Optimal number of agents in a collective search, and when to launch them
Abstract: Search processes often involve multiple agents that collectively search a randomly located target. While increasing the number of agents usually decreases the time at which the first agent finds the target, it also requires resources to create and sustain more agents. In this manuscript, we raise the question of the optimal timing for launching multiple agents in a search in order to reach the best compromise between minimizing the overall search time and minimizing the costs associated with launching and sustaining agents. After introducing a general formalism for independent agents in which we allow them to be launched at arbitrary times, we investigate by means of analytical calculations and numerical optimization the optimal launch strategies to optimize the quantiles of the search cost and its mean. Finally, we compare our results with the case of stochastic resetting and study the conditions under which it is preferable to launch new searchers rather than resetting the first one to its initial position.
- T cell migration, search strategies and mechanisms. Nature Reviews Immunology, 16(3):193–201, 2016.
- David JT Sumpter. Collective animal behavior. Princeton University Press, 2010.
- The physics of foraging: an introduction to random searches and biological encounters. Cambridge University Press, 2011.
- Lévy flight search patterns of wandering albatrosses. Nature, 381(6581):413–415, 1996.
- Optimizing the success of random searches. nature, 401(6756):911–914, 1999.
- Intermittent random walks for an optimal search strategy: one-dimensional case. Journal of Physics: Condensed Matter, 19(6):065142, 2007.
- Cuckoo search via lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC), pages 210–214. Ieee, 2009.
- The lévy flight paradigm: random search patterns and mechanisms. Ecology, 90(4):877–887, 2009.
- Intermittent search strategies. Reviews of Modern Physics, 83(1):81, 2011.
- First order transition for the optimal search time of lévy flights with resetting. Physical review letters, 113(22):220602, 2014.
- A Chechkin and Igor M Sokolov. Random search with resetting: a unified renewal approach. Physical review letters, 121(5):050601, 2018.
- Paul C Bressloff. Search processes with stochastic resetting and multiple targets. Physical Review E, 102(2):022115, 2020.
- Stochastic resetting and applications. Journal of Physics A: Mathematical and Theoretical, 53(19):193001, 2020.
- Search with home returns provides advantage under high uncertainty. Physical Review Research, 2(4):043174, 2020.
- Optimizing persistent random searches. Physical review letters, 108(8):088103, 2012.
- Optimal non-markovian search strategies with n-step memory. Physical Review Letters, 127(7):070601, 2021.
- Self-interacting random walks: Aging, exploration, and first-passage times. Physical Review X, 12(1):011052, 2022.
- Optimal non-markovian composite search algorithms for spatially correlated targets. Europhysics Letters, 139(3):32003, 2022.
- Environmental memory facilitates search with home returns. arXiv preprint arXiv:2306.12126, 2023.
- First passages for a search by a swarm of independent random searchers. Journal of Statistical Mechanics: Theory and Experiment, 2011(06):P06022, 2011.
- Collective motion due to individual escape and pursuit response. Physical Review Letters, 102(1):010602, 2009.
- Optimizing the search for resources by sharing information: Mongolian gazelles as a case study. Physical Review Letters, 110(24):248106, 2013.
- Group chasing tactics: how to catch a faster prey. New Journal of Physics, 19(5):053003, 2017.
- Group Chase and Escape: Fusion of Pursuits-Escapes and Collective Motions. Springer Nature, 2019.
- Spatial structure arising from chase-escape interactions with crowding. Scientific reports, 9(1):14988, 2019.
- We use the notation ∇i=∂tisubscript∇𝑖subscriptsubscript𝑡𝑖\nabla_{i}=\partial_{t_{i}}∇ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT = ∂ start_POSTSUBSCRIPT italic_t start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT end_POSTSUBSCRIPT.
- Barry D Hughes. Random walks and random environments. Oxford University Press, 1996.
- Sidney Redner. A guide to first-passage processes. Cambridge university press, 2001.
- R Rammal. Random walk statistics on fractal structures. Journal of Statistical Physics, 36:547–560, 1984.
- Probing microscopic origins of confined subdiffusion by first-passage observables. Proceedings of the National Academy of Sciences, 105(15):5675–5680, 2008.
- Distribution of first-passage times to specific targets on compactly explored fractal structures. Physical Review E, 83(2):020104, 2011.
- Persistence and first-passage properties in nonequilibrium systems. Advances in Physics, 62(3):225–361, 2013.
- Alignment interaction and band formation in assemblies of autochemorepulsive walkers. Phys. Rev. E, 108:034604, Sep 2023.
- Asymptotic behavior of the” true” self-avoiding walk. Physical Review B, 27(3):1635, 1983.
- Mitigating long queues and waiting times with service resetting. PNAS nexus, 1(3):pgac070, 2022.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
