Line coverage is the task of servicing a given set of one‐dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the
Line Coverage with Multiple Robots
The line coverage problem is the coverage of
linear environment features (e.g., road networks, power lines),
modeled as 1D segments, by one or more robots while respecting
resource constraints (e.g., battery capacity, flight time) for each
of the robots. The robots incur direction dependent costs and
resource demands as they traverse the edges. We treat the line
coverage problem as an optimization problem, with the total
cost of the tours as the objective, by formulating it as a mixed
integer linear program (MILP). The line coverage problem is
NP-hard and hence we develop a heuristic algorithm, Merge-
Embed-Merge (MEM). We compare it against the optimal
MILP approach and a baseline heuristic algorithm, Extended
Path Scanning. We show the MEM algorithm is fast and suitable
for real-time applications. To tackle large-scale problems, our
approach performs graph simplification and graph partitioning,
followed by robot tour generation for each of the partitioned
subgraphs. We demonstrate our approach on a large graph
with 4,658 edges and 4,504 vertices that represents an urban
region of about 16 sq. km. We compare the performance of the
algorithms on several small road networks and experimentally
demonstrate the approach using UAVs on the UNC Charlotte
campus road network.
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- NSF-PAR ID:
- 10176413
- Date Published:
- Journal Name:
- IEEE International Conference on Robotics and Automation
- ISSN:
- 1049-3492
- Page Range / eLocation ID:
- 3248-3254
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract required graph , that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network. -
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Abstract Motivation Cancer phylogenies are key to studying tumorigenesis and have clinical implications. Due to the heterogeneous nature of cancer and limitations in current sequencing technology, current cancer phylogeny inference methods identify a large solution space of plausible phylogenies. To facilitate further downstream analyses, methods that accurately summarize such a set T of cancer phylogenies are imperative. However, current summary methods are limited to a single consensus tree or graph and may miss important topological features that are present in different subsets of candidate trees.
Results We introduce the Multiple Consensus Tree (MCT) problem to simultaneously cluster T and infer a consensus tree for each cluster. We show that MCT is NP-hard, and present an exact algorithm based on mixed integer linear programming (MILP). In addition, we introduce a heuristic algorithm that efficiently identifies high-quality consensus trees, recovering all optimal solutions identified by the MILP in simulated data at a fraction of the time. We demonstrate the applicability of our methods on both simulated and real data, showing that our approach selects the number of clusters depending on the complexity of the solution space T.
Availability and implementation https://github.com/elkebir-group/MCT.
Supplementary information Supplementary data are available at Bioinformatics online.
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LaValle, Steve M. ; Lin, Ming ; Ojala, Timo ; Shell, Dylan ; Yu, Jingjin (Ed.)The line coverage problem is the task of servicing a given set of one-dimensional features in an environment. Its applications include the inspection of road networks, power lines, and oil and gas lines. The line coverage problem is a generalization of the standard arc routing problems, and is NP-hard in general. We address the single robot line coverage problem where the service and deadhead costs are distinct and asymmetric. We model the problem as an optimization problem that minimizes the total cost of travel on a given graph. We present approximation algorithms to obtain bounded solutions efficiently, using the minimum cost flow problem. We build the main algorithm in stages by considering three simpler subproblems. The subproblems are based on the structure of the required graph, i.e., the graph induced by the features that require servicing. We fi rst present an optimal algorithm for the case of Eulerian graphs with only required edges. Next we consider general graphs, not necessarily Eulerian, with only required edges and present a 2-approximation algorithm. Finally, we consider the general case with both required and non-required edges. The approximation algorithm is dependent on the Asymmetric Traveling Salesperson Problem (ATSP), and is bounded by alpha(C) + 2, where alpha(C) is the approximation factor of the ATSP algorithm with C connected components. Our upper bound is also an improvement over the existing results for the asymmetric rural postman problem.more » « less
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null (Ed.)The performance of multimodal mobility systems relies on the seamless integration of conventional mass transit services and the advent of Mobility-on-Demand (MoD) services. Prior work is limited to individually improving various transport networks' operations or linking a new mode to an existing system. In this work, we attempt to solve transit network design and pricing problems of multimodal mobility systems en masse. An operator (public transit agency or private transit operator) determines frequency settings of the mass transit system, flows of the MoD service, and prices for each trip to optimize the overall welfare. A primal-dual approach, inspired by the market design literature, yields a compact mixed integer linear programming (MILP) formulation. However, a key computational challenge remains in allocating an exponential number of hybrid modes accessible to travelers. We provide a tractable solution approach through a decomposition scheme and approximation algorithm that accelerates the computation and enables optimization of large-scale problem instances. Using a case study in Nashville, Tennessee, we demonstrate the value of the proposed model. We also show that our algorithm reduces the average runtime by 60% compared to advanced MILP solvers. This result seeks to establish a generic and simple-to-implement way of revamping and redesigning regional mobility systems in order to meet the increase in travel demand and integrate traditional fixed-line mass transit systems with new demand-responsive services.more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA40945.2020.9197292
