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We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements, we derive a polynomial time, complete algorithm that produces solutions with constant-factor optimality guarantees on both makespan and distance optimality, in expectation, under the assumption that the robot labels are uniformly randomly distributed. Our algorithm only requires a small constant-factor expansion of the initial and goal configuration footprints for solving the problem, i.e., the problem can be solved in a fairly small bounded region. Beside theoretical guarantees, we present a thorough computational evaluation of the proposed solution. In addition to the baseline implementation, adapting an effective (but non-polynomial time) routing subroutine, we also provide a highly efficient implementation that quickly computes near-optimal solutions. Hardware experiments on the microMVP platform composed of non-holonomic robots confirms the practical applicability of our algorithmic pipeline.
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Interval-Based Dynamic Discretization Discovery for Solving the Continuous-Time Service Network Design Problem
We introduce an effective and efficient iterative algorithm for solving the continuous-time service network design problem. The algorithm achieves its efficiency by carefully and dynamically refining partially time-expanded network models so that only a small number of small integer programs, defined over these networks, need to be solved. An extensive computational study shows that the algorithm performs well in practice, often using time-expanded network models with size much less than 1% (in terms of number of variables and constraints) of a full time-expanded network model. The algorithm is inspired by and has many similarities to the dynamic discretization discovery algorithm introduced in Boland et al. [Boland N, Hewitt M, Marshall L, Savelsbergh M (2017) The continuous-time service network design problem. Oper. Res. 65(5):1303–1321.], but generates smaller partially time-expanded models, produces high-quality solutions more quickly, and converges more quickly.
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- Award ID(s):
- 1662848
- PAR ID:
- 10226533
- Date Published:
- Journal Name:
- Transportation Science
- Volume:
- 55
- Issue:
- 1
- ISSN:
- 0041-1655
- Page Range / eLocation ID:
- 29 to 51
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/trsc.2020.0994
