Showing papers on "Admissible heuristic published in 2020"

Long-Distance Path Planning for Unmanned Surface Vehicles in Complex Marine Environment

Abstract: Many missions require unmanned surface vehicles to operate in complex environments over large distances. Marine environments are dynamic in nature and change over time as a result of tides, weather, and environmental restrictions. As a result, the available free traversal space for a marine vehicle in the given map can change over time. This requires the marine vehicle to dynamically generate and update the traversal map to represent the free space. This paper presents techniques for speeding up A* search on the nodes of visibility graphs. We use a quadtree representation of the marine environment to enable the algorithm to efficiently compute the nodes of the visibility graphs. We have developed an admissible heuristic that considers the large islands while estimating cost-to-go, and provide better estimates than a Euclidean distance-based heuristic. Due to the large size of the marine environment, the branching factor of the search tree can become large and reduce the efficiency of the path planner. We have developed an approach that focuses the search by only considering the child nodes lying in the local region around each node. Our experiments demonstrate that by focusing the search, we can reduce the computational time without significantly sacrificing the optimality of the computed path. We also present an extension to the algorithm for handling dynamic environments with time-varying free spaces. We incorporated the depth charts developed by the National Oceanic and Atmospheric Administration (NOAA), Silver Spring, MD, USA, along with the tide predictions to estimate the time-varying free space that can be used by the planner.

Learning Differentiable Programs with Admissible Neural Heuristics

Abstract: We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

Scheduling Robotic Cellular Manufacturing Systems With Timed Petri Net, A* Search, and Admissible Heuristic Function

Abstract: System scheduling is a decision-making process that plays an important role in improving the performance of robotic cellular manufacturing (RCM) systems. Timed Petri nets (PNs) are a formalism suitable for graphically and concisely modeling such systems and obtaining their reachable state graphs. Within their reachability graphs, timed PNs' evolution and intelligent search algorithms can be combined to find an efficient operation sequence from an initial state to a goal one for the underlying systems of the nets. To schedule RCM systems, this work proposes an A* search with a new heuristic function based on timed PNs. When compared with related approaches, the proposed one can deal with token remaining time, weighted arcs, and multiple resource copies commonly seen in the PN models of RCM systems. The admissibility of the proposed heuristic function is proved. Finally, experimental results are given to show the effectiveness and efficiency of the proposed method and heuristic function.

Section Patterns: Efficiently Solving Narrow Passage Problems in Multilevel Motion Planning

Abstract: Sampling-based planning methods often become inefficient due to narrow passages. Narrow passages induce a higher runtime, because the chance to sample them becomes vanishingly small. In recent work, we showed that narrow passages can be approached by relaxing the problem using admissible lower-dimensional projections of the state space. Those relaxations often increase the volume of narrow passages under projection. Solving the relaxed problem is often efficient and produces an admissible heuristic we can exploit. However, given a base path, i.e. a solution to a relaxed problem, there are currently no tailored methods to efficiently exploit the base path. To efficiently exploit the base path and thereby its admissible heuristic, we develop section patterns, which are solution strategies to efficiently exploit base paths in particular around narrow passages. To coordinate section patterns, we develop the pattern dance algorithm, which efficiently coordinates section patterns to reactively traverse narrow passages. We combine the pattern dance algorithm with previously developed multilevel planning algorithms and benchmark them on challenging planning problems like the Bugtrap, the double L-shape, an egress problem and on four pregrasp scenarios for a 37 degrees of freedom shadow hand mounted on a KUKA LWR robot. Our results confirm that section patterns are useful to efficiently solve high-dimensional narrow passage motion planning problems.

An Admissible Heuristic to Improve Convergence in Kinodynamic Planners Using Motion Primitives

Abstract: This letter introduces a new heuristic function that can be incorporated in any kinodynamic planner using motion primitives, to the purpose of increasing its convergence rate. The heuristic function is proven to be admissible and, hence, the optimality properties of the planning algorithm are preserved. Notably, it can be applied to planning problems with generic agent motion models and cost criteria, since it depends only on the database of motion primitives. The proposed heuristic has been integrated into a randomized sampling-based and a deterministic kinodynamic planner, and its effectiveness has been shown in numerical examples with different agent motion models and cost criteria.

Learning Heuristic A*: Efficient Graph Search using Neural Network

Abstract: In this paper, we consider the path planning problem on a graph. To reduce computation load by efficiently exploring the graph, we model the heuristic function as a neural network, which is trained by a training set derived from optimal paths to estimate the optimal cost between a pair of vertices on the graph. As such heuristic function cannot be proved to be an admissible heuristic to guarantee the global optimality of the path, we adapt an admissible heuristic function for the terminating criteria. Thus, proposed Learning Heuristic A* (LHA*) guarantees the bounded suboptimality of the path. The performance of LHA* was demonstrated by simulations in a maze-like map and compared with the performance of weighted A* with the same suboptimality bound.

Physics-guided Energy-efficient Path Selection Using On-board Diagnostics Data

Abstract: Given a spatial graph, an origin and a destination, and on-board diagnostics (OBD) data, the energy-efficient path selection problem aims to find the path with the least expected energy consumption (EEC). Two main objectives of smart cities are sustainability and prosperity, both of which benefit from reducing the energy consumption of transportation. The challenges of the problem include the dependence of EEC on the physical parameters of vehicles, the autocorrelation of the EEC on segments of paths, the high computational cost of EEC estimation, and potential negative EEC. However, the current cost estimation models for the path selection problem do not consider vehicles’ physical parameters. Moreover, the current path selection algorithms follow the “path + edge” pattern when exploring candidate paths, resulting in redundant computation. Our preliminary work introduced a physics-guided energy consumption model and proposed a maximal-frequented-path-graph shortest-path algorithm using the model. In this work, we propose an informed algorithm using an admissible heuristic and propose an algorithm to handle negative EEC. We analyze the proposed algorithms theoretically and evaluate the proposed algorithms via experiments with real-world and synthetic data. We also conduct two case studies using real-world data and a road test to validate the proposed method.

Learning Differentiable Programs with Admissible Neural Heuristics

Abstract: We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

Solving the Longest Simple Path Problem with Heuristic Search.

Abstract: Prior approaches for finding the longest simple path (LSP) in a graph used constraints solvers and genetic algorithms In this work, we solve the LSP problem with heuristic search We first introduce several methods for pruning dominated path prefixes Then, we propose several admissible heuristic functions for this problem Experimental results demonstrate the large impact of the proposed heuristics and pruning rules

Symbolic Algorithms for Token Swapping

Abstract: We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in each vertex. The goal is to move each token to its destination vertex using swap operations. In the token swapping problem, the goal is to find a solution with a minimum number of swaps. In the permutation routing via matchings problem, the goal is to find a solution with a minimum number of steps, where a step is a set of disjoint swaps which can be performed in parallel. First, we present an A* search algorithm. This algorithm can find optimal solutions if used with an admissible heuristic. We also evaluate the use of non-admissible heuristics. In this case, we prove that the result will deviate from an optimum result by at most an even number of swaps. We also present an algorithm based on Boolean satisfiability. We evaluate our methods on a large set of practical benchmarks.

Fast a on road networks using a scalable separator-based heuristic

Abstract: Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and throughput. We present a novel method to compute an effective admissible heuristic for the fastest-path travel time between two points on a road map, which can be used to significantly accelerate the classical A* algorithm when computing fastest paths. Our basic method - called the Hierarchical Separator Heuristic (HSH) - is based on a hierarchical set of linear separators of the map represented by a binary tree, where all the separators are parallel lines in a specific direction. A preprocessing step computes a short vector of values per road junction based on the separator tree, which is then stored with the map and used to efficiently compute the heuristic at the online query stage. We demonstrate experimentally that this method scales well to any map size, providing a high-quality heuristic, thus very efficient A* search, for fastest-path queries between points at all distances - especially small and medium range. We show how to significantly improve the basic HSH method by combining separator hierarchies in multiple directions and by partitioning the linear separators. Experimental results on real-world road maps show that HSH achieves accuracy above 95% in estimating the true travel time between two junctions at the price of storing approximately 25 values per junction.

Solving the Steiner Tree Problem with few Terminals

Abstract: The Steiner tree problem is a well-known problem in network design, routing, and VLSI design. Given a graph, edge costs, and a set of dedicated vertices (terminals), the Steiner tree problem asks to output a sub-graph that connects all terminals at minimum cost. A state-of-the-art algorithm to solve the Steiner tree problem by means of dynamic programming is the Dijkstra-Steiner algorithm. The algorithm builds a Steiner tree of the entire instance by systematically searching for smaller instances, based on subsets of the terminals, and combining Steiner trees for these smaller instances. The search heavily relies on a guiding heuristic function in order to prune the search space. However, to ensure correctness, this algorithm allows only for limited heuristic functions, namely, those that satisfy a so-called consistency condition. In this paper, we enhance the Dijkstra-Steiner algorithm and establish a revisited algorithm, called DS*. The DS* algorithm allows for arbitrary lower bounds as heuristics relaxing the previous condition on the heuristic function. Notably, we can now use linear programming based lower bounds. Further, we capture new requirements for a heuristic function in a condition, which we call admissibility. We show that admissibility is indeed weaker than consistency and establish correctness of the DS* algorithm when using an admissible heuristic function. We implement DS* and combine it with modern preprocessing, resulting in an open-source solver (DS*Solve). Finally, we compare its performance on standard benchmarks and observe a competitive behavior.

Sequencing operator counts with state-space search

Abstract: A search algorithm with an admissible heuristic function is the most common approach to optimally solve classical planning tasks Recently Daviesetal(2015) introduced the solver OpSeq using Logic-Based Benders Decomposition to solve planning tasks optimally In this approach, the master problem is an integer program derived from the operator-counting framework that generates operator counts, ie, an assignment of integer counts for each task operator Then, the operator counts sequencing subproblem verifies if a plan satisfying these operator counts exists, or generates a necessary violated constraint to strengthen the master problem In OpSeq the subproblem is solved by a SAT solver In this paper we show that operator counts sequencing can be better solved by state-space search We introduce OpSearch, an A∗-based algorithm to solve the operator counts sequencing subproblem: it either finds an optimal plan, or uses the frontier of the search to derive a violated constraint We show that using a standard search framework has two advantages: i) search scales better than a SAT-based approach for solving the operator counts sequencing, ii) explicit information in the search frontier can be used to derive stronger constraints We present results on the IPC-2011 benchmarks showing that this approach solves more planning tasks, using less memory On tasks solved by both methods OpSearch usually requires to solve fewer operator counts sequencing problems than OpSeq, evidencing the stronger constraints generated by OpSearch

Solving the Steiner Tree Problem with few Terminals

Abstract: The Steiner tree problem is a well-known problem in network design, routing, and VLSI design. Given a graph, edge costs, and a set of dedicated vertices (terminals), the Steiner tree problem asks to output a sub-graph that connects all terminals at minimum cost. A state-of-the-art algorithm to solve the Steiner tree problem by means of dynamic programming is the Dijkstra-Steiner algorithm. The algorithm builds a Steiner tree of the entire instance by systematically searching for smaller instances, based on subsets of the terminals, and combining Steiner trees for these smaller instances. The search heavily relies on a guiding heuristic function in order to prune the search space. However, to ensure correctness, this algorithm allows only for limited heuristic functions, namely, those that satisfy a so-called consistency condition. In this paper, we enhance the Dijkstra-Steiner algorithm and establish a revisited algorithm, called DS*. The DS* algorithm allows for arbitrary lower bounds as heuristics relaxing the previous condition on the heuristic function. Notably, we can now use linear programming based lower bounds. Further, we capture new requirements for a heuristic function in a condition, which we call admissibility. We show that admissibility is indeed weaker than consistency and establish correctness of the DS* algorithm when using an admissible heuristic function. We implement DS* and combine it with modern preprocessing, resulting in an open-source solver (DS* Solve). Finally, we compare its performance on standard benchmarks and observe a competitive behavior.

An Investigation of Problem Instance Difficulty for Case-Based Reasoning and Heuristic Search.

Abstract: For managing the ever increasing variability of hardware/software interfaces (HSIs), e.g., in automotive systems, there is a need for the reuse of already existing HSIs. This reuse should be automated, and we (meta-)modeled the HSI domain for design space exploration. These models together with additionally defined transformation rules that lead from a model of one specific HSI to another one facilitate automatic adaptations of HSI instances in these models and, hence, both case-based reasoning (CBR) and (heuristic) search. Using these approaches for solving concrete problem instances, estimating their difficulty really matters, but there is not much theory available.