{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T01:38:59Z","timestamp":1768268339128,"version":"3.49.0"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61573233"],"award-info":[{"award-number":["61573233"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12271111"],"award-info":[{"award-number":["12271111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Key Project of Natural Science Foundation of Guangdong Province","award":["2015A030311017"],"award-info":[{"award-number":["2015A030311017"]}]},{"name":"the team project of the University of Guangdong province","award":["2015KCXTD018"],"award-info":[{"award-number":["2015KCXTD018"]}]},{"name":"Special Support Plan for High-Level Talents of Guangdong Province","award":["2019TQ05X571"],"award-info":[{"award-number":["2019TQ05X571"]}]},{"name":"Project of Guangdong Province Innovative Team","award":["2020WCXTD011"],"award-info":[{"award-number":["2020WCXTD011"]}]},{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"crossref","award":["2022A1515011726"],"award-info":[{"award-number":["2022A1515011726"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Target search using a swarm of robots is a classic research topic that poses challenges, particularly in conducting multi-target searching in unknown environments. Key challenges include high communication cost among robots, unknown positions of obstacles, and the presence of multiple targets. To address these challenges, we propose a novel <jats:bold>R<\/jats:bold>obotic <jats:bold>F<\/jats:bold>low <jats:bold>D<\/jats:bold>irection <jats:bold>A<\/jats:bold>lgorithm (RFDA), building upon the modified Flow Direction Algorithm (FDA) to suit the characteristics of the robot\u2019s motion. RFDA efficiently reduces the communication cost and navigates around unknown obstacles. The algorithm also accounts for scenarios involving isolated robots. The pipeline of the proposed RFDA method is outlined as follows: (1). <jats:bold>Learning strategy<\/jats:bold>: a neighborhood information based learning strategy is adopted to enhance the FDA\u2019s position update formula. This allows swarm robots to systematically locate the target (the lowest height) in a stepwise manner. (2). <jats:bold>Adaptive inertia weighting<\/jats:bold>: An adaptive inertia weighting mechanism is employed to maintain diversity among robots during the search and avoid premature convergence. (3). <jats:bold>Sink-filling process<\/jats:bold>: The algorithm simulates the sink-filling process and moving to the aspect slope to escape from local optima. (4). <jats:bold>Isolated robot scenario<\/jats:bold>: The case of an isolated robot (a robot without neighbors) is considered. Global optimal information is only required when the robot is isolated or undergoing the sink-filling process, thereby reducing communication costs. We not only demonstrate the probabilistic completeness of RFDA but also validate its effectiveness by comparing it with six other competing algorithms in a simulated environment. Experiments cover various aspects such as target number, population size, and environment size. Our findings indicate that RFDA outperforms other methods in terms of the number of required iterations and the full success rate. The Friedman and Wilcoxon tests further demonstrate the superiority of RFDA.<\/jats:p>","DOI":"10.1007\/s40747-024-01564-3","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T20:03:31Z","timestamp":1722456211000},"page":"7741-7764","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A FDA-based multi-robot cooperation algorithm for multi-target searching in unknown environments"],"prefix":"10.1007","volume":"10","author":[{"given":"Wenwen","family":"Ye","sequence":"first","affiliation":[]},{"given":"Jia","family":"Cai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3658-6317","authenticated-orcid":false,"given":"Shengping","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"issue":"21","key":"1564_CR1","doi-asserted-by":"publisher","first-page":"13451","DOI":"10.1007\/s00500-021-06095-4","volume":"25","author":"S Emamgholizadeh","year":"2021","unstructured":"Emamgholizadeh S, Mohammadi B (2021) New hybrid nature-based algorithm to integration support vector machine for prediction of soil cation exchange capacity. Soft Comput 25(21):13451\u201313464","journal-title":"Soft Comput"},{"issue":"2","key":"1564_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asej.2022.101876","volume":"14","author":"S Emamgholizadeh","year":"2023","unstructured":"Emamgholizadeh S, Bazoobandi A, Mohammadi B, Ghorbani H, Sadeghi MA (2023) Prediction of soil cation exchange capacity using enhanced machine learning approaches in the southern region of the caspian sea. Ain Shams Eng J 14(2):101876","journal-title":"Ain Shams Eng J"},{"key":"1564_CR3","doi-asserted-by":"crossref","unstructured":"Shih P-S, Liu S, Yu X-H (2022) Ant colony optimization for multi-phase traffic signal control. In: 2022 IEEE 7th International Conference on intelligent transportation engineering (ICITE), pp. 517\u2013521","DOI":"10.1109\/ICITE56321.2022.10101431"},{"issue":"1","key":"1564_CR4","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1109\/TCBB.2015.2443789","volume":"14","author":"B Zhang","year":"2015","unstructured":"Zhang B, Duan H (2015) Three-dimensional path planning for uninhabited combat aerial vehicle based on predator-prey pigeon-inspired optimization in dynamic environment. IEEE\/ACM Trans Comput Biol Bioinf 14(1):97\u2013107","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"issue":"1","key":"1564_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11721-012-0075-2","volume":"7","author":"M Brambilla","year":"2013","unstructured":"Brambilla M, Ferrante E, Birattari M, Dorigo M (2013) Swarm robotics: a review from the swarm engineering perspective. Swarm Intell 7(1):1\u201341","journal-title":"Swarm Intell"},{"key":"1564_CR6","unstructured":"Batra S, Huang Z, Petrenko A, Kumar T, Molchanov A, Sukhatme GS (2022) Decentralized control of quadrotor swarms with end-to-end deep reinforcement learning. In: Conference on robot learning, pp. 576\u2013586"},{"key":"1564_CR7","doi-asserted-by":"publisher","first-page":"36","DOI":"10.3389\/frobt.2020.00036","volume":"7","author":"M Schranz","year":"2020","unstructured":"Schranz M, Umlauft M, Sende M, Elmenreich W (2020) Swarm robotic behaviors and current applications. Front Robot AI 7:36","journal-title":"Front Robot AI"},{"issue":"5","key":"1564_CR8","doi-asserted-by":"publisher","first-page":"2383","DOI":"10.3390\/app11052383","volume":"11","author":"ZH Ismail","year":"2021","unstructured":"Ismail ZH, Hamami MGM (2021) Systematic literature review of swarm robotics strategies applied to target search problem with environment constraints. Appl Sci 11(5):2383","journal-title":"Appl Sci"},{"key":"1564_CR9","doi-asserted-by":"publisher","unstructured":"Hamami MGM, Ismail ZH (2022) A systematic review on particle swarm optimization towards target search in the swarm robotics domain. Arch Comput Methods Eng, 1\u201320. https:\/\/doi.org\/10.1007\/s11831-022-09819-3","DOI":"10.1007\/s11831-022-09819-3"},{"key":"1564_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.simpat.2022.102599","volume":"120","author":"K Wang","year":"2022","unstructured":"Wang K, Liu Z, Zhu Z, Qi G, Yao J, Miao G (2022) Formation optimization of blockchain-assisted swarm robotics systems against failures based on energy balance. Simul Model Pract Theory 120:102599","journal-title":"Simul Model Pract Theory"},{"key":"1564_CR11","doi-asserted-by":"crossref","unstructured":"Zhu Q, Liang A, Guan H (2011) A pso-inspired multi-robot search algorithm independent of global information. In: 2011 IEEE Symposium on swarm intelligence, pp. 1\u20137","DOI":"10.1109\/SIS.2011.5952586"},{"issue":"1","key":"1564_CR12","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s11721-007-0002-0","volume":"1","author":"R Poli","year":"2007","unstructured":"Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33\u201357","journal-title":"Particle swarm optimization. Swarm Intell"},{"key":"1564_CR13","doi-asserted-by":"crossref","unstructured":"Pugh J, Martinoli A (2007) Inspiring and modeling multi-robot search with particle swarm optimization. In: 2007 IEEE Swarm Intelligence Symposium, pp. 332\u2013339","DOI":"10.1109\/SIS.2007.367956"},{"key":"1564_CR14","doi-asserted-by":"crossref","unstructured":"Doctor S, Venayagamoorthy GK, Gudise VG (2004) Optimal pso for collective robotic search applications. In: Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No. 04TH8753), 2, 1390\u20131395","DOI":"10.1109\/CEC.2004.1331059"},{"key":"1564_CR15","doi-asserted-by":"crossref","unstructured":"Pugh J, Martinoli A (2006) Multi-robot learning with particle swarm optimization. In: Proceedings of the Fifth International Joint Conference on autonomous agents and multiagent systems, pp. 441\u2013448","DOI":"10.1145\/1160633.1160715"},{"key":"1564_CR16","doi-asserted-by":"crossref","unstructured":"Songdong X, Jianchao Z (2008) Sense limitedly, interact locally: the control strategy for swarm robots search. In: 2008 IEEE International Conference on networking, sensing and control, pp. 402\u2013407","DOI":"10.1109\/ICNSC.2008.4525249"},{"issue":"4","key":"1564_CR17","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s00158-010-0618-3","volume":"44","author":"Q Tang","year":"2011","unstructured":"Tang Q, Eberhard P (2011) A pso-based algorithm designed for a swarm of mobile robots. Struct Multidiscip Optim 44(4):483\u2013498","journal-title":"Struct Multidiscip Optim"},{"key":"1564_CR18","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cie.2021.107224","volume":"156","author":"H Karami","year":"2021","unstructured":"Karami H, Anaraki MV, Farzin S, Mirjalili S (2021) Flow direction algorithm (fda): a novel optimization approach for solving optimization problems. Comput Ind Eng 156:107\u2013224","journal-title":"Comput Ind Eng"},{"key":"1564_CR19","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.neucom.2015.11.007","volume":"177","author":"M Dadgar","year":"2016","unstructured":"Dadgar M, Jafari S, Hamzeh A (2016) A pso-based multi-robot cooperation method for target searching in unknown environments. Neurocomputing 177:62\u201374","journal-title":"Neurocomputing"},{"key":"1564_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115795","volume":"186","author":"H Tang","year":"2021","unstructured":"Tang H, Sun W, Lin A, Xue M, Zhang X (2021) A gwo-based multi-robot cooperation method for target searching in unknown environments. Expert Syst Appl 186:115795","journal-title":"Expert Syst Appl"},{"key":"1564_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejco.2022.100029","volume":"10","author":"J Schmidt","year":"2022","unstructured":"Schmidt J, Irnich S (2022) New neighborhoods and an iterated local search algorithm for the generalized traveling salesman problem. EURO J Comput Optim 10:100029","journal-title":"EURO J Comput Optim"},{"key":"1564_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.119789","volume":"222","author":"KV Tiwari","year":"2023","unstructured":"Tiwari KV, Sharma SK (2023) An optimization model for vehicle routing problem in last-mile delivery. Expert Syst Appl 222:119789","journal-title":"Expert Syst Appl"},{"key":"1564_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.iot.2023.100697","volume":"22","author":"MI Khaleel","year":"2023","unstructured":"Khaleel MI (2023) Efficient job scheduling paradigm based on hybrid sparrow search algorithm and differential evolution optimization for heterogeneous cloud computing platforms. Internet of Things 22:100697","journal-title":"Internet of Things"},{"key":"1564_CR24","doi-asserted-by":"crossref","unstructured":"Couceiro MS, Rocha RP, Ferreira NM (2011) A novel multi-robot exploration approach based on particle swarm optimization algorithms. In: 2011 IEEE International Symposium on safety, security, and rescue robotics, pp. 327\u2013332","DOI":"10.1109\/SSRR.2011.6106751"},{"issue":"7","key":"1564_CR25","doi-asserted-by":"publisher","first-page":"86","DOI":"10.5772\/60624","volume":"12","author":"MN Rastgoo","year":"2015","unstructured":"Rastgoo MN, Nakisa B, Ahmad Nazri MZ (2015) A hybrid of modified pso and local search on a multi-robot search system. Int J Adv Rob Syst 12(7):86","journal-title":"Int J Adv Rob Syst"},{"key":"1564_CR26","doi-asserted-by":"publisher","first-page":"76328","DOI":"10.1109\/ACCESS.2019.2921621","volume":"7","author":"J Yang","year":"2019","unstructured":"Yang J, Wang X, Bauer P (2019) Extended pso based collaborative searching for robotic swarms with practical constraints. IEEE Access 7:76328\u201376341","journal-title":"IEEE Access"},{"key":"1564_CR27","doi-asserted-by":"crossref","unstructured":"Yang J, Xiong R, Xiang X, Shi Y (2020) Exploration enhanced rpso for collaborative multitarget searching of robotic swarms. Complexity 2020(1):8863526","DOI":"10.1155\/2020\/8863526"},{"key":"1564_CR28","doi-asserted-by":"publisher","first-page":"226484","DOI":"10.1109\/ACCESS.2020.3045177","volume":"8","author":"Y Du","year":"2020","unstructured":"Du Y (2020) A novel approach for swarm robotic target searches based on the dpso algorithm. IEEE Access 8:226484\u2013226505","journal-title":"IEEE Access"},{"key":"1564_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107297","volume":"105","author":"N Nedjah","year":"2021","unstructured":"Nedjah N, Ribeiro LM, Macedo Mourelle L (2021) Communication optimization for efficient dynamic task allocation in swarm robotics. Appl Soft Comput 105:107297","journal-title":"Appl Soft Comput"},{"issue":"2","key":"1564_CR30","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1162\/106454699568728","volume":"5","author":"M Dorigo","year":"1999","unstructured":"Dorigo M, Di Caro G, Gambardella LM (1999) Ant algorithms for discrete optimization. Artif Life 5(2):137\u2013172","journal-title":"Artif Life"},{"key":"1564_CR31","doi-asserted-by":"crossref","unstructured":"Hoff NR, Sagoff A, Wood RJ, Nagpal R (2010) Two foraging algorithms for robot swarms using only local communication. In: 2010 IEEE International Conference on robotics and biomimetics, pp. 123\u2013130","DOI":"10.1109\/ROBIO.2010.5723314"},{"key":"1564_CR32","unstructured":"Karaboga D, et al (2005) An idea based on honey bee swarm for numerical optimization. Technical report, Technical report-tr06, Erciyes university, engineering faculty, computer\u00a0.."},{"key":"1564_CR33","doi-asserted-by":"crossref","unstructured":"Banharnsakun A, Achalakul T, Batra RC (2012) Target finding and obstacle avoidance algorithm for microrobot swarms. In: 2012 IEEE International Conference on systems, man, and cybernetics (SMC), pp. 1610\u20131615","DOI":"10.1109\/ICSMC.2012.6377967"},{"key":"1564_CR34","doi-asserted-by":"crossref","unstructured":"Pham DT, Ghanbarzadeh A, Ko\u00e7 E, Otri S, Rahim S, Zaidi M (2006) The bees algorithm-a novel tool for complex optimisation problems. In: Intelligent Production Machines and Systems, pp. 454\u2013459","DOI":"10.1016\/B978-008045157-2\/50081-X"},{"key":"1564_CR35","unstructured":"Jevti\u0107 A, Gazi P, Andina D, Jamshidi M (2010) Building a swarm of robotic bees. In: 2010 World Automation Congress, pp. 1\u20136"},{"issue":"3","key":"1564_CR36","doi-asserted-by":"publisher","first-page":"209","DOI":"10.3233\/MGS-2006-2301","volume":"2","author":"K Krishnanand","year":"2006","unstructured":"Krishnanand K, Ghose D (2006) Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications. Multiagent Grid Syst 2(3):209\u2013222","journal-title":"Multiagent Grid Syst"},{"key":"1564_CR37","unstructured":"Krishnanand KN, Ghose D (2005) Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. In: Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005., pp. 84\u201391"},{"key":"1564_CR38","first-page":"23","volume":"3","author":"S Das","year":"2009","unstructured":"Das S, Biswas A, Dasgupta S, Abraham A (2009) Bacterial foraging optimization algorithm: theoretical foundations, analysis, and applications. Found Comput Intell 3:23\u201355","journal-title":"Found Comput Intell"},{"key":"1564_CR39","doi-asserted-by":"crossref","unstructured":"Yang B, Ding Y, Hao K (2014) Target searching and trapping for swarm robots with modified bacterial foraging optimization algorithm. In: Proceeding of the 11th World Congress on Intelligent Control and Automation, pp. 1348\u20131353","DOI":"10.1109\/WCICA.2014.7052915"},{"key":"1564_CR40","doi-asserted-by":"crossref","unstructured":"Yang X-S (2009) Firefly algorithms for multimodal optimization. In: International Symposium on stochastic algorithms, pp. 169\u2013178","DOI":"10.1007\/978-3-642-04944-6_14"},{"key":"1564_CR41","doi-asserted-by":"crossref","unstructured":"Palmieri N, Marano S (2016) Discrete firefly algorithm for recruiting task in a swarm of robots. In: Nature-Inspired Computation in Engineering, pp. 133\u2013150","DOI":"10.1007\/978-3-319-30235-5_7"},{"key":"1564_CR42","doi-asserted-by":"crossref","unstructured":"Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. In: International Conference in swarm intelligence, pp. 355\u2013364","DOI":"10.1007\/978-3-642-13495-1_44"},{"key":"1564_CR43","doi-asserted-by":"crossref","unstructured":"Zheng Z, Tan Y (2013) Group explosion strategy for searching multiple targets using swarm robotic. In: 2013 IEEE Congress on evolutionary computation, pp. 821\u2013828","DOI":"10.1109\/CEC.2013.6557653"},{"key":"1564_CR44","doi-asserted-by":"crossref","unstructured":"Yang X-S, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464\u2013483","DOI":"10.1108\/02644401211235834"},{"key":"1564_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2019.112945","volume":"141","author":"H Tang","year":"2020","unstructured":"Tang H, Sun W, Yu H, Lin A, Xue M (2020) A multirobot target searching method based on bat algorithm in unknown environments. Expert Syst Appl 141:112945","journal-title":"Expert Syst Appl"},{"key":"1564_CR46","doi-asserted-by":"crossref","unstructured":"Shi Y (2015) An optimization algorithm based on brainstorming process. In: Emerging Research on Swarm Intelligence and Algorithm Optimization, pp. 1\u201335","DOI":"10.4018\/978-1-4666-6328-2.ch001"},{"key":"1564_CR47","doi-asserted-by":"crossref","unstructured":"Shi Y (2015) Brain storm optimization algorithm in objective space. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 1227\u20131234","DOI":"10.1109\/CEC.2015.7257029"},{"key":"1564_CR48","doi-asserted-by":"crossref","unstructured":"Yang J, Shen Y, Shi Y (2020) Brain storm robotics: an automatic design framework for multi-robot systems. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1\u20138","DOI":"10.1109\/CEC48606.2020.9185787"},{"key":"1564_CR49","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361","journal-title":"Adv Eng Softw"},{"key":"1564_CR50","doi-asserted-by":"crossref","unstructured":"Jain U, Tiwari R, Godfrey WW (2018) Odor source localization by concatenating particle swarm optimization and grey wolf optimizer. In: Advanced computational and communication paradigms, pp. 145\u2013153","DOI":"10.1007\/978-981-10-8237-5_14"},{"issue":"4","key":"1564_CR51","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1007\/s00521-015-1920-1","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053\u20131073","journal-title":"Neural Comput Appl"},{"key":"1564_CR52","doi-asserted-by":"crossref","unstructured":"Hamami MGM, Ismail ZH (2022) Dragonfly algorithm for multi-target search problem in swarm robotic with dynamic environment size. In: International Conference on industrial, engineering and other applications of applied intelligent systems, pp. 253\u2013261","DOI":"10.1007\/978-3-031-08530-7_21"},{"key":"1564_CR53","doi-asserted-by":"crossref","unstructured":"Castell\u00f3\u00a0Ferrer E (2019) The blockchain: a new framework for robotic swarm systems. In: Proceedings of the Future Technologies Conference (FTC) 2018: 2, 1037\u20131058","DOI":"10.1007\/978-3-030-02683-7_77"},{"key":"1564_CR54","doi-asserted-by":"publisher","first-page":"54","DOI":"10.3389\/frobt.2020.00054","volume":"7","author":"V Strobel","year":"2020","unstructured":"Strobel V, Castell\u00f3 Ferrer E, Dorigo M (2020) Blockchain technology secures robot swarms: a comparison of consensus protocols and their resilience to byzantine robots. Front Robot AI 7:54","journal-title":"Front Robot AI"},{"key":"1564_CR55","doi-asserted-by":"publisher","DOI":"10.1016\/j.rico.2022.100141","volume":"8","author":"HJ Lopes","year":"2022","unstructured":"Lopes HJ, Lima DA (2022) Surveillance task optimized by evolutionary shared tabu inverted ant cellular automata model for swarm robotics navigation control. Results Control Optim 8:100141","journal-title":"Results Control Optim"},{"key":"1564_CR56","doi-asserted-by":"crossref","unstructured":"Huang C-Y, Li J-Y, Huang J-Y, Lee W-P (2023) A blockchain-based service-oriented framework to enable cooperation of swarm robots. In: International Conference on swarm intelligence, pp. 3\u201315","DOI":"10.1007\/978-3-031-36625-3_1"},{"key":"1564_CR57","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/j.asoc.2019.01.023","volume":"77","author":"J Li","year":"2019","unstructured":"Li J, Tan Y (2019) A probabilistic finite state machine based strategy for multi-target search using swarm robotics. Appl Soft Comput 77:467\u2013483","journal-title":"Appl Soft Comput"},{"key":"1564_CR58","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.108873","volume":"122","author":"KA-R Youssefi","year":"2022","unstructured":"Youssefi KA-R, Rouhani M, Mashhadi HR, Elmenreich W (2022) A swarm intelligence-based robotic search algorithm integrated with game theory. Appl Soft Comput 122:108873","journal-title":"Appl Soft Comput"},{"key":"1564_CR59","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s11721-020-00182-2","volume":"14","author":"AS Wu","year":"2020","unstructured":"Wu AS, Wiegand RP, Pradhan R (2020) Response probability enhances robustness in decentralized threshold-based robotic swarms. Swarm Intell 14:233\u2013258","journal-title":"Swarm Intell"},{"issue":"14","key":"1564_CR60","doi-asserted-by":"publisher","first-page":"2482","DOI":"10.3390\/math10142482","volume":"10","author":"YT Dos Passos","year":"2022","unstructured":"Dos Passos YT, Duquesne X, Marcolino LS (2022) On the throughput of the common target area for robotic swarm strategies. Mathematics 10(14):2482","journal-title":"Mathematics"},{"key":"1564_CR61","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-019-2332-4","volume":"18","author":"S Mahanti","year":"2019","unstructured":"Mahanti S, Das S, Behera BK, Panigrahi PK (2019) Quantum robots can fly; play games: an ibm quantum experience. Quantum Inf Process 18:1\u201310","journal-title":"Quantum Inf Process"},{"key":"1564_CR62","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2023.104362","volume":"161","author":"A Chella","year":"2023","unstructured":"Chella A, Gaglio S, Mannone M, Pilato G, Seidita V, Vella F, Zammuto S (2023) Quantum planning for swarm robotics. Robot Auton Syst 161:104362","journal-title":"Robot Auton Syst"},{"issue":"3","key":"1564_CR63","doi-asserted-by":"publisher","first-page":"372","DOI":"10.3390\/math10030372","volume":"10","author":"M Mannone","year":"2022","unstructured":"Mannone M, Seidita V, Chella A (2022) Categories, quantum computing, and swarm robotics: A case study. Mathematics 10(3):372","journal-title":"Mathematics"},{"key":"1564_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2023.101297","volume":"79","author":"M Mannone","year":"2023","unstructured":"Mannone M, Seidita V, Chella A (2023) Modeling and designing a robotic swarm: A quantum computing approach. Swarm Evol Comput 79:101297","journal-title":"Swarm Evol Comput"},{"issue":"3","key":"1564_CR65","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.3390\/app11031347","volume":"11","author":"L Jiang","year":"2021","unstructured":"Jiang L, Mo H, Tian P (2021) A bacterial chemotaxis-inspired coordination strategy for coverage and aggregation of swarm robots. Appl Sci 11(3):1347","journal-title":"Appl Sci"},{"key":"1564_CR66","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.swevo.2019.03.013","volume":"48","author":"A Yadav","year":"2019","unstructured":"Yadav A et al (2019) Aefa: artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93\u2013108","journal-title":"Swarm Evol Comput"},{"key":"1564_CR67","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2021.107250","volume":"157","author":"L Abualigah","year":"2021","unstructured":"Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-Qaness MA, Gandomi AH (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250","journal-title":"Comput Ind Eng"},{"issue":"4","key":"1564_CR68","doi-asserted-by":"publisher","first-page":"2627","DOI":"10.1007\/s00366-022-01604-x","volume":"39","author":"A Seyyedabbasi","year":"2023","unstructured":"Seyyedabbasi A, Kiani F (2023) Sand cat swarm optimization: A nature-inspired algorithm to solve global optimization problems. Eng Comput 39(4):2627\u20132651","journal-title":"Eng Comput"},{"key":"1564_CR69","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2020.100665","volume":"54","author":"J Carrasco","year":"2020","unstructured":"Carrasco J, Garc\u00eda S, Rueda M, Das S, Herrera F (2020) Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: practical guidelines and a critical review. Swarm Evol Comput 54:100665","journal-title":"Swarm Evol Comput"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01564-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-024-01564-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01564-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T22:11:52Z","timestamp":1729116712000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-024-01564-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,31]]},"references-count":69,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["1564"],"URL":"https:\/\/doi.org\/10.1007\/s40747-024-01564-3","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,31]]},"assertion":[{"value":"28 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}