Task Allocation for Multi-agent Systems via Unequal-dimensional Optimal Transport
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913732851924992 |
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| author | Dong, Anqi Johansson, Karl H. Karlsson, Johan |
| author_facet | Dong, Anqi Johansson, Karl H. Karlsson, Johan |
| contents | We consider a probabilistic model for large-scale task allocation problems for multi-agent systems, aiming to determine an optimal deployment strategy that minimizes the overall transport cost. Specifically, we assign transportation agents to delivery tasks with given pick-up and drop-off locations, pairing the spatial distribution of transport resources with the joint distribution of task origins and destinations. This aligns with the optimal mass transport framework where the problem and is in the unequal-dimensional setting. The task allocation problem can be thus seen as a linear programming problem that minimizes a quadratic transport cost functional, optimizing the energy of all transport units. The problem is motivated by time-sensitive medical deliveries using drones, such as emergency equipment and blood transport. In this paper, we establish the existence, uniqueness, and smoothness of the optimal solution, and illustrate its properties through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Task Allocation for Multi-agent Systems via Unequal-dimensional Optimal Transport Dong, Anqi Johansson, Karl H. Karlsson, Johan Systems and Control Multiagent Systems Optimization and Control 91B32, 93A16, 91B68, 90B06 We consider a probabilistic model for large-scale task allocation problems for multi-agent systems, aiming to determine an optimal deployment strategy that minimizes the overall transport cost. Specifically, we assign transportation agents to delivery tasks with given pick-up and drop-off locations, pairing the spatial distribution of transport resources with the joint distribution of task origins and destinations. This aligns with the optimal mass transport framework where the problem and is in the unequal-dimensional setting. The task allocation problem can be thus seen as a linear programming problem that minimizes a quadratic transport cost functional, optimizing the energy of all transport units. The problem is motivated by time-sensitive medical deliveries using drones, such as emergency equipment and blood transport. In this paper, we establish the existence, uniqueness, and smoothness of the optimal solution, and illustrate its properties through numerical simulations. |
| title | Task Allocation for Multi-agent Systems via Unequal-dimensional Optimal Transport |
| topic | Systems and Control Multiagent Systems Optimization and Control 91B32, 93A16, 91B68, 90B06 |
| url | https://arxiv.org/abs/2503.09369 |