Dynamic programming algorithm for determining 'best fit', part I
Dynamic programming algorithm for estimating best fit, and solution to example problem
PROBLEM SOLVING↗
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A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer
Differential dynamic programming algorithm for discrete time orbit transfer optimization
Gershwin, S. B.↗
A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer
Discrete time differential dynamic programming algorithm with application to optimal orbit transfer
Gershwin, S. B.↗
Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae
The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.
Rosu, Grigore↗
Configuring Airspace Sectors with Approximate Dynamic Programming
In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.
Bloem, Michael↗
Models and Algorithms for Equilibrium Analysis of Mixed-Material Nucleic Acid Systems
Dynamic programming algorithms within the NUPACK software suite enable analysis of equilibrium base-pairing properties for complex and test tube ensembles containing arbitrary numbers of interacting nucleic acid strands. Currently, calculations are limited to single-material systems that are either all-RNA or all-DNA. Here, to enable analysis of mixed-material systems that are critical for modern applications in vitro, in situ, and in vivo, we develop physical models and dynamic programming algorithms that allow the material of the system to be specified at nucleotide resolution. Free energy parameter sets are constructed for both RNA/DNA and RNA/2'OMe-RNA mixed-material systems by combining available empirical mixed-material parameters with single-material parameter sets to enable treatment of the full complex and test tube ensembles. New dynamic programming recursions account for the material of each nucleotide throughout the recursive process. For a complex with N nucleotides, the mixed-material dynamic programming algorithms maintain the O(N 3 ) time complexity of the single-material algorithms, enabling efficient calculation of diverse physical quantities over complex and test tube ensembles (e.g., complex partition function, equilibrium complex concentrations, equilibrium base-pairing probabilities, minimum free energy secondary structure(s), and Boltzmann-sampled secondary structures) at a cost increase of roughly 2.0-3.5×. The results of existing single-material algorithms are exactly reproduced when applying the new mixed-material algorithms to single-material systems. Accuracy is significantly enhanced using mixed-material models and algorithms to predict RNA/DNA and RNA/2'OMe-RNA duplex melting temperatures from the experimental literature as well as RNA/DNA melt profiles from new experiments. In conclusion, mixed-material analyses can be performed online using the NUPACK web app (www.nupack.org) or locally using the NUPACK Python module.
2′OMe-RNA↗
New second-order and first-order algorithms for determining optimal control - A differential dynamic programming approach.
Differential dynamic programming algorithms of second and first order for optimal control, considering nonlinear unconstrained and constrained problems
Jacobson, D. H.↗
An algorithm for the solution of dynamic linear programs
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.
Psiaki, Mark L.↗
Simulation and analysis of optimal self-paced second order control systems
Local variation of dynamic programming algorithm and computer simulation of optimal second-order self-pace control systems
CONTROL SYSTEM↗
Synthesizing Monitors for Safety Properties
The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in time analysis of software. An algorithm which takes a past time LTL formula and generates an efficient dynamic programming algorithm is presented. The generated algorithm tests whether the formula is satisfied by a finite trace of events given as input and runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula. Further optimizations of the algorithm are suggested. Past time operators suitable for writing succinct specifications axe introduced and shown definitionally equivalent to the standard operators. This work is part of the PathExplorer project, the objective of which it is to construct a flexible framework for monitoring and analyzing program executions.
Havelund, Klaus↗
Design and Evaluation of a Dynamic Programming Flight Routing Algorithm Using the Convective Weather Avoidance Model
The optimization of traffic flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and efficiency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air traffic constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.
Ng, Hok K.↗
Joint Chance-Constrained Dynamic Programming
This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.
Ono, Masahiro↗
Modeling human decision making behavior in supervisory control
An optimal decision control model was developed, which is based primarily on a dynamic programming algorithm which looks at all the available task possibilities, charts an optimal trajectory, and commits itself to do the first step (i.e., follow the optimal trajectory during the next time period), and then iterates the calculation. A Bayesian estimator was included which estimates the tasks which might occur in the immediate future and provides this information to the dynamic programming routine. Preliminary trials comparing the human subject's performance to that of the optimal model show a great similarity, but indicate that the human skips certain movements which require quick change in strategy.
Tulga, M. K.↗
Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing
A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.
Ono, Masahiro↗
Search Problems in Mission Planning and Navigation of Autonomous Aircraft
An architecture for the control of an autonomous aircraft is presented. The architecture is a hierarchical system representing an anthropomorphic breakdown of the control problem into planner, navigator, and pilot systems. The planner system determines high level global plans from overall mission objectives. This abstract mission planning is investigated by focusing on the Traveling Salesman Problem with variations on local and global constraints. Tree search techniques are applied including the breadth first, depth first, and best first algorithms. The minimum-column and row entries for the Traveling Salesman Problem cost matrix provides a powerful heuristic to guide these search techniques. Mission planning subgoals are directed from the planner to the navigator for planning routes in mountainous terrain with threats. Terrain/threat information is abstracted into a graph of possible paths for which graph searches are performed. It is shown that paths can be well represented by a search graph based on the Voronoi diagram of points representing the vertices of mountain boundaries. A comparison of Dijkstra's dynamic programming algorithm and the A* graph search algorithm from artificial intelligence/operations research is performed for several navigation path planning examples. These examples illustrate paths that minimize a combination of distance and exposure to threats. Finally, the pilot system synthesizes the flight trajectory by creating the control commands to fly the aircraft.
Krozel, James A.↗
A k-mer based approach for classifying viruses without taxonomy identifies viral associations in human autism and plant microbiomes
Viruses are an underrepresented taxa in the study and identification of microbiome constituents; however, they play an essential role in health, microbiome regulation, and transfer of genetic material. Only a few thousand viruses have been isolated, sequenced, and assigned a taxonomy, which limits the ability to identify and quantify viruses in the microbiome. Additionally, the vast diversity of viruses represents a challenge for classification, not only in constructing a viral taxonomy, but also in identifying similarities between a virus’ genotype and its phenotype. However, the diversity of viral sequences can be leveraged to classify their sequences in metagenomic and metatranscriptomic samples, even if they do not have a taxonomy. To identify and quantify viruses in transcriptomic and genomic samples, we developed a dynamic programming algorithm for creating a classification tree out of 715,672 metagenome viruses. To create the classification tree, we clustered proportional similarity scores generated from the k-mer profiles of each of the metagenome viruses to create a database of metagenomic viruses. The resulting Kraken2 database of the metagenomic viruses can be found here: https://www.osti.gov/biblio/1615774 and is compatible with Kraken2. We then integrated the viral classification database with databases created with genomes from NCBI for use with ParaKraken (a parallelized version of Kraken provided in Supplemental Zip 1), a metagenomic/transcriptomic classifier. To illustrate the breadth of our utility for classifying metagenome viruses, we analyzed data from a plant metagenome study identifying genotypic and compartment specific differences between two Populus genotypes in three different compartments. We also identified a significant increase in abundance of eight viral sequences in post mortem brains in a human metatranscriptome study comparing Autism Spectrum Disorder patients and controls. We also show the potential accuracy for classifying viruses by utilizing both the JGI and NCBI viral databases to identify the uniqueness of viral sequences. Finally, we validate the accuracy of viral classification with NCBI databases containing viruses with taxonomy to identify pathogenic viruses in known COVID-19 and cassava brown streak virus infection samples. Our method represents the compulsory first step in better understanding the role of viruses in the microbiome by allowing for a more complete identification of sequences without taxonomy. Better classification of viruses will improve identifying associations between viruses and their hosts as well as viruses and other microbiome members. Despite the lack of taxonomy, this database of metagenomic viruses can be used with any tool that utilizes a taxonomy, such as Kraken, for accurate classification of viruses.
59 BASIC BIOLOGICAL SCIENCES↗
Adaptive PID Gain Scheduling Control for Hydropower Turbine Using Neural CDE and Stochastic Distribution Shaping
This paper introduces a gain-scheduling PID controller design strategy for hydroturbine frequency control mode. This scheme first uses real data to learn the nonlinear dynamics of the hydroturbine using neural controlled differential equations and then perturbs the obtained nonlinear system at different equilibrium points, based on which a static output feedback adaptive dynamic programming algorithm is then used to optimize the PID gains for each equilibrium point. Moreover, a continuous-time version of stochastic distribution control is proposed to further fine-tune the optimized PID gains. Finally, the controller is obtained by implementing linear interpolation between the optimized PID control gains. The simulation results show that the proposed gain-scheduling PID controller can control a larger range of operation points compared with the given fixed PID controller and the baseline method. Compared with the given fixed PID controller, the proposed gain-scheduling PID controller can regulate hydroturbine frequency against disturbances induced by power-load variation with over 50% less overshoot for some operation points.
13 HYDRO ENERGY↗
Kraken2 Metagenomic Virus Database
The Database: Kraken2 [1] database built from a classification tree containing over 700k metagenomic viruses from JGI IMG/VR [2]. (1) Wood, D. E., Lu, J., and Langmead, B. (2019). Improved metagenomic analysis with Kraken 2. Genome Biol., 20(1), 1–13. doi: 10.1186/s13059-019-1891-0 (2) Paez-Espino D, Chen I-MA, Palaniappan K, Ratner A, Chu K, Szeto E, et al. IMG/VR: a database of cultured and uncultured DNA Viruses and retroviruses. Nucleic Acids Res. 2017;45:D457-65. For Paper: Title: A k-mer based approach for virus classification in metatranscriptomic and metagenomic samples identifies viral associations in the Populus phytobiome and autism brains Abstract Background Viruses are an underrepresented taxa in the study and identification of microbiome constituents; however, they play an important role in health, microbiome regulation, and transfer of genetic material. Only a few thousand viruses have been isolated, sequenced, and assigned a taxonomy, which further limits the ability to identify and quantify viruses in the microbiome. Additionally, the vast diversity of viruses represents a challenge for classification, not only in constructing a viral taxonomy, but also in identifying similarities between a virus' genotype and its phenotype. However, the diversity of viral sequences can be leveraged to classify their sequences in metagenomic and metatranscriptomic samples. Methods To identify viruses in transcriptomic and genomic samples, we developed a dynamic programming algorithm for creating a classification tree out of 715,672 metagenome viruses. To create the classification tree, we clustered proportional similarity scores generated from the k-mer profiles of each of the metagenome viruses. We then integrated the viral classification tree with the NCBI taxonomy for use with ParaKraken, a metagenomic/transcriptomic classifier. Results To illustrate the breadth of our utility for classifying viruses with ParaKraken, we analyzed data from a plant metagenome study identifying the differences between two Populus genotypes in three different compartments and on a human metatranscriptome study identifying the differences between Autism Spectrum Disorder patients and controls in post mortem brain biopsies. In the Populus study, we identified genotype and compartment specific viral signatures, while in the Autism study we identified a significant increased abundance of eight viral sequences in Autism brain biopsies. Conclusion Viruses represent an important aspect of the microbiome. The ability to classify viruses represents the first step in being able to better understand their role in the microbiome. The viral classification method presented here allows for more complete identification of viral sequences for use in identifying associations between viruses and the host and viruses and other microbiome members. Acknowledgements and Funding This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This research was also supported by the Plant-Microbe Interfaces Scientific Focus Area in the Genomic Science Program, the Office of Biological and Environmental Research (BER) in the U.S. Department of Energy Office of Science, and by the Department of Energy, Laboratory Directed Research and Development funding (ProjectID 8321), at the Oak Ridge National Laboratory. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the US DOE under contract DE-AC05-00OR22725. This research used resources of the Compute and Data Environment for Science (CADES).
59 BASIC BIOLOGICAL SCIENCES↗