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Policy heterogeneity improves collective olfactory search in three-dimensional turbulence

Lorenzo Piro1,*, Robin A. Heinonen1,2, Maurizio Carbone3,4, Luca Biferale1, and Massimo Cencini3,4

  • *Contact author: lorenzo.piro@roma2.infn.it

Phys. Rev. E 113, 044401 – Published 2 April, 2026

DOI: https://doi.org/10.1103/6zls-m67c

Abstract

We examine how heterogeneous swarms, mixing exploratory and exploitative agents with distinct decision rules, consistently outperform homogeneous ones where each agent balances exploration and exploitation individually, performing experiments in two contrasting deployment scenarios. Using odor fields from state-of-the-art direct numerical simulations of the 3D Navier-Stokes equations, we find that policy diversity typically allows the group to reach the source of the odor more efficiently by mitigating the detrimental effects of spatiotemporal turbulent correlations. These findings provide insights into collective search behavior and offer promising strategies for the design of robust, bioinspired search algorithms in engineered systems.

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References (59)

  1. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Intermittent search strategies, Rev. Mod. Phys. 83, 81 (2011).
  2. V. Tejedor, R. Voituriez, and O. Bénichou, Optimizing persistent random searches, Phys. Rev. Lett. 108, 088103 (2012).
  3. A. Chechkin and I. M. Sokolov, Random search with resetting: A unified renewal approach, Phys. Rev. Lett. 121, 050601 (2018).
  4. J. Murlis, J. S. Elkinton, and R. T. Cardé, Odor plumes and how insects use them, Annu. Rev. Entomol. 37, 505 (1992).
  5. T. D. Wyatt, Pheromones and Animal Behaviour: Communication by Smell and Taste (Cambridge University Press, Cambridge, 2003).
  6. K. L. Baker, M. Dickinson, T. M. Findley, D. H. Gire, M. Louis, M. P. Suver, J. V. Verhagen, K. I. Nagel, and M. C. Smear, Algorithms for olfactory search across species, J. Neurosci. 38, 9383 (2018).
  7. A. Francis, S. Li, C. Griffiths, and J. Sienz, Gas source localization and mapping with mobile robots: A review, J. Field Robot. 39, 1341 (2022).
  8. H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, NJ, 1993).
  9. J. P. Crimaldi and J. R. Koseff, High-resolution measurements of the spatial and temporal scalar structure of a turbulent plume, Exp. Fluids 31, 90 (2001).
  10. E. Balkovsky and B. I. Shraiman, Olfactory search at high Reynolds number, Proc. Natl. Acad. Sci. USA 99, 12589 (2002).
  11. A. Celani, E. Villermaux, and M. Vergassola, Odor landscapes in turbulent environments, Phys. Rev. X 4, 041015 (2014).
  12. C. A. Hernandez-Reyes, S. Fukushima, S. Shigaki, D. Kurabayashi, T. Sakurai, R. Kanzaki, and H. Sezutsu, Identification of exploration and exploitation balance in the Silkmoth olfactory search behavior by information-theoretic modeling, Front. Comput. Neurosci. 15, 629380 (2021).
  13. G. Reddy, V. N. Murthy, and M. Vergassola, Olfactory sensing and navigation in turbulent environments, Annu. Rev. Condens. Matter Phys. 13, 191 (2022).
  14. G. E. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis (John Wiley & Sons, Hoboken, NJ, 2011).
  15. M. Vergassola, E. Villermaux, and B. I. Shraiman, ‘Infotaxis’ as a strategy for searching without gradients, Nature (London) 445, 406 (2007).
  16. J.-B. Masson, Olfactory searches with limited space perception, Proc. Natl. Acad. Sci. USA 110, 11261 (2013).
  17. A. Loisy and C. Eloy, Searching for a source without gradients: how good is infotaxis and how to beat it, Proc. R. Soc. London A 478, 20220118 (2022).
  18. J. L. Fernández, R. Sanz, R. G. Simmons, and A. R. Diéguez, Heuristic anytime approaches to stochastic decision processes, J. Heuristics 12, 181 (2006).
  19. A. Loisy and R. A. Heinonen, Deep reinforcement learning for the olfactory search POMDP: A quantitative benchmark, Eur. Phys. J. E 46, 17 (2023).
  20. R. A. Heinonen, L. Biferale, A. Celani, and M. Vergassola, Optimal policies for Bayesian olfactory search in turbulent flows, Phys. Rev. E 107, 055105 (2023).
  21. R. A. Heinonen, L. Biferale, A. Celani, and M. Vergassola, Exploring Bayesian olfactory search in realistic turbulent flows, Phys. Rev. Fluids 10, 064614 (2025).
  22. A. M. Berdahl, A. B. Kao, A. Flack, P. A. H. Westley, E. A. Codling, I. D. Couzin, A. I. Dell, and D. Biro, Collective animal navigation and migratory culture: from theoretical models to empirical evidence, Philos. Trans. R. Soc. B 373, 20170009 (2018).
  23. M. Nagy, A. Horicsányi, E. Kubinyi, I. D. Couzin, G. Vásárhelyi, A. Flack, and T. Vicsek, Synergistic benefits of group search in rats, Curr. Biol. 30, 4733 (2020).
  24. E. D. Karpas, A. Shklarsh, and E. Schneidman, Information socialtaxis and efficient collective behavior emerging in groups of information-seeking agents, Proc. Natl. Acad. Sci. USA 114, 5589 (2017).
  25. C. Song, Y. He, B. Ristic, L. Li, and X. Lei, Multi-agent collaborative infotaxis search based on cognition difference, J. Phys. A 52, 485202 (2019).
  26. M. Durve, L. Piro, M. Cencini, L. Biferale, and A. Celani, Collective olfactory search in a turbulent environment, Phys. Rev. E 102, 012402 (2020).
  27. E. Panizon and A. Celani, Seeking and sharing information in collective olfactory search, Phys. Biol. 20, 065001 (2023).
  28. M. Brambilla, E. Ferrante, M. Birattari, and M. Dorigo, Swarm robotics: A review from the swarm engineering perspective, Swarm Intelligence 7, 1 (2013).
  29. H. L. Kwa, J. Leong Kit, and R. Bouffanais, Balancing collective exploration and exploitation in multi-agent and multi-robot systems: A review, Front. Robot. AI 8, 771520 (2022).
  30. M. M. Shahzad, Z. Saeed, A. Akhtar, H. Munawar, M. H. Yousaf, N. K. Baloach, and F. Hussain, A review of swarm robotics in a NutShell, Drones 7 269 (2023).
  31. U. K. Verfuss, A. S. Aniceto, D. V. Harris, D. Gillespie, S. Fielding, G. Jiménez, P. Johnston, R. R. Sinclair, A. Sivertsen, S. A. Solbø, R. Storvold, M. Biuw, and R. Wyatt, A review of unmanned vehicles for the detection and monitoring of marine fauna, Mar. Pollut. Bull. 140, 17 (2019).
  32. T. Dang, F. Mascarich, S. Khattak, H. D. Nguyen, H. Nguyen, S. Hirsh, R. Reinhart, C. Papachristos, and K. Alexis, Autonomous search for underground mine rescue using aerial robots, in Proceedings of the 2020 IEEE Aerospace Conference (IEEE, Piscataway, NJ, 2020), pp. 1–8.
  33. T. D. Seeley, Adaptive significance of the age polyethism schedule in honeybee colonies, Behav. Ecol. Sociobiol. 11, 287 (1982).
  34. B. Hölldobler and E. O. Wilson, The Ants (Harvard University Press, Cambridge, MA, 1990).
  35. D. Kengyel, H. Hamann, P. Zahadat, G. Radspieler, F. Wotawa, and T. Schmickl, in PRIMA 2015: Principles and Practice of Multi-Agent Systems, edited by Q. Chen, P. Torroni, S. Villata, J. Hsu, and A. Omicini (Springer International Publishing, Cham, 2015), pp. 201–217.
  36. E. Goodale and R. D. Magrath, Species diversity and interspecific information flow, Biol. Rev. 99, 999 (2024).
  37. L. Piro, R. A. Heinonen, M. Cencini, and L. Biferale, Many wrong models approach to localise an odour source in turbulence with static sensors, J. Turbul. 26, 153 (2025).
  38. L. Biferale, F. Bonaccorso, N. Cocciaglia, R. A. Heinonen, and L. Piro, TURB-Smoke. A database of Lagrangian pollutants emitted from point sources in turbulent flows with a mean wind, Sci. Data 13, 428 (2026).
  39. G. de Croon, J. Dupeyroux, S. Fuller, and J. Marshall, Insect-inspired AI for autonomous robots, Sci. Robot. 7, eabl6334 (2022).
  40. A. Girma, N. Bahadori, M. Sarkar, T. G. Tadewos, M. R. Behnia, M. N. Mahmoud, A. Karimoddini, and A. Homaifar, IoT-enabled autonomous system collaboration for disaster-area management, IEEE/CAA J. Autom. Sinica 7, 1249 (2020).
  41. J.-B. Masson, M. B. Bechet, and M. Vergassola, Chasing information to search in random environments, J. Phys. A 42, 434009 (2009).
  42. Although we varied these internal weights, no homogeneous SAI variant could match the performance of the heterogeneous mixture.
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6zls-m67c for supplementary movies and figures.
  44. M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proc. Natl. Acad. Sci. USA 105, 1232 (2008),.
  45. J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, and G. Theraulaz, Deciphering interactions in moving animal groups, PLoS Comput. Biol. 8, e1002678 (2012).
  46. R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proc. IEEE 95, 215 (2007).
  47. J. F. Traniello and R. B. Rosengaus, Ecology, evolution and division of labour in social insects, Anim. Behav. 53, 209 (1997).
  48. A. Duarte, I. Pen, L. Keller, and F. J. Weissing, Evolution of self-organized division of labor in a response threshold model, Behav. Ecol. Sociobiol. 66, 947 (2012).
  49. J. W. Jolles, A. J. King, and S. S. Killen, The role of individual heterogeneity in collective animal behaviour, Trends Ecol. Evol. 35, 278 (2020).
  50. M. Fröhlich, C. Boeckx, and C. Tennie, The role of exploration and exploitation in primate communication, Proc. R. Soc. Lond. B 292, 20241665 (2025).
  51. M. Dorigo, D. Floreano, L. M. Gambardella, F. Mondada, S. Nolfi, T. Baaboura, M. Birattari, M. Bonani, M. Brambilla, A. Brutschy, D. Burnier, A. Campo, A. L. Christensen, A. Decugniere, G. Di Caro, F. Ducatelle, E. Ferrante, A. Forster, J. M. Gonzales, J. Guzzi, et al., Swarmanoid: A novel concept for the study of heterogeneous robotic swarms, IEEE Robot. Autom. Mag. 20, 60 (2013).
  52. B. Khaldi, F. Harrou, and Y. Sun, Collaborative swarm robotics for sustainable environment monitoring and exploration: Emerging trends and research progress, Energy Nexus 17, 100365 (2025).
  53. D. J. Barraclough, M. L. Conroy, and D. Lee, Prefrontal cortex and decision making in a mixed-strategy game, Nat. Neurosci. 7, 404 (2004).
  54. S. H. Singh, F. van Breugel, R. P. N. Rao, and B. W. Brunton, Emergent behaviour and neural dynamics in artificial agents tracking odour plumes, Nat. Mach. Intell. 5, 58 (2023).
  55. M. Rando, M. James, A. Verri, L. Rosasco, and A. Seminara, Q-learning with temporal memory to navigate turbulence, eLife 13, 102906 (2025).
  56. L. Canese, G. C. Cardarilli, L. Di Nunzio, R. Fazzolari, D. Giardino, M. Re, and S. Spanò, Multi-agent reinforcement learning: A review of challenges and applications, Appl. Sci. 11, 4948 (2021).
  57. S. V. Albrecht, F. Christianos, and L. Schäfer, Multi-agent Reinforcement Learning: Foundations and Modern Approaches (MIT Press, Cambridge, MA, 2024).
  58. S. Colabrese, K. Gustavsson, A. Celani, and L. Biferale, Flow navigation by smart microswimmers via reinforcement learning, Phys. Rev. Lett. 118, 158004 (2017).
  59. L. Piro, M. Carbone, R. Heinonen, L. Biferale, and M. Cencini, Data for “Policy heterogeneity improves collective olfactory search in three-dimensional turbulence” [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.19109495.

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