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At least 433 records · Page 24

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NASA NTRS1985

ADS: A FORTRAN program for automated design synthesis: Version 1.10

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired.

Vanderplaats, G. N.↗

NASA NTRS2001

Planning and Scheduling for Fleets of Earth Observing Satellites

We address the problem of scheduling observations for a collection of earth observing satellites. This scheduling task is a difficult optimization problem, potentially involving many satellites, hundreds of requests, constraints on when and how to service each request, and resources such as instruments, recording devices, transmitters, and ground stations. High-fidelity models are required to ensure the validity of schedules; at the same time, the size and complexity of the problem makes it unlikely that systematic optimization search methods will be able to solve them in a reasonable time. This paper presents a constraint-based approach to solving the Earth Observing Satellites (EOS) scheduling problem, and proposes a stochastic heuristic search method for solving it.

Frank, Jeremy↗

NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗

NASA NTRS1994

Portable parallel stochastic optimization for the design of aeropropulsion components

This report presents the results of Phase 1 research to develop a methodology for performing large-scale Multi-disciplinary Stochastic Optimization (MSO) for the design of aerospace systems ranging from aeropropulsion components to complete aircraft configurations. The current research recognizes that such design optimization problems are computationally expensive, and require the use of either massively parallel or multiple-processor computers. The methodology also recognizes that many operational and performance parameters are uncertain, and that uncertainty must be considered explicitly to achieve optimum performance and cost. The objective of this Phase 1 research was to initialize the development of an MSO methodology that is portable to a wide variety of hardware platforms, while achieving efficient, large-scale parallelism when multiple processors are available. The first effort in the project was a literature review of available computer hardware, as well as review of portable, parallel programming environments. The first effort was to implement the MSO methodology for a problem using the portable parallel programming language, Parallel Virtual Machine (PVM). The third and final effort was to demonstrate the example on a variety of computers, including a distributed-memory multiprocessor, a distributed-memory network of workstations, and a single-processor workstation. Results indicate the MSO methodology can be well-applied towards large-scale aerospace design problems. Nearly perfect linear speedup was demonstrated for computation of optimization sensitivity coefficients on both a 128-node distributed-memory multiprocessor (the Intel iPSC/860) and a network of workstations (speedups of almost 19 times achieved for 20 workstations). Very high parallel efficiencies (75 percent for 31 processors and 60 percent for 50 processors) were also achieved for computation of aerodynamic influence coefficients on the Intel. Finally, the multi-level parallelization strategy that will be needed for large-scale MSO problems was demonstrated to be highly efficient. The same parallel code instructions were used on both platforms, demonstrating portability. There are many applications for which MSO can be applied, including NASA's High-Speed-Civil Transport, and advanced propulsion systems. The use of MSO will reduce design and development time and testing costs dramatically.

Sues, Robert H.↗

NASA NTRS1988

A new algorithm for general multiobjective optimization

Described is a new technique for converting a constrained optimization problem to an unconstrained one, and a new method for multiobjective optimization based on that technique. The technique transforms the objective functions into goal constraints. The goal constraints are appended to the set of behavior constraints and the envelope of all functions in the set is searched for an unconstrained minimum. The technique may be categorized as a SUMT algorithm. In multiobjective applications, the approach has the advantage of locating a compromise minimum without the need to optimize for each individual objective function separately. The constrained to unconstrained conversion is described, followed by a description of the multiobjective problem. Two example problems are presented to demonstrate the robustness of the method.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1988

A new algorithm for general multiobjective optimization

The paper describes a new technique for converting a constrained optimization problem to an unconstrained one, and a new method for multiobjective optimization based on that technique. The technique transforms the objective functions into goal constraints. The goal constraints are appended to the set of behavior constraints, and the envelope of all functions in the set is searched for an unconstrained minimum. The technique can be categorized as a SUMT algorithm. In multiobjective applications, the approach has the advantage of locating a compromise minimum without the need to optimize for each individual objective function separately. The constrained to unconstrained conversion is described, followed by a description of the multiobjective problem. Two example problems are presented to demonstrate the robustness of the method.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1993

Synthesis of Optimal Nonlinear Feedback Laws for Dynamic Systems Using Neural Networks

Open-loop solutions of dynamical optimization problems can be numerically computed usingexisting software packages. The computed time histories of the state and control variables, formultiple sets of end conditions can then be used to train a neural network to 'recognize' the optimal,nonlinear feedback relation between the states and controls of the system. The 'learned' network canthen be used to output an approximate optimal control given a full set (or a partial set) of measuredsystem states. With simple neural networks, we have successfully demonstrated the efficacy of theproposed approach using a minimum-time orbit injection problem. The usefulness and limitations ofthis novel approach on real-life optimal guidance and control problems, with many state and control variables as well as path inequality constraints, remain to be seen.

Orbit injection problem↗

NASA NTRS2009

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

Rios, Joseph Lucio↗

NASA NTRS1984

ADS: A FORTRAN program for automated design synthesis, version 1.00

A new general-purpose optimization program for engineering design is described. ADS-1 (Automated Design Synthesis - Version 1) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels, being strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired. The program is demonstrated with a simple structural design example.

Vanderplaats, G. N.↗

NASA NTRS1988

A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.

Nicol, David M.↗

NASA NTRS1991

On computing the global time-optimal motions of robotic manipulators in the presence of obstacles

A method for computing the time-optimal motions of robotic manipulators is presented that considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. The optimization problem is reduced to a search for the time-optimal path in the n-dimensional position space. A small set of near-optimal paths is first efficiently selected from a grid, using a branch and bound search and a series of lower bound estimates on the traveling time along a given path. These paths are further optimized with a local path optimization to yield the global optimal solution. Obstacles are considered by eliminating the collision points from the tessellated space and by adding a penalty function to the motion time in the local optimization. The computational efficiency of the method stems from the reduced dimensionality of the searched spaced and from combining the grid search with a local optimization. The method is demonstrated in several examples for two- and six-degree-of-freedom manipulators with obstacles.

Shiller, Zvi↗

NASA NTRS1993

Genetic algorithms - What fitness scaling is optimal?

A problem of choosing the best scaling function as a mathematical optimization problem is formulated and solved under different optimality criteria. A list of functions which are optimal under different criteria is presented which includes both the best functions empirically proved and new functions that may be worth trying.

Kreinovich, Vladik↗

NASA NTRS1990

An overview of the current state of the art optimization used for trajectory design in the GTS system

The high cost of delivering payloads to orbit demands that launch vehicles be flown in an optimal and reliable manner. Thus, computer simulated trajectories are optimized to obtain maximum vehicle payload capability or a maximum amount of reserve fuel, subject to design constraints. The Generalized Trajectory Simulation (GTS) system developed at The Aerospace Corporation is capable of simulating and optimizing trajectories for a wide variety of boost and reentry problems. Optimization is an integral part of the GTS system. This has resulted in progressive use of optimization. Additionally, the flexibility of the GTS system allows optimum trade studies to be conducted and complicated missions to be designed. This paper describes the integrated and flexible nature of the optimization software in the GTS system. Special features of the NLP2 and NLP3 optimization codes are described. Post optimality, parameter sensitivity analysis and the automatic scaling capability in the GTS system are also described.

Beltracchi, Todd J.↗

NASA NTRS2003

Adaptive Critic Neural Network-Based Terminal Area Energy Management and Approach and Landing Guidance

Reusable Launch Vehicles (RLVs) have different mission requirements than the Space Shuttle, which is used for benchmark guidance design. Therefore, alternative Terminal Area Energy Management (TAEM) and Approach and Landing (A/L) Guidance schemes can be examined in the interest of cost reduction. A neural network based solution for a finite horizon trajectory optimization problem is presented in this paper. In this approach the optimal trajectory of the vehicle is produced by adaptive critic based neural networks, which were trained off-line to maintain a gradual glideslope.

Grantham, Katie↗

NASA NTRS2006

Exploiting Quantum Resonance to Solve Combinatorial Problems

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Zak, Michail↗

NASA NTRS1998

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Giunta, Anthony A.↗

NASA NTRS2010

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Mengshoel, Ole J.↗

NASA NTRS1984

Parameter estimation for the Euler-Bernoulli-beam

An approximation involving cubic spline functions for parameter estimation problems in the Euler-Bernoulli-beam equation (phrased as an optimization problem with respect to the parameters) is described and convergence is proved. The resulting algorithm was implemented and several of the test examples are documented. It is observed that the use of penalty terms in the cost functional can improve the rate of convergence.

Graif, E.↗