The engineering of complex systems or a "system of systems" has become increasingly problematic in recent years, yet effective "architecting" approaches that enable cost/performance trades are stil...
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The engineering of complex systems or a "system of systems" has become increasingly problematic in recent years, yet effective "architecting" approaches that enable cost/performance trades are still immature. This article describes a systematic approach to allocating top-level system-of-systems requirements to component systems, which has been demonstrated on a naval mine countermeasures system-of-systems representation. This integrated analysis produces system effectiveness as a function of cost, corresponding subsystem requirements allocations, and a corresponding force structure or inputs to an overarching force-level cost/performance analysis. Variants of this approach are now being applied to support cost/performance analyses for the Navy Theater Wide Program and to focus future science and technology investments for mine countermeasures.
We develop and analyze a superlinearly convergent affine-scaling interior-point Newton method for infinite-dimensional problems with pointwise bounds in L-p-space. The problem formulation is motivated by optimal contr...
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We develop and analyze a superlinearly convergent affine-scaling interior-point Newton method for infinite-dimensional problems with pointwise bounds in L-p-space. The problem formulation is motivated by optimal control problems with L-p-controls and pointwise control constraints. The finite-dimensional convergence theory by Coleman and Li [SIAM J. Optim., 6 (1996), pp. 418-445] makes essential use of the equivalence of norms and the exact identifiability of the active constraints close to an optimizer with strict complementarity. Since these features are not available in our infinite-dimensional framework, algorithmic changes are necessary to ensure fast local convergence. The main building block is a Newton-like iteration for an affine-scaling formulation of the KKT-condition. We demonstrate in an example that a stepsize rule to obtain an interior iterate may require very small stepsizes even arbitrarily close to a nondegenerate solution. Using a pointwise projection instead we prove superlinear convergence under a weak strict complementarity condition and convergence with Q-rate >1 under a slightly stronger condition if a smoothing step is available. We discuss how the algorithm can be embedded in the class of globally convergent trust-region interior-point methods recently developed by M. Heinkenschloss and the authors. Numerical results for the control of a heating process confirm our theoretical findings.
In this paper we have investigated three optimization approaches for solving the optimal power flow (OPF) problem: active set and penalty (ASP), primal-dual (PD), and primal-dual logarithmic-barrier (PDLB). All three ...
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In this paper we have investigated three optimization approaches for solving the optimal power flow (OPF) problem: active set and penalty (ASP), primal-dual (PD), and primal-dual logarithmic-barrier (PDLB). All three approaches are Newton-based methods. This paper compares the main features of the above and reviews their methodologies. Results obtained in performance tests with traditional networks are summarized. (C) 2000 Elsevier Science S.A. All rights reserved.
One of the important features of any software system is its operational profile. This is simply the set of all operations that a software is designed to perform and the occurence probabilities of these operations. We ...
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One of the important features of any software system is its operational profile. This is simply the set of all operations that a software is designed to perform and the occurence probabilities of these operations. We present a new model on optimal software testing such that testing is done sequentially using a set of test cases. There may be failures due to the operations in each of these cases. The model parameters, consisting of testing costs and failure rates, all depend on the cases used and the operations performed. Our aim is to find the optimal testing durations in all of the cases in order to minimize the total expected cost. This problem leads to interesting decision models involving nonlinear programming formulations that possess explicit analytical solutions under reasonable assumptions. (C) 2000 John Wiley & Sons, Inc.
A direct method for a real-time generation of near-optimal spatial trajectories of short-term maneuvers onboard a flying vehicle with predetermined thrust history is introduced. The paper starts with a survey about th...
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A direct method for a real-time generation of near-optimal spatial trajectories of short-term maneuvers onboard a flying vehicle with predetermined thrust history is introduced. The paper starts with a survey about the founders of the direct methods of calculus of variations and their followers in flight mechanics, both in Russia and in the United States. It then describes a new direct method based on three cues: high-order polynomials from the virtual are as a reference function for aircraft's coordinates, a preset history of one of the controls (thrust), and a few optimization parameters. The trajectory optimization problem is transformed into a nonlinear programming problem and then solved numerically using an appropriate algorithm in accelerated scale of time. A series of examples Is presented. Calculated near-optimal trajectory is compared with real Right data, and with the solution obtained by Pontryagin's maximum principle. Fast convergence of the numerical algorithm, which has been already implemented and tested onboard a real aircraft, is illustrated.
This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain ...
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This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. The convergence and complexity properties of our algorithms are analyzed theoretically and numerically. Examples show the effectiveness of the algorithms. (C) 2000 Elsevier Science B.V. All rights reserved.
The interior-point methods have emerged as highly efficient procedures for solving linear programming problems in recent years. The interior point methods have superior theoretical properties as well as observed compu...
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The interior-point methods have emerged as highly efficient procedures for solving linear programming problems in recent years. The interior point methods have superior theoretical properties as well as observed computational advantages over simplex methods at solving large linear programming problems and are found to be immune to degeneracy. It is a common observation in literature that most nonlinear programming methods that work well for small and medium sized problems are not able to solve large-scale problems efficiently. It is to be expected that interior-point methods, when used in an adaptive sequential linear programming strategy, might prove to be a powerful engineering optimization tool. The development of an adaptive sequential linear programming algorithm, based on an infeasible primal-dual path-following interior-point algorithm and fuzzy heuristics, is considered in this work for the solution of large-scale engineering design optimization problems. Several numerical examples are considered to demonstrate the effectiveness and efficiency of the present method. The examples include a part stamping problem, a turbine rotor design problem, and an optimal control problem related to tidal power generation. The number of design variables and constraints range from 12 to 402 and 20 to 20,300, respectively, for the part stamping problem. The turbine rotor problem involves 905 variables and 1081 constraints, and the optimal control problem has 2002 variables and 1001 constraints. The numerical results clearly demonstrate the superiority of the interior-point methods compared with the well-known simplex-based linear solver in solving large-scale optimum design problems. The superior performance of the present method is shown in terms of both computational time and the ability to handle degenerate problems.
In Cervantes and Biegler (***.E.J. 44 (1998) 1038), we presented a simultaneous nonlinear programming problem (NLP) formulation for the solution of DAE optimization problems. Here, by applying collocation on finite el...
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In Cervantes and Biegler (***.E.J. 44 (1998) 1038), we presented a simultaneous nonlinear programming problem (NLP) formulation for the solution of DAE optimization problems. Here, by applying collocation on finite elements, the DAE system is transformed into a nonlinear system. The resulting optimization problem, in which the element placement is fixed, is solved using a reduced space successive quadratic programming (rSQP) algorithm. The space is partitioned into range and null spaces. This partitioning is performed by choosing a pivot sequence for an LU factorization with partial pivoting which allows us to detect unstable modes in the DAE system. The system is stabilized without imposing new boundary conditions. The decomposition of the range space can be performed in a single step by exploiting the overall sparsity of the collocation matrix but not its almost block diagonal structure. In order to solve larger problems a new decomposition approach and a new method for constructing the quadratic programming (QP) subproblem are presented in this work. The decomposition of the collocation matrix is now performed element by element, thus reducing the storage requirements and the computational effort. Under this scheme, the unstable modes are considered in each element and a range-space move is constructed sequentially based on decomposition in each element. This new decomposition improves the efficiency of our previous approach and at the same time preserves its stability. The performance of the algorithm is tested on several examples. Finally, some future directions for research are discussed. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
In this paper optimal control problems for the stationary Burgers equation are analyzed. To solve the optimal control problems the augmented Lagrangian-SQP method is applied. This algorithm has second-order convergenc...
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In this paper optimal control problems for the stationary Burgers equation are analyzed. To solve the optimal control problems the augmented Lagrangian-SQP method is applied. This algorithm has second-order convergence rate depending upon a second-order sufficient optimality condition. Using piecewise linear finite elements it is proved that the discretized augmented Lagrangian-SQP method is well-defined and has second-order rate of convergence. This result is based on the proof of a uniform discrete Babuska-Brezzi condition and a uniform second-order sufficient optimality condition.
To optimize large-scale queuing systems configurations, OR professionals typically use discrete event simulation packages to examine in detail the movement of entities through such systems, assuming stochastic but fix...
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To optimize large-scale queuing systems configurations, OR professionals typically use discrete event simulation packages to examine in detail the movement of entities through such systems, assuming stochastic but fixed arrival patterns. Demand aspects are, however, routinely ignored as few attempts are made to capture the feedback effect of queue performance on the arrival process. Econometricians, on the other hand, use a simultaneous equations estimation approach relying on past data, but they typically disregard the technological insights provided by simulation. This paper combines both tools to study the ailing port system of Calcutta, India, and concludes that raising prices will improve both economic and engineering performances. Microeconomic models of shipowner behavior are constructed to explain the nature of the empirical findings. Finally, full-equilibrium demand elasticities are calculated using the dual prices from an appropriate nonlinear program, which are then compared to the benchmark value expected of profit-maximizing behavior.
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