Optimal Search Strategies under Finite Resource Constraints

Abstract

Improving target search is a challenge faced by many natural and artificial agents, often requiring the use of energetic or material resources. These inputs may be supplied by an external controller or generated by the searcher itself, for example, through the deposition of cues along its trajectory. Although such resources are commonly modeled as costly but available without an explicit limit, in practice, they can often only be produced in finite amounts. Here, we go beyond the assumption of an unlimited supply of resources by investigating searches in which a finite resource budget must be allocated throughout the search process. To investigate this problem, we equip a one-dimensional diffusive searcher with three types of resources: an external force, a supply of partially reflecting flags, and auto-chemotactic cues. We derive exact optimal resource-allocation protocols for informed search processes in which the agent has continuous access to its past and current positions, which we find to always require resource allocation to be spatially concentrated. We then determine the corresponding protocols for blind searchers and show that resource usage must be more evenly distributed. Non-Markovian cues that generate environmental memory are found to substantially improve search performance when the agent has access to positional information, even under finite-resource constraints. In contrast, their benefits are considerably more limited for blind search, particularly when the cues provide no directional information.

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BibTeX RIS

BibTeX

@misc{meyer2026optimal,
  title = {{Optimal Search Strategies under Finite Resource Constraints}},
  author = {Hugues Meyer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33316},
  eprint = {2610.33316},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33316},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Optimal Search Strategies under Finite Resource Constraints
AU  - Hugues Meyer
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33316
UR  - https://arxiv.org/abs/2610.33316
AB  - Improving target search is a challenge faced by many natural and artificial agents, often requiring the use of energetic or material resources. These inputs may be supplied by an external controller or generated by the searcher itself, for example, through the deposition of cues along its trajectory. Although such resources are commonly modeled as costly but available without an explicit limit, in practice, they can often only be produced in finite amounts. Here, we go beyond the assumption of an unlimited supply of resources by investigating searches in which a finite resource budget must be allocated throughout the search process. To investigate this problem, we equip a one-dimensional diffusive searcher with three types of resources: an external force, a supply of partially reflecting flags, and auto-chemotactic cues. We derive exact optimal resource-allocation protocols for informed search processes in which the agent has continuous access to its past and current positions, which we find to always require resource allocation to be spatially concentrated. We then determine the corresponding protocols for blind searchers and show that resource usage must be more evenly distributed. Non-Markovian cues that generate environmental memory are found to substantially improve search performance when the agent has access to positional information, even under finite-resource constraints. In contrast, their benefits are considerably more limited for blind search, particularly when the cues provide no directional information.
ER  -

Abstract

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