{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T13:36:27Z","timestamp":1789824987296,"version":"4.0.1"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,6]],"date-time":"2019-03-06T00:00:00Z","timestamp":1551830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This research focused on the resolution of a dynamic prey\u2013predator spatial model. This model has six life cycles and simulates a theoretical population of prey and predators. Cellular automata represent a set of prey and predators. The cellular automata move in a discrete space in a 2d lattice that has the shape of a torus. African buffaloes represent the predators, and the grasslands represent the prey in the African savanna. Each buffalo moves in the discrete space using the proper motion equation of the African buffalo optimization metaheuristic. Two types of approaches were made with five experiments each. The first approach was the development of a dynamic prey\u2013predator spatial model using the movement of the African buffalo optimization metaheuristic. The second approach added the characteristic of regulating the population of buffaloes using autonomous multi-agents that interact with the model dynamic prey\u2013predator spatial model. According to the obtained results, it was possible to adjust and maintain a balance of prey and predators during a determined period using multi-agents, therefore preventing predators from destroying an entire population of prey in the coexistence space.<\/jats:p>","DOI":"10.3390\/a12030059","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T10:52:22Z","timestamp":1551955942000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Autonomous Population Regulation Using a Multi-Agent System in a Prey\u2013Predator Model That Integrates Cellular Automata and the African Buffalo Optimization Metaheuristic"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6367-9802","authenticated-orcid":false,"given":"Boris","family":"Almonacid","sequence":"first","affiliation":[{"name":"Global Change Science, Vi\u00f1a del Mar 2520000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6221-9217","authenticated-orcid":false,"given":"Fabi\u00e1n","family":"Asp\u00e9e","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Bologna, 40126 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco","family":"Yimes","sequence":"additional","affiliation":[{"name":"WiseConn, Vi\u00f1a del Mar 2520000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,6]]},"reference":[{"key":"ref_1","unstructured":"Yang, X.S. (2010). Nature-Inspired Metaheuristic Algorithms, Luniver Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yang, X.S. (2009, January 26\u201328). Firefly algorithms for multimodal optimization. Proceedings of the International Symposium on Stochastic Algorithms, Sapporo, Japan.","DOI":"10.1007\/978-3-642-04944-6_14"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yang, X.S., and Deb, S. (2009, January 9\u201311). Cuckoo search via L\u00e9vy flights. Proceedings of the World Congress on Nature & Biologically Inspired Computing, NaBIC 2009, Coimbatore, India.","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yang, X.S. (2010). A new metaheuristic bat-inspired algorithm. Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Springer.","DOI":"10.1007\/978-3-642-12538-6_6"},{"key":"ref_5","first-page":"101","article-title":"African Buffalo Optimization (ABO): A New Meta-Heuristic Algorithm","volume":"3","author":"Odili","year":"2015","journal-title":"J. Adv. Appl. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.procs.2015.12.291","article-title":"African Buffalo Optimization: A Swarm-Intelligence Technique","volume":"76","author":"Odili","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_7","unstructured":"Yang, X.S. (2012, January 3\u20137). Flower pollination algorithm for global optimization. Proceedings of the 11th International Conference, UCNC 2012, Orl\u00e9an, France."},{"key":"ref_8","first-page":"739768","article-title":"The coral reefs optimization algorithm: A novel metaheuristic for efficiently solving optimization problems","volume":"2014","year":"2014","journal-title":"Sci. World J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1177\/003754970107600201","article-title":"A new heuristic optimization algorithm: Harmony search","volume":"76","author":"Geem","year":"2001","journal-title":"Simulation"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hamadneh, N., Khan, W., and Tilahun, S. (2018). Optimization of microchannel heat sinks using prey-predator algorithm and artificial neural networks. Machines, 6.","DOI":"10.3390\/machines6020026"},{"key":"ref_11","unstructured":"Mart\u00ednez-Molina, M., Moreno-Armend\u00e1riz, M.A., Cruz-Cort\u00e9s, N., and Mora, J.C.S.T. (December, January 26). Modeling prey-predator dynamics via particle swarm optimization and cellular automata. Proceedings of the Mexican International Conference on Artificial Intelligence, Puebla, Mexico."},{"key":"ref_12","first-page":"243","article-title":"Prey-Predator dynamics and swarm intelligence on a cellular automata model","volume":"11","author":"Molina","year":"2012","journal-title":"Appl. Comput. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.jtbi.2013.07.015","article-title":"On the spatial dynamics and oscillatory behavior of a predator-prey model based on cellular automata and local particle swarm optimization","volume":"336","author":"Molina","year":"2013","journal-title":"J. Theor. Biol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.ecocom.2015.03.001","article-title":"Analyzing the spatial dynamics of a prey\u2013predator lattice model with social behavior","volume":"22","author":"Molina","year":"2015","journal-title":"Ecol. Complex."},{"key":"ref_15","unstructured":"Wolfram, S. (1986). Theory and Applications of Cellular Automata, World Scientific."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.tcs.2004.11.021","article-title":"Theory of cellular automata: A survey","volume":"334","author":"Kari","year":"2005","journal-title":"Theor. Comput. Sci."},{"key":"ref_17","first-page":"1742","article-title":"Prey adaptation as a cause of predator-prey cycles","volume":"51","author":"Abrams","year":"1997","journal-title":"Evolution"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1006\/jtbi.2000.2203","article-title":"The influence of predator\u2013prey population dynamics on the long-term evolution of food web structure","volume":"208","author":"Drossel","year":"2001","journal-title":"J. Theor. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.jde.2004.01.004","article-title":"Strategy and stationary pattern in a three-species predator\u2013prey model","volume":"200","author":"Pang","year":"2004","journal-title":"J. Differ. Equ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.physd.2004.05.007","article-title":"Stationary patterns for a prey\u2013predator model with prey-dependent and ratio-dependent functional responses and diffusion","volume":"196","author":"Wang","year":"2004","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1016\/j.spa.2010.03.011","article-title":"Evolution in predator\u2013prey systems","volume":"120","author":"Durrett","year":"2010","journal-title":"Stoch. Process. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s00285-015-0895-y","article-title":"Stochastic eco-evolutionary model of a prey-predator community","volume":"72","author":"Costa","year":"2016","journal-title":"J. Math. Biol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1146\/annurev.ecolsys.31.1.79","article-title":"The evolution of predator-prey interactions: Theory and evidence","volume":"31","author":"Abrams","year":"2000","journal-title":"Annu. Rev. Ecol. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-2789(84)90245-8","article-title":"Universality and complexity in cellular automata","volume":"10","author":"Wolfram","year":"1984","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/S0198-9715(99)00015-0","article-title":"Modeling urban dynamics through GIS-based cellular automata","volume":"23","author":"Batty","year":"1999","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1068\/a251175","article-title":"Cellular automata and fractal urban form: A cellular modelling approach to the evolution of urban land-use patterns","volume":"25","author":"White","year":"1993","journal-title":"Environ. Plan. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00224-012-9386-3","article-title":"Stochastic cellular automata solutions to the density classification problem","volume":"53","author":"Fates","year":"2013","journal-title":"Theory Comput. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2111","DOI":"10.1007\/s00500-014-1395-5","article-title":"An outer\u2013inner fuzzy cellular automata algorithm for dynamic uncertainty multi-project scheduling problem","volume":"19","author":"Hu","year":"2015","journal-title":"Soft Comput."},{"key":"ref_29","unstructured":"Tralic, D., Rosin, P.L., Sun, X., and Grgic, S. (2014, January 12\u201315). Detection of duplicated image regions using cellular automata. Proceedings of the 2014 International Conference on Systems, Signals and Image Processing (IWSSIP), Dubrovnik, Croatia."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/j.proeng.2016.07.517","article-title":"Improving the Efficiency of Cellular Automata for Sewer Network Design Optimization Problems Using Adaptive Refinement","volume":"154","author":"Afshar","year":"2016","journal-title":"Procedia Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.swevo.2015.07.005","article-title":"Unconventional modelling of complex system via cellular automata and differential evolution","volume":"25","author":"Kotyrba","year":"2015","journal-title":"Swarm Evol. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0167-2789(90)90185-R","article-title":"Invertible cellular automata: A review","volume":"45","author":"Toffoli","year":"1990","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_33","unstructured":"Mitchell, M., Crutchfield, J.P., and Das, R. (1996, January 24\u201327). Evolving cellular automata with genetic algorithms: A review of recent work. Proceedings of the First International Conference on Evolutionary Computation and Its Applications (EvCA\u201996), Moscow, Russia."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.landurbplan.2010.03.001","article-title":"Cellular automata models for the simulation of real-world urban processes: A review and analysis","volume":"96","author":"Miranda","year":"2010","journal-title":"Landsc. Urban Plan."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Pandey, G., Rao, K.R., and Mohan, D. (2015). A review of cellular automata model for heterogeneous traffic conditions. Traffic and Granular Flow\u201913, Springer.","DOI":"10.1007\/978-3-319-10629-8_52"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4531","DOI":"10.1103\/PhysRevE.50.4531","article-title":"Automata network predator-prey model with pursuit and evasion","volume":"50","author":"Boccara","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1006\/tpbi.1997.1338","article-title":"Spatial aspects of interspecific competition","volume":"53","author":"Durrett","year":"1998","journal-title":"Theor. Popul. Biol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.simpat.2003.08.006","article-title":"Effects of cell size and configuration in cellular automata based prey\u2013predator modelling","volume":"11","author":"Chen","year":"2003","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1088\/1751-8113\/40\/5\/002","article-title":"The threshold of coexistence and critical behaviour of a predator\u2013prey cellular automaton","volume":"40","author":"Arashiro","year":"2007","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_40","first-page":"337","article-title":"A predator-prey cellular automaton with parasitic interactions and environmental effects","volume":"83","author":"Farina","year":"2008","journal-title":"Fundam. Inf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1145\/295685.295720","article-title":"An XML framework for agent-based E-commerce","volume":"42","author":"Glushko","year":"1999","journal-title":"Commun. ACM"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1145\/295685.295716","article-title":"Agents that buy and sell","volume":"42","author":"Maes","year":"1999","journal-title":"Commun. ACM"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.eswa.2005.04.039","article-title":"Multi-agent framework for third party logistics in E-commerce","volume":"29","author":"Ying","year":"2005","journal-title":"Expert Syst. Appl."},{"key":"ref_44","first-page":"11","article-title":"An agent-based intelligent tutoring system for enhancing e-learning\/e-teaching","volume":"2","year":"2005","journal-title":"Int. J. Inst. Technol. Distance Learn."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.compedu.2010.01.005","article-title":"Agent based affective tutoring systems: A pilot study","volume":"55","author":"Mao","year":"2010","journal-title":"Comput. Educ."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Jara-Roa, D., Valdiviezo-D\u00edaz, P., Agila-Palacios, M., Sarango-Lapo, C., and Rodriguez-Artacho, M. (2010, January 14\u201316). An adaptive multi-agent based architecture for engineering education. Proceedings of the 2010 IEEE Education Engineering (EDUCON), Madrid, Spain.","DOI":"10.1109\/EDUCON.2010.5492574"},{"key":"ref_47","unstructured":"Mathieu, P., and Secq, Y. (2012, January 6\u20138). Environment updating and agent scheduling policies in agent-based simulators. Proceedings of the 4th International Conference on Agents and Artificial Intelligence (ICAART), Vilamoura, Portugal."},{"key":"ref_48","unstructured":"Rihawi, O., Secq, Y., and Mathieu, P. (2014, January 6\u20138). Effective distribution of large scale situated agent-based simulations. Proceedings of the 6th International Conference on Agents and Artificial Intelligence, Angers, France."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Hassani, K., Asgari, A., and Lee, W.S. (2015, January 1\u20133). A case study on collective intelligence based on energy flow. Proceedings of the 2015 IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS), Douai, France.","DOI":"10.1109\/EAIS.2015.7368805"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"161","DOI":"10.30707\/LiB3.1Karsai","article-title":"Bottom-up ecology: An agent-based model on the interactions between competition and predation","volume":"3","author":"Karsai","year":"2016","journal-title":"Lett. Biomath."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"L\u00fctz, A.F., Cazaubiel, A., and Arenzon, J.J. (2017). Cyclic Competition and Percolation in Grouping Predator-Prey Populations. Games, 8.","DOI":"10.3390\/g8010010"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Almonacid, B. (2017, January 19\u201323). Simulation of a Dynamic Prey-Predator Spatial Model Based on Cellular Automata Using the Behavior of the Metaheuristic African Buffalo Optimization. Proceedings of the Natural and Artificial Computation for Biomedicine and Neuroscience, Corunna, Spain.","DOI":"10.1007\/978-3-319-59740-9_17"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Odili, J.B., Kahar, M.N.M., Anwar, S., and Azrag, M.A.K. (2015, January 19\u201321). A comparative study of African Buffalo Optimization and Randomized Insertion Algorithm for asymmetric Travelling Salesman\u2019s Problem. Proceedings of the 2015 4th International Conference on Software Engineering and Computer Systems (ICSECS), Kuantan, Malaysia.","DOI":"10.1109\/ICSECS.2015.7333089"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.9734\/BJMCS\/2015\/17145","article-title":"Numerical Function Optimization Solutions Using the African Buffalo Optimization Algorithm (ABO)","volume":"10","author":"Odili","year":"2015","journal-title":"Br. J. Math. Comput. Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1155\/2016\/1510256","article-title":"Solving the Traveling Salesman\u2019s Problem Using the African Buffalo Optimization","volume":"2016","author":"Odili","year":"2016","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_56","first-page":"911","article-title":"Solving Traveling Salesman\u2019s Problem Using African Buffalo Optimization, Honey Bee Mating Optimization & Lin-Kerninghan Algorithms","volume":"34","author":"Odili","year":"2016","journal-title":"World Appl. Sci. J."},{"key":"ref_57","first-page":"356","article-title":"African Buffalo Optimization and the randomized insertion algorithm for the asymmetric travelling salesman\u2019s problems","volume":"87","author":"Odili","year":"2016","journal-title":"J. Theor. Appl. Inf. Technol."},{"key":"ref_58","unstructured":"Odili, J.B., Nizam, M., Kahar, M., and Noraziah, A. (2016, January 24\u201325). African Buffalo Optimization approach to the design of PID controller in automatic voltage regulator system. Proceedings of the National Conference for Postgraduate Research, Gambang, Malaysia."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"627","DOI":"10.18520\/cs\/v114\/i03\/627-636","article-title":"African Buffalo Optimization for global optimization","volume":"114","author":"Odili","year":"2018","journal-title":"Curr. Sci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/3\/59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:49Z","timestamp":1760186209000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/3\/59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,6]]},"references-count":59,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["a12030059"],"URL":"https:\/\/doi.org\/10.3390\/a12030059","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,6]]}}}