The development of the two-step optimization approach, as seen in Part I of the paper, can then be extended to a total water system. The total water system comprises two subsystems: namely, water-using units and waste...
详细信息
The development of the two-step optimization approach, as seen in Part I of the paper, can then be extended to a total water system. The total water system comprises two subsystems: namely, water-using units and wastewater treatment system. In this paper, the proposed approach utilizes mixed integer linear programming (MILP) and nonlinear programming (NLP) in the two-step optimization approach to generate multiple optimum solutions, called "class of good solutions", for the total water system design problem. A case study from the literature is used to illustrate the proposed approach, and comparisons with the results from the current techniques were then made to demonstrate the proposed method's strength.
In this paper, an algorithm is introduced to find an optimal solution for an optimization problem that arises in total least squares with inequality constraints, and in the correction of infeasible linear systems of i...
详细信息
In this paper, an algorithm is introduced to find an optimal solution for an optimization problem that arises in total least squares with inequality constraints, and in the correction of infeasible linear systems of inequalities. The stated problem is a nonconvex program with a special structure that allows the use of a reformulation-linearization-convexification technique for its solution. A branch-and-bound method for finding a global optimum for this problem is introduced based on this technique. Some computational experiments are included to highlight the efficacy of the proposed methodology. Inconsistent systems play a major role on the reformulation of models and are a consequence of lack of communication between decision makers. The problem of finding an optimal correction for some measure is of crucial importance in this context. The use of the Frobenius norm as a measure seems to be quite natural and leads to a nonconvex fractional programming problem. Despite being a difficult global optimization, it is possible to process it by using a branch-and-bound algorithm incorporating a local nonlinear programming method. (c) 2006 Elsevier Ltd. All rights reserved.
The maneuver characteristics of rotorcraft are analyzed using a nonlinear optimal control theory. The flight path deviations from a prescribed maneuver trajectory are penalized in the optimal control formulation to av...
详细信息
The maneuver characteristics of rotorcraft are analyzed using a nonlinear optimal control theory. The flight path deviations from a prescribed maneuver trajectory are penalized in the optimal control formulation to avoid numerical difficulties. The system optimality is represented by a two-point boundary value problem and solved via a multiple-shooting method. The focus of this paper is on the model-selection strategies for resolving the problems of numerical instability and high computational overhead when complex rotor dynamics are included in the mathematical model. Four different types of rotorcraft models are identified, two of which are linear models with or without rotor dynamics, as well as two models that include nonlinear dynamics for the rotor in its formulation. The effect each model was found to impart on the numerical analysis is reported. The relative computational efficiency is assessed in terms of computation time and the number of function calls for each model. The applications encompass the analyses for bob-up, turn, and slalom maneuvers and the results are used as guidelines for the selection of appropriate rotorcraft models.
This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piec...
详细信息
This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to sepal-able ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability. (C) 2007 Elsevier B.V. All rights reserved.
Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in t...
详细信息
Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations. (C) 2007 Elsevier Ltd. All rights reserved.
Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems in which the constraints are o...
详细信息
Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems in which the constraints are only of the lower-level type. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved using the constant positive linear dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The resolution of location problems in which many constraints of the lower-level set are nonlinear is addressed, employing the spectral projected gradient method for solving the subproblems. Problems of this type with more than 3 x 10(6) variables and 14 x 10(6) constraints are solved in this way, using moderate computer time. All the codes are available at http://***/similar to egbirgin/tango/.
We present a multi-resolution-based approach for solving trajectory optimization problems. The original optimal control problem is solved using a direct method, thereby being transcribed into a nonlinear programming p...
详细信息
We present a multi-resolution-based approach for solving trajectory optimization problems. The original optimal control problem is solved using a direct method, thereby being transcribed into a nonlinear programming problem that is solved using standard nonlinear programming codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable nonuniform grid over which the nonlinear programming problem is subsequently solved. This tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance conflicting objectives, such as accuracy of the solution, convergence, and speed of computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples.
Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue ...
详细信息
Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue optimization model for CDMA networks inspired by bid pricing models from the airline industry. We describe the optimality conditions for the model and develop a supergradient algorithm to solve it. We provide computational results that show the effects of the distribution and variance of demand. Finally, we discuss areas of future research, including a method to optimize the locations of the towers. (c) 2007 Elsevier B.V. All rights reserved.
In this paper, the task to start the operation of an evaporation system with hybrid dynamics is considered. The evaporator system was provided as a benchmark for hybrid control by a major chemical company. Rigorous mo...
详细信息
In this paper, the task to start the operation of an evaporation system with hybrid dynamics is considered. The evaporator system was provided as a benchmark for hybrid control by a major chemical company. Rigorous modeling gives rise to a hybrid automaton with high-dimensional nonlinear DAE dynamics that describe the continuous evolution in different discrete modes of operation. The problem of optimized start-up is solved by a branch-and-bound algorithm with embedded nonlinear dynamic optimization over a finite look-ahead horizon. The nonlinear optimization problems are solved by nonlinear programming and by evolutionary algorithms. Important elements of this formulation of the optimization problems are the introduction of a dynamic choice of the time intervals over which the zero-order hold controls are constant and the utilization of tailored penalty functions in order to obtain solutions which are close to the bounds of the feasible state regions. The two approaches are compared with respect to their performance for the evaporation system. 2007 Elsevier Ltd. All rights reserved.
Customer demand is sensitive to the price paid for the service in many service environments. Using queueing theory framework, we develop profit maximization models for jointly determining the price and the staffing le...
详细信息
Customer demand is sensitive to the price paid for the service in many service environments. Using queueing theory framework, we develop profit maximization models for jointly determining the price and the staffing level in a service company. The models include constraints on the average waiting time and the blocking probability. We show convexity of the single-variable Subproblem under certain plausible assumptions on the demand and staffing cost functions. Using numerical examples, we investigate the sensitivity of the price and the staffing level to changes in the marginal service cost and the user-specified constraint on the congestion measure. Copyright (C) 2008 John Wiley & Sons, Ltd.
暂无评论