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NASA NTRS1972

A survey of compiler optimization techniques

Major optimization techniques of compilers are described and grouped into three categories: machine dependent, architecture dependent, and architecture independent. Machine-dependent optimizations tend to be local and are performed upon short spans of generated code by using particular properties of an instruction set to reduce the time or space required by a program. Architecture-dependent optimizations are global and are performed while generating code. These optimizations consider the structure of a computer, but not its detailed instruction set. Architecture independent optimizations are also global but are based on analysis of the program flow graph and the dependencies among statements of source program. A conceptual review of a universal optimizer that performs architecture-independent optimizations at source-code level is also presented.

Schneck, P. B.↗

NASA NTRS1971

Optimization of life support systems and their systems reliability

The identification, analysis, and optimization of life support systems and subsystems have been investigated. For each system or subsystem that has been considered, the procedure involves the establishment of a set of system equations (or mathematical model) based on theory and experimental evidences; the analysis and simulation of the model; the optimization of the operation, control, and reliability; analysis of sensitivity of the system based on the model; and, if possible, experimental verification of the theoretical and computational results. Research activities include: (1) modeling of air flow in a confined space; (2) review of several different gas-liquid contactors utilizing centrifugal force: (3) review of carbon dioxide reduction contactors in space vehicles and other enclosed structures: (4) application of modern optimal control theory to environmental control of confined spaces; (5) optimal control of class of nonlinear diffusional distributed parameter systems: (6) optimization of system reliability of life support systems and sub-systems: (7) modeling, simulation and optimal control of the human thermal system: and (8) analysis and optimization of the water-vapor eletrolysis cell.

Fan, L. T.↗

NASA NTRS1973

Effects of inclination and eccentricity on optimal trajectories between earth and Venus

The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.

Gravier, J.-P.↗

NASA NTRS1975

Deterministic optimal maneuver strategy for multi-target missions

This paper presents an optimal strategy for making impulsive correction to a multi-target trajectory by a single maneuver. The concept of an optimal maneuver time is introduced. The choice of suitable weighting functions is explored to enable one to properly translate the subjective desire of mission success into an objective cost function whose minimization yields the optimal strategy. It is shown that a number of strategies previously formulated are derivable from one general expression. A number of other interesting properties of the optimal strategy are described. Numerical results are presented for a typical two-target mission. It is shown that the strategy formulated is optimal. For some perturbations, there exists an optimal maneuver time different from the time of initiation of the perturbation. That is, the physical properties of the trajectory can be exploited to select the optimal time of making a corrective maneuver.

Dwivedi, N. P.↗

NASA NTRS1981

Optimal trajectories in atmospheric flight

Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.

Vinh, N. X.↗

NASA NTRS1982

Fuel optimal maneuvers for spacecraft with fixed thrusters

Several mathematical models, including a minimum integral square criterion problem, were used for the qualitative investigation of fuel optimal maneuvers for spacecraft with fixed thrusters. The solutions consist of intervals of "full thrust" and "coast" indicating that thrusters do not need to be designed as "throttleable" for fuel optimal performance. For the primary model considered, singular solutions occur only if the optimal solution is "pure translation". "Time optimal" singular solutions can be found which consist of intervals of "coast" and "full thrust". The shape of the optimal fuel consumption curve as a function of flight time was found to depend on whether or not the initial state is in the region admitting singular solutions. Comparisons of fuel optimal maneuvers in deep space with those relative to a point in circular orbit indicate that qualitative differences in the solutions can occur. Computation of fuel consumption for certain "pure translation" cases indicates that considerable savings in fuel can result from the fuel optimal maneuvers.

Carter, T. C.↗

NASA NTRS1983

Optimal short range trajectories for helicopters

An optimal flight path algorithm using a simplified altitude state model and an apriori climb-cruise-descent flight profile has been developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. The performance model is based on standard flight manual data and is such that on-line trajectory optimization is feasible with a relatively small computer. The results show that the optimal flight path and optimal cruise altitude can represent a 10 percent fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability due to helicopter weight, ambient winds and the relative cost trade-off between time and fuel. In general, 'reasonable' variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost.

Slater, G. L.↗

NASA NTRS1985

An Integrated Control and Minimum Mass Structural Optimization Algorithm for Large Space Structures

A new approach is discussed for solving dual structural control optimization problems for high-order flexible space structures, where reduced-order structural models are employed and minimum mass designs are sought. For a given initial structural design, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the structural design variables is then determined and used to obtain successive structural redesigns, using a constrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. The minimum mass design is obtained by solving a sequence of neighboring optimal constant mass designs, where the sequence of optimal performance indices has a minimum at the optimal minimum mass design. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.

Messac, A.↗

NASA NTRS1986

An improved multilevel optimization approach for the design of complex engineering systems

Multilevel optimization methods are being considered for the design of complex systems on distributed networks of computers or even parallel processors. An obstacle to the use of multilevel methods is that they can be computationally expensive because of the cycling necessary to account for the coupling between the subproblems. This research effort aims at increasing the efficiency of multilevel optimization by adapting two techniques that are widely used in conventional one-level optimization: constraint approximation and temporary constraint deletion. These improvements are implemented and tested on three-, ten- and 52-bar planar truss designs. The results show that for larger problems (approximately 100 design variables and larger), the cost of analysis dominates the total cost so that multilevel optimization is no more expensive than one-level optimization. If parallel processing is used or the analysis process itself is decomposed, then multilevel optimization stands to become more economical than one-level optimization.

Barthelemy, J.-F. M.↗

NASA NTRS1984

Application of numerical optimization to rotor aerodynamic design

Based on initial results obtained from the performance optimization code, a number of observations can be made regarding the utility of optimization codes in supporting design of rotors for improved performance. (1) The primary objective of improving the productivity and responsiveness of current design methods can be met. (2) The use of optimization allows the designer to consider a wider range of design variables in a greatly compressed time period. (3) Optimization requires the user to carefully define his problem to avoid unproductive use of computer resources. (4) Optimization will increase the burden on the analyst to validate designs and to improve the accuracy of analysis methods. (5) Direct calculation of finite difference derivatives by the optimizer was not prohibitive for this application but was expensive. Approximate analysis in some form would be considered to improve program response time. (6) Program developement is not complete and will continue to evolve to integrate new analysis methods, design problems, and alternate optimizer options.

Pleasants, W. A., III↗

NASA NTRS1984

Optimization applications in aircraft engine design and test

Starting with the NASA-sponsored STAEBL program, optimization methods based primarily upon the versatile program COPES/CONMIN were introduced over the past few years to a broad spectrum of engineering problems in structural optimization, engine design, engine test, and more recently, manufacturing processes. By automating design and testing processes, many repetitive and costly trade-off studies have been replaced by optimization procedures. Rather than taking engineers and designers out of the loop, optimization has, in fact, put them more in control by providing sophisticated search techniques. The ultimate decision whether to accept or reject an optimal feasible design still rests with the analyst. Feedback obtained from this decision process has been invaluable since it can be incorporated into the optimization procedure to make it more intelligent. On several occasions, optimization procedures have produced novel designs, such as the nonsymmetric placement of rotor case stiffener rings, not anticipated by engineering designers. In another case, a particularly difficult resonance contraint could not be satisfied using hand iterations for a compressor blade, when the STAEBL program was applied to the problem, a feasible solution was obtained in just two iterations.

Pratt, T. K.↗

NASA NTRS1986

Optimization methods and silicon solar cell numerical models

The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

Girardini, K.↗

NASA NTRS1988

The Sizing and Optimization Language, (SOL): Computer language for design problems

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

Lucas, Stephen H.↗

NASA NTRS1987

Time optimal paths and acceleration lines of robotic manipulators

The concept of acceleration lines and their correlation with time-optimal paths of robotic manipulators is presented. The acceleration lines represent the directions of maximum tip acceleration from a point in the manipulator work-space, starting at a zero velocity. These lines can suggest the number and shapes of time-optimal paths for a class of manipulators. It is shown that nonsingular time-optimal paths are tangent to one of the acceleration lines near the end-points. A procedure for obtaining near-optimal paths, utilizing the acceleration lines, is developed. These paths are obtained by connecting the end-points with B splines tangent to the acceleration lines. The near-minimum paths are shown to yield better traveling times than the straight-line path between the same end-points. The near-minimum paths can be used as initial conditions in existing optimization methods to speed-up convergence and computation time. This method can be used for online robot path planning and for interactive designs of robotic-cell layouts. Examples of time-optimal paths of a two-link manipulator, obtained by other optimization procedures and their acceleration lines, are shown.

Shiller, Zvi↗

NASA NTRS1988

An initiative in multidisciplinary optimization of rotorcraft

Described is a joint NASA/Army initiative at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The activity is being guided by a Steering Committee made up of key NASA and Army researchers and managers. The committee, which has been named IRASC (Integrated Rotorcraft Analysis Steering Committee), has defined two principal foci for the activity: a white paper which sets forth the goals and plans of the effort; and a rotor design project which will validate the basic constituents, as well as the overall design methodology for multidisciplinary optimization. The paper describes the optimization formulation in terms of the objective function, design variables, and constraints. Additionally, some of the analysis aspects are discussed and an initial attempt at defining the interdisciplinary couplings is summarized. At this writing, some significant progress has been made, principally in the areas of single discipline optimization. Results are given which represent accomplishments in rotor aerodynamic performance optimization for minimum hover horsepower, rotor dynamic optimization for vibration reduction, and rotor structural optimization for minimum weight.

Adelman, Howard M.↗

NASA NTRS1989

Optimization by decomposition: A step from hierarchic to non-hierarchic systems

A new, non-hierarchic decomposition is formulated for system optimization that uses system analysis, system sensitivity analysis, temporary decoupled optimizations performed in the design subspaces corresponding to the disciplines and subsystems, and a coordination optimization concerned with the redistribution of responsibility for the constraint satisfaction and design trades among the disciplines and subsystems, and a coordination optimization concerned with the redistribution of responsibility for the constraint satisfaction and design trades among the disciplines and subsystems. The approach amounts to a variation of the well-known method of subspace optimization modified so that the analysis of the entire system is eliminated from the subspace optimization and the subspace optimizations may be performed concurrently.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1989

An initiative in multidisciplinary optimization of rotorcraft

Described is a joint NASA/Army initiative at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The activity is being guided by a Steering Committee made up of key NASA and Army researchers and managers. The committee, which has been named IRASC (Integrated Rotorcraft Analysis Steering Committee), has defined two principal foci for the activity: a white paper which sets forth the goals and plans of the effort; and a rotor design project which will validate the basic constituents, as well as the overall design methodology for multidisciplinary optimization. The optimization formulation is described in terms of the objective function, design variables, and constraints. Additionally, some of the analysis aspects are discussed and an initial attempt at defining the interdisciplinary couplings is summarized. At this writing, some significant progress has been made, principally in the areas of single discipline optimization. Results are given which represent accomplishments in rotor aerodynamic performance optimization for minimum hover horsepower, rotor dynamic optimization for vibration reduction, and rotor structural optimization for minimum weight.

Adelman, Howard M.↗

NASA NTRS1989

Structural optimization of rotor blades with straight and swept tips subject to aeroelastic constraints

The main conclusions obtained in the present study are summarized. Their application to the structural optimization of a helicopter blade should be limited by the assumptions used in obtaining the numerical results presented here. The optimum design procedure described here is very efficient, and can produce improved designs with a very limited number of precise analyses. The method of constructing the approximate problem is such that previously conducted aeroelastic analyses can be reused in a new optimization problem. For example, if an optimization study is preceded by a parametric study in which the effect of various combinations of blade design parameters is examined, all the aeroelastic analyses performed for the parametric study can be reutilized in the optimization study. This is not possible when the approximate problem is built from Taylor series expansions. The results of the optimization are quite sensitive to the aeroelastic stability margins required of the blade. In the optimization of case 2, changing the aeroelastic stability constraints from simply requiring that the blade be stable in hover, to requiring that the stability margins be maintained during the course of the optimization, reduced the gains in n/rev vibration levels by more than 50 percent. The introduction of tip sweep can reduce the n/rev vertical hub shears beyond the level that can be obtained by just modifying the mass and stiffness distributions of the blade.

Friedmann, Peretz P.↗