Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the c...
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Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its 'pure' counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://***/similar to egbirgin/tango/.
The filled function method is an approach to find global minima of multidimensional multimodal functions. This paper proposes a class of new filled functions that are continuously differentiable and do not include exp...
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The filled function method is an approach to find global minima of multidimensional multimodal functions. This paper proposes a class of new filled functions that are continuously differentiable and do not include exponential terms. The performance of the new function in numerical experiments for a large set of testing functions up to 40 dimensions is quite satisfactory.
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...
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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.
Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of con...
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Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a genetic algorithm with a local search strategy based on the interior point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case. (C) 2007 Elsevier B.V. All rights reserved.
Most pharmaceutical companies that rely heavily on their sales force for success do not fully understand the effect of details made in previous quarters have on the current quarter, which is also known as the carryove...
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Most pharmaceutical companies that rely heavily on their sales force for success do not fully understand the effect of details made in previous quarters have on the current quarter, which is also known as the carryover effect. This paper proposes an expert system that utilizes neural networks with nonlinear programming to accurately derive the carryover effect at the customer level. Results suggest that using this adaptive and easy-to-implement expert system helped a firm increase its sales by 3.4% while reducing its sales force expenditure by 8.9%, compared to the control group. The implications of this approach are considered. (C) 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...
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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.
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...
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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.
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...
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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.
Wireless ad hoc networks have attracted a lot of attentions recently. Resource allocation in such networks needs to address both fairness and overall network performance. Pricing is a prospective direction to regulate...
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Wireless ad hoc networks have attracted a lot of attentions recently. Resource allocation in such networks needs to address both fairness and overall network performance. Pricing is a prospective direction to regulate behaviors of individual nodes while providing incentives for cooperation. In this work, we develop some pricing strategies for resource allocation by taking account of factors like multiple transmission rates and energy consumption of nodes, which have not been well studied in former works. Multi-rate transmission capability is commonly seen in most wireless products nowadays, while energy is one of the most important resources in portable devices. We propose a clique-based model which allows us to achieve optimal resource utilization and fairness among network flows when multi-rate transmission is considered. We also show how to extend the model to dynamically adjust prices based on energy consumptions of flows. In particular, our model takes into account energy consumptions in the transmitters' side, the receivers' side, and those that are non-transmitters and non-receivers but are interfered by these activities. So our model can more accurately reflect the real energy constraint in a wireless network. Simulation results are presented to show the convergence and other properties of these strategies. (C) 2008 Elsevier B.V. All rights reserved.
Low-thrust propulsion systems offer a fuel-efficient means to maneuver satellites to new orbits;however, they can only perform such maneuvers when they are continuously operated for a long time. Such long-term maneuve...
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Low-thrust propulsion systems offer a fuel-efficient means to maneuver satellites to new orbits;however, they can only perform such maneuvers when they are continuously operated for a long time. Such long-term maneuvers occur over many orbital revolutions, often rendering short time scale trajectory optimization methods ineffective. An approach to multirevolution large time scale optimal control of an electrodynamic tether is investigated for a tethered satellite system in low Earth orbit with atmospheric drag. Control is assumed to be periodic over several orbits because, under the assumptions of a nearly circular orbit, periodic control yields the only solution that significantly contributes to secular changes in the orbital parameters. The optimal control problem is constructed in such a way as to maneuver the satellite to a new orbit while minimizing a cost function subject to the constraints of the time-averaged equations of motion by controlling current in the tether. Three optimal maneuvers were investigated for a 4 km tether in a 270 km initial orbit: maximum climb, maximum final inclination, and a minimum time orbit change. The resulting control solutions were propagated to verify their accuracy.
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