Lila: Optimal Dispatching in Probabilistic Temporal Networks using Monte Carlo Tree Search
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Chien, Steve A.↗
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Adapting Random Tree Search to Fixed Wing Aerial Vehicles with Closed-Loop Prediction and Hybrid Control
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Deal, Samuel [Georgia Institute of Technology]↗
Leveraging Monte Carlo Tree Search to Improve Teaming Performance in Multi-AgentAdversarial Environments
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Connelly, Matthew Ryan [Sandia National Laboratori↗
Expected performance of m-solution backtracking
This paper derives upper bounds on the expected number of search tree nodes visited during an m-solution backtracking search, a search which terminates after some preselected number m problem solutions are found. The search behavior is assumed to have a general probabilistic structure. The results are stated in terms of node expansion and contraction. A visited search tree node is said to be expanding if the mean number of its children visited by the search exceeds 1 and is contracting otherwise. It is shown that if every node expands, or if every node contracts, then the number of search tree nodes visited by a search has an upper bound which is linear in the depth of the tree, in the mean number of children a node has, and in the number of solutions sought. Also derived are bounds linear in the depth of the tree in some situations where an upper portion of the tree contracts (expands), while the lower portion expands (contracts). While previous analyses of 1-solution backtracking have concluded that the expected performance is always linear in the tree depth, the model allows superlinear expected performance.
Nicol, D. M.↗
The CluMPR galaxy cluster-finding algorithm and DESI legacy survey galaxy cluster catalogue
ABSTRACT Galaxy clusters enable unique opportunities to study cosmology, dark matter, galaxy evolution, and strongly lensed transients. We here present a new cluster-finding algorithm, CluMPR (Clusters from Masses and Photometric Redshifts), that exploits photometric redshifts (photo-z’s) as well as photometric stellar mass measurements. CluMPR uses a 2D binary search tree to search for overdensities of massive galaxies with similar redshifts on the sky and then probabilistically assigns cluster membership by accounting for photo-z uncertainties. We leverage the deep DESI Legacy Survey grzW1W2 imaging over one-third of the sky to create a catalogue of $\sim 300\, 000$ galaxy cluster candidates out to z = 1, including tabulations of member galaxies and estimates of each cluster’s total stellar mass. Compared to other methods, CluMPR is particularly effective at identifying clusters at the high end of the redshift range considered (z = 0.75–1), with minimal contamination from low-mass groups. These characteristics make it ideal for identifying strongly lensed high-redshift supernovae and quasars that are powerful probes of cosmology, dark matter, and stellar astrophysics. As an example application of this cluster catalogue, we present a catalogue of candidate wide-angle strongly lensed quasars in Appendix C. The nine best candidates identified from this sample include two known lensed quasar systems and a possible changing-look lensed QSO with SDSS spectroscopy. All code and catalogues produced in this work are publicly available (see Data Availability).
79 ASTRONOMY AND ASTROPHYSICS↗
Efficient Merge and Insert Operations for Binary Heaps and Trees
Binary heaps and binary search trees merge efficiently. We introduce a new amortized analysis that allows us to prove the cost of merging either binary heaps or balanced binary trees is O(l), in the amortized sense. The standard set of other operations (create, insert, delete, extract minimum, in the case of binary heaps, and balanced binary trees, as well as a search operation for balanced binary trees) remain with a cost of O(log n). For binary heaps implemented as arrays, we show a new merge algorithm that has a single operation cost for merging two heaps, a and b, of O(absolute value of a + min(log absolute value of b log log absolute value of b. log absolute value of a log absolute value of b). This is an improvement over O(absolute value of a + log absolute value of a log absolute value of b). The cost of the new merge is so low that it can be used in a new structure which we call shadow heaps. to implement the insert operation to a tunable efficiency. Shadow heaps support the insert operation for simple priority queues in an amortized time of O(f(n)) and other operations in time O((log n log log n)/f (n)), where 1 less than or equal to f (n) less than or equal to log log n. More generally, the results here show that any data structure with operations that change its size by at most one, with the exception of a merge (aka meld) operation, can efficiently amortize the cost of the merge under conditions that are true for most implementations of binary heaps and search trees.
Kuszmaul, Christopher Lee↗
An implementation of a tree code on a SIMD, parallel computer
We describe a fast tree algorithm for gravitational N-body simulation on SIMD parallel computers. The tree construction uses fast, parallel sorts. The sorted lists are recursively divided along their x, y and z coordinates. This data structure is a completely balanced tree (i.e., each particle is paired with exactly one other particle) and maintains good spatial locality. An implementation of this tree-building algorithm on a 16k processor Maspar MP-1 performs well and constitutes only a small fraction (approximately 15%) of the entire cycle of finding the accelerations. Each node in the tree is treated as a monopole. The tree search and the summation of accelerations also perform well. During the tree search, node data that is needed from another processor is simply fetched. Roughly 55% of the tree search time is spent in communications between processors. We apply the code to two problems of astrophysical interest. The first is a simulation of the close passage of two gravitationally, interacting, disk galaxies using 65,636 particles. We also simulate the formation of structure in an expanding, model universe using 1,048,576 particles. Our code attains speeds comparable to one head of a Cray Y-MP, so single instruction, multiple data (SIMD) type computers can be used for these simulations. The cost/performance ratio for SIMD machines like the Maspar MP-1 make them an extremely attractive alternative to either vector processors or large multiple instruction, multiple data (MIMD) type parallel computers. With further optimizations (e.g., more careful load balancing), speeds in excess of today's vector processing computers should be possible.
Olson, Kevin M.↗
Automatic creation of object hierarchies for ray tracing
Various methods for evaluating generated trees are proposed. The use of the hierarchical extent method of Rubin and Whitted (1980) to find the objects that will be hit by a ray is examined. This method employs tree searching; the construction of a tree of bounding volumes in order to determine the number of objects that will be hit by a ray is discussed. A tree generation algorithm, which uses a heuristic tree search strategy, is described. The effects of shuffling and sorting on the input data are investigated. The cost of inserting an object into the hierarchy during the construction of a tree algorithm is estimated. The steps involved in estimating the number of intersection calculations are presented.
Goldsmith, Jeffrey↗
A VLSI chip set for real time vector quantization of image sequences
The architecture and implementation of a VLSI chip set that vector quantizes (VQ) image sequences in real time is described. The chip set forms a programmable Single-Instruction, Multiple-Data (SIMD) machine which can implement various vector quantization encoding structures. Its VQ codebook may contain unlimited number of codevectors, N, having dimension up to K = 64. Under a weighted least squared error criterion, the engine locates at video rates the best code vector in full-searched or large tree searched VQ codebooks. The ability to manipulate tree structured codebooks, coupled with parallelism and pipelining, permits searches in as short as O (log N) cycles. A full codebook search results in O(N) performance, compared to O(KN) for a Single-Instruction, Single-Data (SISD) machine. With this VLSI chip set, an entire video code can be built on a single board that permits realtime experimentation with very large codebooks.
Baker, Richard L.↗
Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization
Herein this article presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture’s integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.
97 MATHEMATICS AND COMPUTING↗
Bounding the Resource Availability of Partially Ordered Events with Constant Resource Impact
We compare existing techniques to bound the resource availability of partially ordered events. We first show that, contrary to intuition, two existing techniques, one due to Laborie and one due to Muscettola, are not strictly comparable in terms of the size of the search trees generated under chronological search with a fixed heuristic. We describe a generalization of these techniques called the Flow Balance Constraint to tightly bound the amount of available resource for a set of partially ordered events with piecewise constant resource impact We prove that the new technique generates smaller proof trees under chronological search with a fixed heuristic, at little increase in computational expense. We then show how to construct tighter resource bounds but at increased computational cost.
Frank, Jeremy↗
Automated model formulation for time-varying flexible structures
Presented here is an identification technique that uses the sensor information to choose a new model out of a finite set of discrete model space, in order to follow the observed changes to the given time varying flexible structure. Boundary condition sets or other information on model variations are used to organize the set of possible models laterally into a search tree with levels of abstraction used to order the models vertically within branches. An object-oriented programming approach is used to represent the model set in the search tree. A modified A (asterisk) best first search algorithm finds the model where the model response best matches the current observations. Several extensions to this methodology are discussed. Methods of possible integration of rules with the current search algorithm are considered to give weight to interpreted trends that may be found in a series of observations. This capability might lead, for instance, to identifying a model that incorporates a progressive damage rather than with incorrect paramenters such as added mass. Another new direction is to consider the use of noisy time domain sensor feedback rather than frequency domain information in the search algorithm to improve the real-time capability of the developed procedure.
Glass, B. J.↗
An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services
Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions can change over time), causing the estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse—our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Multiprocessor sparse L/U decomposition with controlled fill-in
Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.
Alaghband, G.↗
An Online Search Method for Representative Risky Fault Chains Based on Reinforcement Learning and Knowledge Transfer
In the analysis of cascading outages and blackouts in power systems, risky cascading fault chains should be accurately identified in order to do further block or alleviate blackouts. However, the huge computational burden makes online analysis difficult. In this paper, an online search method for representative risky fault chains based on reinforcement learning and knowledge transfer is proposed. This method aims at promoting efficiency by exploiting similarities of adjacent power flow snapshots in operations. After the “representative risky fault chain” is defined, a framework of tree search based on Markov Decision Process and Q-learning is constructed. The knowledge in past runs is accumulated offline and then applied online, with a mechanism of knowledge transition and extension. The proposed learning based approach is verified on an illustrative 39-bus system with different loading levels, and simulations are carried out on a realworld 1000-bus power grid in China to show the effectiveness and efficiency of the proposed approach.
Blackout↗
Explorations of Quantum-Classical Approaches to Scheduling a Mars Lander Activity Problem
An effective approach to solving problems involving mixed (continuous and discrete) variables and constraints, such as hybrid systems, is to decompose them into subproblems and integrate dedicated solvers geared toward those subproblems. Here, we introduce a new framework based on a tree search algorithm to solve hybrid discrete-continuous problems that incorporates: (1) a quantum annealer that samples from the configuration space for the discrete portion and provides information about the quality of the samples, and (2) a classical computer that makes use of information from the quantum annealer to prune and focus the search as well as check a continuous constraint. We consider four variants of our algorithm, each with progressively more guidance from the results provided by the quantum annealer. We empirically test our algorithm and compare the variants on a simplified Mars Lander task scheduling problem. Variants with more guidance from the quantum annealer have better performance.
scheduling↗
Accelerated Sequence Design of Star Block Copolymers: An Unbiased Exploration Strategy via Fusion of Molecular Dynamics Simulations and Machine Learning
Star block copolymers (s-BCPs) have potential applications as novel surfactants or amphiphiles for emulsification, compatibilization, chemical transformations, and separations. s-BCPs have chain architectures where three or more linear diblock copolymer arms comprised of two chemically distinct linear polymers, e.g., solvophobic and solvophilic chains, are covalently joined at one point. The chemical composition of each of the subunit polymer chains comprising the arms, their molecular weights, and the number of arms can be varied to tailor the surface and interfacial activity of these architecturally unique molecules. Further, this makes identification of the optimal s-BCP design nontrivial as the total number of plausible s-BCP architectures is experimentally or computationally intractable. In this work, we use molecular dynamics (MD) simulations coupled with a reinforcement learning-based Monte Carlo tree search (MCTS) to identify s-BCP designs that minimize the interfacial tension between polar and nonpolar solvents. We first validate the MCTS approach for the design of small- and medium-sized s-BCPs and then use it to efficiently identify sequences of copolymer blocks for large-sized s-BCPs. The structural origins of interfacial tension in these systems are also identified by using the configurations obtained from MD simulations. Chemical insights into the arrangement of copolymer blocks that promote lower interfacial tension were mined using machine learning (ML) techniques. Overall, this work provides an efficient approach to solve design problems via fusion of simulations and ML and provides important groundwork for future experimental investigation of s-BCPs for various applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Learning with Delayed Rewards—A Case Study on Inverse Defect Design in 2D Materials
Defect dynamics in materials are of central importance to a broad range of technologies from catalysis to energy storage systems to microelectronics. Material functionality depends strongly on the nature and organization of defects-their arrangements often involve intermediate or transient states that present a high barrier for transformation. The lack of knowledge of these intermediate states and the presence of this energy barrier presents a serious challenge for inverse defect design, especially for gradient-based approaches. Here, we present a reinforcement learning (RL) [Monte Carlo Tree Search (MCTS)] based on delayed rewards that allow for efficient search of the defect configurational space and allows us to identify optimal defect arrangements in low-dimensional materials. Using a representative case of two-dimensional MoS 2 , we demonstrate that the use of delayed rewards allows us to efficiently sample the defect configurational space and overcome the energy barrier for a wide range of defect concentrations (from 1.5 to 8% S vacancies)-the system evolves from an initial randomly distributed S vacancies to one with extended S line defects consistent with previous experimental studies. Detailed analysis in the feature space allows us to identify the optimal pathways for this defect transformation and arrangement. Comparison with other global optimization schemes like genetic algorithms suggests that the MCTS with delayed rewards takes fewer evaluations and arrives at a better quality of the solution. The implications of the various sampled defect configurations on the 2H to 1T phase transitions in MoS 2 are discussed. In this study, we introduce a RL strategy employing delayed rewards that can accelerate the inverse design of defects in materials for achieving targeted functionality.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗