryagin's Minimum Principle (PMP), in which one needs to solve a set of highly nonlinear...
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The time-optimal control problem of a hovering quad-rotor helicopter is addressed in this paper. Instead of utilizing the Pontryagin's Minimum Principle (PMP), in which one needs to solve a set of highly nonlinear differential equations, a nonlinear programming (NLP) method is proposed. In this novel method, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. The optimization object is to minimize the sampling period such that it will be below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the formulated NLP problem, genetic algorithms (GAs) are adopted. With the proposed method, one can find a time-optimal movement of the helicopter between two configurations. To show the feasibility of the proposed method, simulation results are included for illustration.
The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed its fuzzy random variables with fuzzy prior dist...
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The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed its fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called "Resolution Identity" in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO). (c) 2005 Elsevier Inc. All rights reserved.
Recently, nonlinear programming solvers have been used to solve a range of mathematical programs with equilibrium constraints (MPECs). In particular, sequential quadratic programming (SQP) methods have been very succe...
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Recently, nonlinear programming solvers have been used to solve a range of mathematical programs with equilibrium constraints (MPECs). In particular, sequential quadratic programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. SQP is shown to converge superlinearly under reasonable assumptions near a strongly stationary point. A number of examples are presented that show that some of the assumptions are difficult to relax.
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