Because the internal pressure of a reservoir can recover only a fraction of its oil reserve, system operators apply artificial lifting techniques to force the flow of oil to the surface. A favored technique is gas-lif...
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Because the internal pressure of a reservoir can recover only a fraction of its oil reserve, system operators apply artificial lifting techniques to force the flow of oil to the surface. A favored technique is gas-lifting which consists of injecting compressed gas into the production tubing to reduce the weight of the oil column and, thereby, sustain a continuous flow of oil. The optimal allocation of a limited amount of compressed gas to wells gives rise to the gas-lift optimization problem, a mixed-integer nonlinear programming problem, whose decision variables determine which wells should produce and the rate of gas injected into the active ones. This paper investigates a piecewise linear formulation of the problem, presenting some properties of the polyhedron associated with the space of feasible solutions, and delivering families of valid inequalities that are shown to improve the performance of optimization software.
In this paper we formulate a nonlinear optimization model to estimate population class sizes based on sample information. The model is nonconvex and has several local minima corresponding to different populations that...
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In this paper we formulate a nonlinear optimization model to estimate population class sizes based on sample information. The model is nonconvex and has several local minima corresponding to different populations that could have been the source of the sample data. We show that many if not all local solutions can be found using a new global optimization algorithm called OptQuest/NLP (OQNLP). This can be used to estimate the number of individuals in a population with unique or rarely occurring characteristics, which is useful for assessing disclosure risk. It can also be used to estimate the number of classes in a population, a problem with applications in a variety of disciplines.
In this short note we consider a sequential quadratic programming (SQP) - type method with conic subproblems and compare this method with a standard SQP method in which the conic constraint is linearized at each step....
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In this short note we consider a sequential quadratic programming (SQP) - type method with conic subproblems and compare this method with a standard SQP method in which the conic constraint is linearized at each step. For both approaches we restrict our attention to convex subproblems since these are easy to solve and guarantee a certain global descent property. Using the example of a simple nonlinear program (NLP) and its conic reformulation we show that the SQP method with conic subproblems displays a slower rate of convergence than standard SQP methods. We then explain why an SQP subproblem that is based on a better approximation of the feasible set of the NLP results in a much slower algorithm.
We introduce a new approach in the methodology development for interactive multiobjective optimization. Thepresentation is given in the context of the interactive NIMBUS method, where the solution process is based on ...
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We introduce a new approach in the methodology development for interactive multiobjective optimization. Thepresentation is given in the context of the interactive NIMBUS method, where the solution process is based on the classification of objective functions. The idea is to formulate several scalarizing functions, all using the same preference information of the decision maker. Thus, opposed to fixing one scalarizing function (as is done in most methods), we utilize several scalarizing functions in a synchronous way. This means that we as method developers do not make the choice between different scalarizing functions but calculate the results of different scalarizing functions and leave the final decision to the expert, the decision maker. Simultaneously, (s)he obtains a better view of the solutions corresponding to her/his preferences expressed once during each iteration. In this paper, we describe a synchronous variant of the NIMBUS method. In addition, we introduce a new version of its implementation WWW-NIMBUS operating on the Internet. WWW-NIMBUS is a software system capable of solving even computationally demanding nonlinear problems. The new version of WWW-NIMBUS can handle versatile types of multiobjective optimization problems and includes new desirable features increasing its user-friendliness. (c) 2004 Elsevier B.V. All rights reserved.
In practical environmental systems with the effects of economics-of-scale (EOS), most relationships among different system components are nonlinear in nature, which can be described precisely only if a nonlinear model...
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In practical environmental systems with the effects of economics-of-scale (EOS), most relationships among different system components are nonlinear in nature, which can be described precisely only if a nonlinear model is employed. In this study, an interval nonlinear programming (INLP) model is developed and applied to the planning of a municipal solid waste (MSW) management system with EOS effects on system costs. The INLP has a nonlinear objective function and linear constraints. It handles nonlinearity presented as exponential functions. When exponential term p = 1 (in the INLP's objective function), the model becomes an interval linear program;when p = 2, it becomes an interval quadratic program. Therefore, the INLP is flexible in reflecting a variety of system complexities. A solution algorithm with satisfactory performance is proposed. Application of the proposed method to the planning of waste management activities in the Hamilton-Wentworth Region, Ontario, Canada, indicated that reasonable solutions have been generated. In general, the INLP model could reflect uncertain and nonlinear characteristics of MSW management systems with EOS effects. The modeling results provided useful decision support for the Region's waste management activities. (c) 2005 Elsevier B.V. All rights reserved.
Simulated Moving Bed (SMB) was developed as a realization of continuous countercurrent operation of chromatographic separation. An SMB unit consists of several columns of the same length connected in series, where fee...
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Simulated Moving Bed (SMB) was developed as a realization of continuous countercurrent operation of chromatographic separation. An SMB unit consists of several columns of the same length connected in series, where feed and desorbent are supplied and extract and raffinate are withdrawn continuously. This operation is repeated by shifting the supply/withdrawal points at a regular interval, making the operation symmetric. In this study, we explore asymmetric operation and design through a full-cycle optimization model, where the operation of the entire cycle is described within a nonlinear programming (NLP) problem and the Partial Differential Algebraic Equations (PDAEs) are fully discretized both in temporal and spatial domains. The NLP problem is implemented within the AMPL modeling environment and is solved using IPOPT, an interior-point NLP solver. We found that this problem is solved efficiently, and introducing a full-cycle formulation has the potential to improve the performance of SMB, as shown through single and multi-objective optimization studies. (c) 2006 Elsevier B.V. All rights reserved.
A heuristic is developed for a common production/inventory problem characterized by multiple products, stochastic seasonal demand, lost sales, and a constraint on overall production. Heuristics are needed since the ca...
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A heuristic is developed for a common production/inventory problem characterized by multiple products, stochastic seasonal demand, lost sales, and a constraint on overall production. Heuristics are needed since the calculation of optimal policies is impractical for real-world instances of this problem. The proposed heuristic is compared with those in current use as well as optimal solutions under a variety of conditions. The proposed heuristic is both near optimal and superior to existing heuristics. The heuristic deviated from optimality by an average of 1.7% in testing using dynamic programming as a benchmark. This compares favorably against linear-programming-based heuristics and practitioner heuristics, which deviated from optimality by 4.5 to 10.6%.
Method of feasible directions (MFD) is an important method for solving nonlinearly constrained optimization. However, various types of MFD all need an initial feasible point, which can not be found easily in generally...
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Method of feasible directions (MFD) is an important method for solving nonlinearly constrained optimization. However, various types of MFD all need an initial feasible point, which can not be found easily in generally. In addition, the computational cost of some MFD with superlinearly convergent property is rather high. On the other hand, the strongly sub-feasible direction method does not need an initial feasible point, but most of the proposed algorithm do not have the superlinearly convergent property, and can not guarantee that the iteration point is feasible after finite iterations. In this paper, we present a new superlinearly convergent algorithm with arbitrary initial point. At each iteration, a master direction is obtained by solving one direction finding subproblem (DFS), and an auxiliary direction is yielded by an explicit formula. After finite iterations, the iteration point goes into the feasible set and the master direction is a feasible direction of descent. Since a new generalized projection technique is contained in the auxiliary direction formula, under some mild assumptions without the strict complementarity, the global convergence and superlinear convergence of the algorithm can be obtained. (c) 2006 Elsevier Inc. All rights reserved.
The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinea...
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The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinear equality and inequality constraints. A procedure based on nonlinear programming is introduced and numerical experiments which show that the new procedure is reliable are exhibited. Scope and purpose We address the problem of packing orthogonal rectangles within an arbitrary convex region. We aim to show that smooth nonlinear programming models are a reliable alternative for packing problems and that well-known general-purpose methods based on continuous optimization can be used to solve the models. Numerical experiments illustrate the capabilities and limitations of the approach. (c) 2005 Elsevier Ltd. All rights reserved.
In this paper, a line search sequential quadratic programming (SQP) approach to a system of nonlinear equations (SNE) is taken. In this method, the system of nonlinear equations is transformed into a constrained nonli...
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In this paper, a line search sequential quadratic programming (SQP) approach to a system of nonlinear equations (SNE) is taken. In this method, the system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved using SQP algorithms with a line search strategy. Furthermore, at each step, some equations, which are satisfied at the current point, are treated as constraints and the others act as objective functions. In essence, constrained optimization strategies are utilized to cope with the system of nonlinear equations. (c) 2006 Elsevier Ltd. All rights reserved.
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