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At least 289 records · Page 16

Iterative-deepening heuristic search for optimal and semi-optimal resource allocation

It is demonstrated that when iterative-deepening A asterisk (IDA asterisk) is applied to one type of resource allocation problem, it uses far less storage than A asterisk, but opens far more nodes and thus has unacceptable time complexity. This is shown to be due, at least in part, to the low-valued effective branching factor that is a characteristic of problems with real-valued cost functions. The semi-optimal, epsilon-admissible IDA asterisk sub epsilon search algorithm that the authors described was shown to open fewer nodes than both A asterisk and IDA asterisk with storage complexity proportional to the depth of the search tree.

Bridges, Susan M.↗

Machine Learning Based Path Planning for Improved Rover Navigation

Enhanced AutoNav (ENav), the baseline surface navigation software for NASA’s Perseverance rover, sorts a list of candidate paths for the rover to traverse, then uses the Approximate Clearance Evaluation (ACE) algorithm to evaluate whether the most highly ranked paths are safe. ACE is crucial for maintaining the safety of the rover, but is computationally expensive. If the most promising candidates in the list of paths are all found to be infeasible, ENav must continue to search the list and run time-consuming ACE evaluations until a feasible path is found. In this paper, we present two heuristics that, given a terrain heightmap around the rover, produce cost estimates that more effectively rank the candidate paths before ACE evaluation. The first heuristic uses Sobel operators and convolution to incorporate the cost of traversing high-gradient terrain. The second heuristic uses a machine learning (ML) model to predict areas that will be deemed untraversable by ACE. We used physics simulations to collect training data for the ML model and to run Monte Carlo trials to quantify navigation performance across a variety of terrains with various slopes and rock distributions. Compared to ENav's baseline performance, integrating the heuristics can lead to a significant reduction in ACE evaluations and average computation time per planning cycle, increase path efficiency, and maintain or improve the rate of successful traverses. This strategy of targeting specific bottlenecks with ML while maintaining the original ACE safety checks provides an example of how ML can be infused into planetary science missions and other safety-critical software.

Yue, Yisong↗

Physics Informed Neural Nets for Systems Health Management

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Development in data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. The research work presents application of physics-informed neural nets application to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage.

Physics Informed↗

Using Induction to Refine Information Retrieval Strategies

Conceptual information retrieval systems use structured document indices, domain knowledge and a set of heuristic retrieval strategies to match user queries with a set of indices describing the document's content. Such retrieval strategies increase the set of relevant documents retrieved (increase recall), but at the expense of returning additional irrelevant documents (decrease precision). Usually in conceptual information retrieval systems this tradeoff is managed by hand and with difficulty. This paper discusses ways of managing this tradeoff by the application of standard induction algorithms to refine the retrieval strategies in an engineering design domain. We gathered examples of query/retrieval pairs during the system's operation using feedback from a user on the retrieved information. We then fed these examples to the induction algorithm and generated decision trees that refine the existing set of retrieval strategies. We found that (1) induction improved the precision on a set of queries generated by another user, without a significant loss in recall, and (2) in an interactive mode, the decision trees pointed out flaws in the retrieval and indexing knowledge and suggested ways to refine the retrieval strategies.

Baudin, Catherine↗

Kodiak: An Implementation Framework for Branch and Bound Algorithms

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Smith, Andrew P.↗

Fuzzy Adaptive Control for Intelligent Autonomous Space Exploration Problems

The principal objective of the research reported here is the re-design, analysis and optimization of our newly developed neural network fuzzy adaptive controller model for complex processes capable of learning fuzzy control rules using process data and improving its control through on-line adaption. The learned improvement is according to a performance objective function that provides evaluative feedback; this performance objective is broadly defined to meet long-range goals over time. Although fuzzy control had proven effective for complex, nonlinear, imprecisely-defined processes for which standard models and controls are either inefficient, impractical or cannot be derived, the state of the art prior to our work showed that procedures for deriving fuzzy control, however, were mostly ad hoc heuristics. The learning ability of neural networks was exploited to systematically derive fuzzy control and permit on-line adaption and in the process optimize control. The operation of neural networks integrates very naturally with fuzzy logic. The neural networks which were designed and tested using simulation software and simulated data, followed by realistic industrial data were reconfigured for application on several platforms as well as for the employment of improved algorithms. The statistical procedures of the learning process were investigated and evaluated with standard statistical procedures (such as ANOVA, graphical analysis of residuals, etc.). The computational advantage of dynamic programming-like methods of optimal control was used to permit on-line fuzzy adaptive control. Tests for the consistency, completeness and interaction of the control rules were applied. Comparisons to other methods and controllers were made so as to identify the major advantages of the resulting controller model. Several specific modifications and extensions were made to the original controller. Additional modifications and explorations have been proposed for further study. Some of these are in progress in our laboratory while others await additional support. All of these enhancements will improve the attractiveness of the controller as an effective tool for the on line control of an array of complex process environments.

Esogbue, Augustine O.↗

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigation of electrodynamic stabilization and control of long orbiting tethers

An algorithm for using electric currents to control pendular oscillations induced by various perturbing forces on the Skyhook wire is considered. Transverse and vertical forces on the tether; tether instability modes and causes during retrieval by space shuttle; simple and spherical pendulum motion and vector damping; and current generation and control are discussed. A computer program for numerical integration of the in-plane and out-of-plane displacements of the tether vs time was developed for heuristic study. Some techniques for controlling instabilities during payload retrieval and methods for employing the tether for launching satellites from the space shuttle are considered. Derivations and analyses of a general nature used in all of the areas studied are included.

Arnold, D. A.↗

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

Automated Point Cloud Correspondence Detection for Underwater Mapping Using AUVs

An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.

Sonar↗

WHAMII - An enumeration and insertion procedure with binomial bounds for the stochastic time-constrained traveling salesman problem

This paper presents an algorithm (WHAMII) designed to solve the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation and Control Conference. The problem under consideration is a stochastic generalization of the traveling salesman problem in which travel costs can incur a penalty with a given probability. The variability in travel costs leads to a probability constraint with respect to violating the budget allocation. Given the small size of the problem (eleven cities), an approach is considered that combines partial tour enumeration with a heuristic city insertion procedure. For computational efficiency during both the enumeration and insertion procedures, precalculated binomial probabilities are used to determine an upper bound on the actual probability of violating the budget constraint for each tour. The actual probability is calculated for the final best tour, and additional insertions are attempted until the actual probability exceeds the bound.

Dahl, Roy W.↗

A linguistic geometry for 3D strategic planning

This paper is a new step in the development and application of the Linguistic Geometry. This formal theory is intended to discover the inner properties of human expert heuristics, which have been successful in a certain class of complex control systems, and apply them to different systems. In this paper we investigate heuristics extracted in the form of hierarchical networks of planning paths of autonomous agents. Employing Linguistic Geometry tools the dynamic hierarchy of networks is represented as a hierarchy of formal attribute languages. The main ideas of this methodology are shown in this paper on the new pilot example of the solution of the extremely complex 3D optimization problem of strategic planning for the space combat of autonomous vehicles. This example demonstrates deep and highly selective search in comparison with conventional search algorithms.

Stilman, Boris↗

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗

Resource constrained design of artificial neural networks using comparator neural network

We present a systematic design method executed under resource constraints for automating the design of artificial neural networks using the back error propagation algorithm. Our system aims at finding the best possible configuration for solving the given application with proper tradeoff between the training time and the network complexity. The design of such a system is hampered by three related problems. First, there are infinitely many possible network configurations, each may take an exceedingly long time to train; hence, it is impossible to enumerate and train all of them to completion within fixed time, space, and resource constraints. Second, expert knowledge on predicting good network configurations is heuristic in nature and is application dependent, rendering it difficult to characterize fully in the design process. A learning procedure that refines this knowledge based on examples on training neural networks for various applications is, therefore, essential. Third, the objective of the network to be designed is ill-defined, as it is based on a subjective tradeoff between the training time and the network cost. A design process that proposes alternate configurations under different cost-performance tradeoff is important. We have developed a Design System which schedules the available time, divided into quanta, for testing alternative network configurations. Its goal is to select/generate and test alternative network configurations in each quantum, and find the best network when time is expended. Since time is limited, a dynamic schedule that determines the network configuration to be tested in each quantum is developed. The schedule is based on relative comparison of predicted training times of alternative network configurations using comparator network paradigm. The comparator network has been trained to compare training times for a large variety of traces of TSSE-versus-time collected during back-propagation learning of various applications.

Wah, Benjamin W.↗

Fast and robust strategies for large-scale mixed-integer SCOPF

This project develops scalable, computationally efficient algorithms to solve realistic large-scale power system optimization problems, including systems with more than 8,000 buses, as part of a larger series of competitions run by ARPA-E. These problems are critical because the secure and reliable operation of the power grid is becoming increasingly challenging, especially under conditions of increased uncertainty and variability. The economic feasibility of our methods is high, given that they are purely software-based solutions designed to operate power grids more efficiently. The technical effectiveness balances heuristics and approximations to provide a trade-off between speed and accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A linguistic geometry for space applications

We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

Stilman, Boris↗