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Algorithms construction for aerospace vehicle trajectory optimization, considering quasi- linearization method for computation of variable time optimum trajectories
In this work, we propose a Generalized Disjunctive Programming (GDP) model that optimizes both long-term capacity planning (such as the number and size of dispatchable/renewable generators, batteries, and transmission lines) and hourly operation (such as on/off schedules of dispatchable generators, power output from each generator, and power flow) to maximize power system reliability while minimizing total cost and CO2 emissions.
The optimization of space operations is examined in the light of optimization heuristics for computer algorithms and iterative search techniques. Specific attention is given to the search concepts known collectively as intelligent perturbation algorithms (IPAs) and their application to crew/resource allocation problems. IPAs iteratively examine successive schedules which become progressively more efficient, and the characteristics of good perturbation operators are listed. IPAs can be applied to aerospace systems to efficiently utilize crews, payloads, and resources in the context of systems such as Space-Station scheduling. A program is presented called the MFIVE Space Station Scheduling Worksheet which generates task assignments and resource usage structures. The IPAs can be used to develop flexible manifesting and scheduling for the Industrial Space Facility.
Long-duration surface missions to the Moon and Mars will require bases to accommodate habitats for the astronauts. Transporting the materials and equipment required to build the necessary habitats is costly and difficult. The materials chosen for the habitat walls play a direct role in protection against each of the mentioned hazards. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Clearly, an optimization method is warranted for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat wall design tool utilizing genetic algorithms (GAs) has been developed. GAs use a "survival of the fittest" philosophy where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multiobjective formulation of up-mass, heat loss, structural analysis, meteoroid impact protection, and radiation protection. This Technical Publication presents the research and development of this tool as well as a technique for finding the optimal GA search parameters.
Soils in natural and managed ecosystems and wetlands are well known sources of methane, nitrous oxides, and reactive nitrogen gases, but the magnitudes of gas flux to the atmosphere are still poorly constrained. Thus, the reasons for the large increases in atmospheric concentrations of methane and nitrous oxide since the preindustrial time period are not well understood. The low atmospheric concentrations of methane and nitrous oxide, despite being more potent greenhouse gases than carbon dioxide, complicate empirical studies to provide explanations. In addition to climate concerns, the emissions of reactive nitrogen gases from soils are important to the changing nitrogen balance in the earth system, subject to human management, and may change substantially in the future. Thus improved modeling of the emission fluxes of these species from the land surface is important. Currently, there are emission modules for methane and some nitrogen species in the Community Earth System Model’s Community Land Model (CLM-ME/N); however, there are large uncertainties and problems in the simulations, resulting in coarse estimates. In this proposal, we seek to improve these emission modules by combining state-of-the-art process modules for emissions, available data, and new optimization methods. In earth science problems, we often have substantial data and knowledge of processes in disparate systems, and thus we need to combine data and a general process level understanding into a model for projections of future climate that are as accurate as possible. The best methodologies for optimization of parameters in earth system models are still being developed. In this proposal we will develop and apply surrogate algorithms that a) were especially developed for computationally expensive simulations like CLM-ME/N models; b) were (in the earlier surrogate optimization Stochastic RBF) demonstrated to perform very well on computationally expensive complex partial differential equations in earth science with limited numbers of simulations; and, c) will be (as part of the proposed research) significantly improved both by adding asynchronous parallelism, early truncation of unsuccessful simulations, and the improvement of both serial and parallel performance by the use of derivative and sensitivity information from global and local surrogate approximations S(x) . The algorithm development and testing will be focused on the CLM-ME/N model application, but the methods are general and are expected to also perform well on optimization for parameter estimation of other climate models and other classes of continuous multimodal optimization problems arising from complex simulation models. In addition, this proposal will compile available datasets of emissions of methane, nitrous oxides and reactive nitrogen species and develop protocols for site level comparisons with the CLM-ME/N. Once the model parameters are optimized against site level data, the model will be simulated at the global level and compared to atmospheric concentration measurements for the current climate, and future emissions will be estimated using climate change as simulated by the CESM. This proposal combines experts in earth system modeling, optimization, computer science, and process level understanding of soil gas emissions in an interdisciplinary team in order to improve the modeling of methane and nitrogen gas emissions. This proposal thus meets the requirements of the SciDAC RFP, by integrating state-of-the-art computer science and earth system to build an improved earth system model.
We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.
Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. Here, we quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.
Discrete time differential dynamic programming algorithm with application to optimal orbit transfer
Phasor measurement units (PMUs) play an important role in the wide‐area monitoring and protection of modern power systems. Historically, their deployment was limited by the prohibitive cost of the device itself. Therefore, the objective of the conventional optimal PMU placement problem was to find minimum number of devices, which when carefully placed throughout the network, maximised observability subject to different constraints. Due to improvements in relay technology, digital relays can now serve as both relays and PMUs. Under such circumstances, the substation installations consume the largest portion of the deployment cost, and not the devices themselves. Thus, for minimising cost of synchrophasor deployment, number of substation installations must be minimised. This study uses binary particle swarm optimisation to minimise number of substations in which installations must be performed for making all voltage levels observable, while being subject to various practical constraints. Standard IEEE systems have been used to explain the technique. Finally, a large‐scale network of Dominion Virginia Power is used as the test bed for implementation.
Herein we demonstrate how to use model optimization to determine a set of best-fit parameters for a landform model simulating gully incision and headcut retreat. To achieve this result we employed the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), an iterative process in which samples are created based on a distribution of parameter values that evolve over time to better fit an objective function. CMA-ES efficiently finds optimal parameters, even with high-dimensional objective functions that are non-convex, multimodal, and non-separable. We ran model instances in parallel on a high-performance cluster, and from hundreds of model runs we obtained the best parameter choices. This method is far superior to brute-force search algorithms, and has great potential for many applications in earth science modeling. We found that parameters representing boundary conditions tended to converge toward an optimal single value, whereas parameters controlling geomorphic processes are defined by a range of optimal values.
This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarm rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.
Algorithms and computation techniques for solving trajectory optimization problems
A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.
A robust trajectory optimization approach for guidance algorithm gain selection for powered descent and landing is developed. This approach uses a genetic algorithm to determine optimal guidance algorithm parameters while incorporating uncertainty information from linear covariance analysis. The optimal guidance algorithm parameters are determined while accounting for environment, navigation, and vehicle property uncertainty and sensor suite fidelity. As a demonstration of this method, the optimal gains for the fractional polynomial powered descent guidance are found for the braking phase of a robotic lunar landing mission. Scenarios with differing sensor suites and sensor qualities are considered, with objective functions to minimize variability in propellant usage or terminal position. Results show that the optimal guidance algorithm gains for a given trajectory differ based on the sensor suite, and optimal guidance algorithm gains may result in up to 20% performance improvements over the baseline in propellant usage and landed accuracy.
Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.
SPLICER computer program used to solve search and optimization problems. Genetic algorithms adaptive search procedures (i.e., problem-solving methods) based loosely on processes of natural selection and Darwinian "survival of fittest." Algorithms apply genetically inspired operators to populations of potential solutions in iterative fashion, creating new populations while searching for optimal or nearly optimal solution to problem at hand. Written in Think C.
An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.
This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.