Regionalization techniques group spatial areas into a set of homogeneous regions to analyze and draw conclusions about spatial phenomena. A recent regionalization problem, called MP-regions, groups spatial areas to produce a maximum number of regions by enforcing a user-defined constraint at the regional level. The MP-regions problem is NP-hard. Existing approximate algorithms for MP-regions do not scale for large datasets due to their high computational cost and inherently centralized approaches to process data. This article introduces a parallel scalable regionalization framework (
Learning Models for Predictive Adaptation in State Lattices
Approaches to autonomous navigation for unmanned ground vehicles rely on motion planning algorithms that optimize maneuvers under kinematic and environmental constraints. Algorithms that combine heuristic search with local optimization are well suited to domains where solution optimality is favored over speed and memory resources are limited as they often improve the optimality of solutions without increasing the sampling density. To address the runtime performance limitations of such algorithms, this paper introduces Predictively Adapted State Lattices, an extension of recombinant motion planning search space construction that adapts the representation by selecting regions to optimize using a learned model trained to predict the expected improvement. The model aids in prioritizing computations that optimize regions where significant improvement is anticipated. We evaluate the performance of the proposed method through statistical and qualitative comparisons to alternative State Lattice approaches for a simulated mobile robot with nonholonomic constraints. Results demonstrate an advance in the ability of recombinant motion planning search spaces to improve relative optimality at reduced runtime in varyingly complex environments.
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- Award ID(s):
- 1637813
- NSF-PAR ID:
- 10076482
- Date Published:
- Journal Name:
- 11th International Conference on Field and Service Robotics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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PAGE ) to support MP-regions on large datasets. The proposed framework works in two stages. The first stage finds an initial solution through randomized search, and the second stage improves this solution through efficient heuristic search. To build an initial solution efficiently, we extend traditional spatial partitioning techniques to enable parallelized region building without violating the spatial constraints. Furthermore, we optimize the region building efficiency and quality by tuning the randomized area selection to trade off runtime with region homogeneity. The experimental evaluation shows the superiority of our framework to support an order of magnitude larger datasets efficiently compared to the state-of-the-art techniques while producing high-quality solutions. -
We study the chance-constrained bin packing problem, with an application to hospital operating room planning. The bin packing problem allocates items of random sizes that follow a discrete distribution to a set of bins with limited capacity, while minimizing the total cost. The bin capacity constraints are satisfied with a given probability. We investigate a big-M and a 0-1 bilinear formulation of this problem. We analyze the bilinear structure of the formulation and use the lifting techniques to identify cover, clique, and projection inequalities to strengthen the formulation. We show that in certain cases these inequalities are facet-defining for a bilinear knapsack constraint that arises in the reformulation. An extensive computational study is conducted for the operating room planning problem that minimizes the number of open operating rooms. The computational tests are performed using problems generated based on real data from a hospital. A lower-bound improvement heuristic is combined with the cuts proposed in this paper in a branch-and-cut framework. The computations illustrate that the techniques developed in this paper can significantly improve the performance of the branch-and-cut method. Problems with up to 1,000 scenarios are solved to optimality in less than an hour. A safe approximation based on conditional value at risk (CVaR) is also solved. The computations show that the CVaR approximation typically leaves a gap of one operating room (e.g., six instead of five) to satisfy the chance constraint. Summary of Contribution: This paper investigates a branch-and-cut algorithm for a chance-constrained bin packing problem with multiple bins. The chance-constrained bin packing provides a modeling framework for applied operations research problems, such as health care, scheduling, and so on. This paper studies alternative computational approaches to solve this problem. Moreover, this paper uses real data from a hospital operating room planning setting as an application to test the algorithmic ideas. This work, therefore, is at the intersection of computing and operations research. Several interesting ideas are developed and studied. These include a strengthened big-M reformulation, analysis of a bilinear reformulation, and identifying certain facet-defining inequalities for this formulation. This paper also gives a lower-bound generation heuristic for a model that minimizes the number of bins. Computational experiments for an operating room planning model that uses data from a hospital demonstrate the computational improvement and importance of the proposed approaches. The techniques proposed in this paper and computational experiments further enhance the interface of computing and operations research.more » « less
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Abstract Statistical relational learning (SRL) frameworks are effective at defining probabilistic models over complex relational data. They often use weighted first-order logical rules where the weights of the rules govern probabilistic interactions and are usually learned from data. Existing weight learning approaches typically attempt to learn a set of weights that maximizes some function of data likelihood; however, this does not always translate to optimal performance on a desired domain metric, such as accuracy or F1 score. In this paper, we introduce a taxonomy of search-based weight learning approaches for SRL frameworks that directly optimize weights on a chosen domain performance metric. To effectively apply these search-based approaches, we introduce a novel projection, referred to as scaled space (SS), that is an accurate representation of the true weight space. We show that SS removes redundancies in the weight space and captures the semantic distance between the possible weight configurations. In order to improve the efficiency of search, we also introduce an approximation of SS which simplifies the process of sampling weight configurations. We demonstrate these approaches on two state-of-the-art SRL frameworks: Markov logic networks and probabilistic soft logic. We perform empirical evaluation on five real-world datasets and evaluate them each on two different metrics. We also compare them against four other weight learning approaches. Our experimental results show that our proposed search-based approaches outperform likelihood-based approaches and yield up to a 10% improvement across a variety of performance metrics. Further, we perform an extensive evaluation to measure the robustness of our approach to different initializations and hyperparameters. The results indicate that our approach is both accurate and robust.more » « less
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Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e., target sequencing). To solve the problem, we leverage Conflict-Based Search (CBS) for MAPF and propose a novel approach called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the collision resolution strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. We also develop two variants of CBSS that trade off runtime against solution optimality. Our test results verify the advantage of CBSS over the baselines in terms of computing cheaper paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. Finally, we run both Gazebo simulation and physical robot tests to validate that the planned paths are executablemore » « less
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Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e., target sequencing). To solve the problem, we leverage Conflict-Based Search (CBS) for MAPF and propose a novel approach called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the collision resolution strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. We also develop two variants of CBSS that trade off runtime against solution optimality. Our test results verify the advantage of CBSS over the baselines in terms of computing cheaper paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. Finally, we run both Gazebo simulation and physical robot tests to validate that the planned paths are executable.more » « less
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