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NASA NTRS2010

Particle Swarm Optimization Toolbox

The Particle Swarm Optimization Toolbox is a library of evolutionary optimization tools developed in the MATLAB environment. The algorithms contained in the library include a genetic algorithm (GA), a single-objective particle swarm optimizer (SOPSO), and a multi-objective particle swarm optimizer (MOPSO). Development focused on both the SOPSO and MOPSO. A GA was included mainly for comparison purposes, and the particle swarm optimizers appeared to perform better for a wide variety of optimization problems. All algorithms are capable of performing unconstrained and constrained optimization. The particle swarm optimizers are capable of performing single and multi-objective optimization. The SOPSO and MOPSO algorithms are based on swarming theory and bird-flocking patterns to search the trade space for the optimal solution or optimal trade in competing objectives. The MOPSO generates Pareto fronts for objectives that are in competition. A GA, based on Darwin evolutionary theory, is also included in the library. The GA consists of individuals that form a population in the design space. The population mates to form offspring at new locations in the design space. These offspring contain traits from both of the parents. The algorithm is based on this combination of traits from parents to hopefully provide an improved solution than either of the original parents. As the algorithm progresses, individuals that hold these optimal traits will emerge as the optimal solutions. Due to the generic design of all optimization algorithms, each algorithm interfaces with a user-supplied objective function. This function serves as a "black-box" to the optimizers in which the only purpose of this function is to evaluate solutions provided by the optimizers. Hence, the user-supplied function can be numerical simulations, analytical functions, etc., since the specific detail of this function is of no concern to the optimizer. These algorithms were originally developed to support entry trajectory and guidance design for the Mars Science Laboratory mission but may be applied to any optimization problem.

Grant, Michael J.↗
NASA NTRS2002

Particle Swarm Optimization

The purpose of this paper is to show how the search algorithm known as particle swarm optimization performs. Here, particle swarm optimization is applied to structural design problems, but the method has a much wider range of possible applications. The paper's new contributions are improvements to the particle swarm optimization algorithm and conclusions and recommendations as to the utility of the algorithm, Results of numerical experiments for both continuous and discrete applications are presented in the paper. The results indicate that the particle swarm optimization algorithm does locate the constrained minimum design in continuous applications with very good precision, albeit at a much higher computational cost than that of a typical gradient based optimizer. However, the true potential of particle swarm optimization is primarily in applications with discrete and/or discontinuous functions and variables. Additionally, particle swarm optimization has the potential of efficient computation with very large numbers of concurrently operating processors.

Venter, Gerhard↗
NASA NTRS2005

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Venter, Gerhard↗
NASA NTRS2002

Multidisciplinary Optimization of a Transport Aircraft Wing using Particle Swarm Optimization

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS2013

Automatic Parameter Tuning for the Morpheus Vehicle Using Particle Swarm Optimization

A high fidelity simulation using a PC based Trick framework has been developed for Johnson Space Center's Morpheus test bed flight vehicle. There is an iterative development loop of refining and testing the hardware, refining the software, comparing the software simulation to hardware performance and adjusting either or both the hardware and the simulation to extract the best performance from the hardware as well as the most realistic representation of the hardware from the software. A Particle Swarm Optimization (PSO) based technique has been developed that increases speed and accuracy of the iterative development cycle. Parameters in software can be automatically tuned to make the simulation match real world subsystem data from test flights. Special considerations for scale, linearity, discontinuities, can be all but ignored with this technique, allowing fast turnaround both for simulation tune up to match hardware changes as well as during the test and validation phase to help identify hardware issues. Software models with insufficient control authority to match hardware test data can be immediately identified and using this technique requires very little to no specialized knowledge of optimization, freeing model developers to concentrate on spacecraft engineering. Integration of the PSO into the Morpheus development cycle will be discussed as well as a case study highlighting the tool's effectiveness.

Birge, B.↗
NASA NTRS2013

Surface Navigation Using Optimized Waypoints and Particle Swarm Optimization

The design priority for manned space exploration missions is almost always placed on human safety. Proposed manned surface exploration tasks (lunar, asteroid sample returns, Mars) have the possibility of astronauts traveling several kilometers away from a home base. Deviations from preplanned paths are expected while exploring. In a time-critical emergency situation, there is a need to develop an optimal home base return path. The return path may or may not be similar to the outbound path, and what defines optimal may change with, and even within, each mission. A novel path planning algorithm and prototype program was developed using biologically inspired particle swarm optimization (PSO) that generates an optimal path of traversal while avoiding obstacles. Applications include emergency path planning on lunar, Martian, and/or asteroid surfaces, generating multiple scenarios for outbound missions, Earth-based search and rescue, as well as human manual traversal and/or path integration into robotic control systems. The strategy allows for a changing environment, and can be re-tasked at will and run in real-time situations. Given a random extraterrestrial planetary or small body surface position, the goal was to find the fastest (or shortest) path to an arbitrary position such as a safe zone or geographic objective, subject to possibly varying constraints. The problem requires a workable solution 100% of the time, though it does not require the absolute theoretical optimum. Obstacles should be avoided, but if they cannot be, then the algorithm needs to be smart enough to recognize this and deal with it. With some modifications, it works with non-stationary error topologies as well.

Birge, Brian↗
NASA NTRS1985

Thickness of the particle swarm in cosmic ray air showers

The average dispersion in arrival time of air shower particles detected with a scintillator at an impact parameter r is described with accuracy 5-10% by the empirical formula sigma = Sigma sub to (1+r/r sub t) sup b, where Sigma sub to = 2.6 ns, r sub t = 30m and b = (1.94 + or - .08) (0.39 + or - .06) sec Theta, for r 2 km, 10 to the 8th power E 10 to the 11th power GeV, and Theta 60 deg. (E is the primary energy and theta is the zenith angle). The amount of fluctuation in sigma sub t due to fluctuations in the level of origin and shower development is less than 20%. These results provide a basis for estimating the impact parameters of very larger showers with data from very small detector arrays (mini-arrays). The energy of such showers can then be estimated from the local particle density. The formula also provides a basis for estimating the angular resolution of air shower array-telescopes.

Linsley, J.↗
NASA NTRS2024

Harnessing Collaborative Learning Automata to Guide Multi-objective Optimization based Inverse Analysis for Structural Damage Identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

Yang Zhang↗
NASA NTRS2002

A Computational Intelligence (CI) Approach to the Precision Mars Lander Problem

A Mars precision landing requires a landed footprint of no more than 100 meters. Obstacles to reducing the landed footprint include trajectory dispersions due to initial atmospheric entry conditions such as entry angle, parachute deployment height, environment parameters such as wind, atmospheric density, parachute deployment dynamics, unavoidable injection error or propagated error from launch, etc. Computational Intelligence (CI) techniques such as Artificial Neural Nets and Particle Swarm Optimization have been shown to have great success with other control problems. The research period extended previous work on investigating applicability of the computational intelligent approaches. The focus of this investigation was on Particle Swarm Optimization and basic Neural Net architectures. The research investigating these issues was performed for the grant cycle from 5/15/01 to 5/15/02. Matlab 5.1 and 6.0 along with NASA's POST were the primary computational tools.

Birge, Brian↗
NASA NTRSDate not supplied

Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.

Linear Covariance Analysis↗
NASA NTRS2012

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.

Communication Network Scheduling↗
NASA NTRS1985

Angular resolution of air-shower array-telescopes

A fundamental limit on the angular resolution of air shower array-telescopes is set by the finite number of shower particles coupled with the finite thickness of the particle swarm. Consequently the angular resolution which can be achieved in practice depends in a determinant manner on the size and number of detectors in an array-telescope, as well as on the detector separation and the timing resolution. It is also necessary to examine the meaning of particle density in whatever type of detector is used. Results are given which can be used to predict the angular resolution of a given instrument for showers of various sizes, and to compare different instruments.

Linsley, J.↗
NASA NTRS1985

Methods for roof-top mini-arrays

To test the idea of the Linsley effect mini array for the study of giant air showers, it is desirable to have a trigger that exploits the effect itself. In addition to the trigger, it is necessary to have a method for measuring the relative arrival times of the particle swarm selected by the trigger. Since the idea of mini arrays is likely to appeal to small research groups, it is desirable to try to design relatively simple and inexpensive methods, and methods that utilize existing detectors. Clusters of small detectors have been designed for operation in the local particle density realm where the probability of or = 2 particles per detector is small. Consequently, this method can discriminate pulses from each detector and thenceforth deal mainly with logic pulses.

Hazen, W. E.↗
NASA NTRS2024

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

Yang Zhang↗
NASA NTRS1985

The LDEF interplanetary dust experiment

Explorer 46 data and the Long Duration Exposure Facility (LDEF) interplanetary dust experiment are examined. Analysis of the Explorer 46 data reveals the existence of particles of 0.1 micron and a mass of 1 x 10 to the -16th gm, the injection of the submicron particles directly by a comet (injection mass of about 5000 tons), and a submicron particle lifetime of about three years. The applications of LDEF data to particles in hyperbolic orbits, particle swarms, morning-to-evening asymmetry, the effects of the earth's orbit eccentricity, and the presence of interstellar dust are discussed. The effects of space debris on data collection are considered.

Singer, S. F.↗
NASA NTRS2009

Angle of Attack Modulation for Mars Entry Terminal State Optimization

From the perspective of atmospheric entry, descent, and landing (EDL), one of the most foreboding destinations in the solar system is Mars due in part to its exceedingly thin atmosphere. To benchmark best possible scenarios for evaluation of potential Mars EDL system designs, a study is conducted to optimize the entry-to-terminal-state portion of EDL for a variety of entry velocities and vehicle masses, focusing on the identification of potential benefits of enabling angle of attack modulation. The terminal state is envisioned as one appropriate for the initiation of terminal descent via parachute or other means. A particle swarm optimizer varies entry flight path angle, ten bank profile points, and ten angle of attack profile points to find maximum-final-altitude trajectories for a 10 30 m ellipsled at 180 different combinations of values for entry mass, entry velocity, terminal Mach number, and minimum allowable altitude. Parametric plots of maximum achievable altitude are shown, as are examples of optimized trajectories. It is shown that appreciable terminal state altitude gains (2.5-4.0 km) over pure bank angle control may be possible if angle of attack modulation is enabled for Mars entry vehicles. Gains of this magnitude could prove to be enabling for missions requiring high-altitude landing sites. Conclusions are also drawn regarding trends in the bank and angle of attack profiles that produce the optimal trajectories in this study, and directions for future work are identified.

Lafleur, Jarret M.↗
NASA NTRS2010

NASA Tech Briefs, June 2010

Topics covered include: Situational Awareness from a Low-Cost Camera System; Data Acquisition System for Multi-Frequency Radar Flight Operations Preparation; Mercury Toolset for Spatiotemporal Metadata; Social Tagging of Mission Data; Integrating Radar Image Data with Google Maps; Demonstration of a Submillimeter-Wave HEMT Oscillator Module at 330 GHz; Flexible Peripheral Component Interconnect Input/Output Card; Interface Supports Lightweight Subsystem Routing for Flight Applications; MMIC Amplifiers and Wafer Probes for 350 to 500 GHz; Public Risk Assessment Program; Particle Swarm Optimization Toolbox; Telescience Support Center Data System Software; Update on PISCES; Ground and Space Radar Volume Matching and Comparison Software; Web-Based Interface for Command and Control of Network Sensors; Orbit Determination Toolbox; Distributed Observer Network; Computer-Automated Evolution of Spacecraft X-Band Antennas; Practical Loop-Shaping Design of Feedback Control Systems; Fully Printed High-Frequency Phased-Array Antenna on Flexible Substrate; Formula for the Removal and Remediation of Polychlorinated Biphenyls in Painted Structures; Integrated Solar Concentrator and Shielded Radiator; Water Membrane Evaporator; Modeling of Failure for Analysis of Triaxial Braided Carbon Fiber Composites; Catalyst for Carbon Monoxide Oxidation; Titanium Hydroxide - a Volatile Species at High Temperature; Selective Functionalization of Carbon Nanotubes: Part II; Steerable Hopping Six-Legged Robot; Launchable and Retrievable Tetherobot; Hybrid Heat Exchangers; Orbital Winch for High-Strength, Space-Survivable Tethers; Parameterized Linear Longitudinal Airship Model; and Physics of Life: A Model for Non-Newtonian Properties of Living Systems.

Source record↗
NASA NTRS2012

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

Mixed Integer Programming↗