{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T21:35:17Z","timestamp":1782250517601,"version":"3.54.5"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T00:00:00Z","timestamp":1704240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T00:00:00Z","timestamp":1704240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003945","name":"Link\u00f6ping University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003945","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Intell Syst"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>According to Moore\u2019s law, computer processing hardware technology performance is doubled every year. To make effective use of this technological development, the algorithmic solutions have to be developed at the same speed. Consequently, it is necessary to design parallel algorithms to be implemented on parallel machines. This helps to exploit the multi-core environment by executing multiple instructions simultaneously on multiple processors. Traveling Salesman (TSP) is a challenging non-deterministic-hard optimization problem that has exponential running time using brute-force methods. TSP is concerned with finding the shortest path starting with a point and returning to that point after visiting the list of points, provided that these points are visited only once. Meta-heuristic optimization algorithms have been used to tackle TSP and find near-optimal solutions in a reasonable time. This paper proposes a parallel River Formation Dynamics Optimization Algorithm (RFD) to solve the TSP problem. The parallelization technique depends on dividing the population into different processors using the Map-Reduce framework in Apache Spark. The experiments are accomplished in three phases. The first phase compares the speedup, running time, and efficiency of RFD on 1 (sequential RFD), 4, 8, and 16 cores. The second phase compares the proposed parallel RFD with three parallel water-based algorithms, namely the Water Flow algorithm, Intelligent Water Drops, and the Water Cycle Algorithm. To achieve fairness, all algorithms are implemented using the same system specifications and the same values for shared parameters. The third phase compares the proposed parallel RFD with the reported results of metaheuristic algorithms that were used to solve TSP in the literature. The results demonstrate that the RFD algorithm has the best performance for the majority of problem instances, achieving the lowest running times across different core counts. Our findings highlight the importance of selecting the most suitable algorithm and core count based on the problem characteristics to achieve optimal performance in parallel optimization.<\/jats:p>","DOI":"10.1007\/s44196-023-00385-5","type":"journal-article","created":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T16:03:36Z","timestamp":1704297816000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Solving Traveling Salesman Problem Using Parallel River Formation Dynamics Optimization Algorithm on Multi-core Architecture Using Apache Spark"],"prefix":"10.1007","volume":"17","author":[{"given":"Esra\u2019a","family":"Alhenawi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruba Abu","family":"Khurma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robertas","family":"Dama\u0161evic\u0306ius","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5394-0678","authenticated-orcid":false,"given":"Abdelazim G.","family":"Hussien","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,1,3]]},"reference":[{"key":"385_CR1","first-page":"225","volume":"7","author":"M J\u00fcnger","year":"1995","unstructured":"J\u00fcnger, M., Reinelt, G., Rinaldi, G.: The traveling salesman problem. Handb. Oper. Res. Manag. Sci. 7, 225\u2013330 (1995)","journal-title":"Handb. Oper. Res. Manag. Sci."},{"issue":"2\u20133","key":"385_CR2","first-page":"157","volume":"164","author":"J Cooper","year":"2019","unstructured":"Cooper, J., Nicolescu, R.: The hamiltonian cycle and travelling salesman problems in cp systems. Fund. Inform. 164(2\u20133), 157\u2013180 (2019)","journal-title":"Fund. Inform."},{"issue":"4","key":"385_CR3","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1080\/17445760.2020.1776867","volume":"35","author":"A Jazayeri","year":"2020","unstructured":"Jazayeri, A., Sayama, H.: A polynomial-time deterministic approach to the travelling salesperson problem. Int. J. Parallel Emerg. Distrib. Syst. 35(4), 454\u2013460 (2020)","journal-title":"Int. J. Parallel Emerg. Distrib. Syst."},{"issue":"3A","key":"385_CR4","first-page":"452","volume":"18","author":"MAW Shalaby","year":"2021","unstructured":"Shalaby, M.A.W., Mohammed, A.R., Kassem, S.S.: Supervised fuzzy c-means techniques to solve the capacitated vehicle routing problem. Int. Arab J. Inf. Technol. 18(3A), 452\u2013463 (2021)","journal-title":"Int. Arab J. Inf. Technol."},{"issue":"4","key":"385_CR5","first-page":"689","volume":"19","author":"N Mahmood","year":"2022","unstructured":"Mahmood, N.: Solving capacitated vehicle routing problem using meerkat clan algorithm. Int. Arab J. Inf. Technol. 19(4), 689\u2013694 (2022)","journal-title":"Int. Arab J. Inf. Technol."},{"key":"385_CR6","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.egyr.2023.06.024","volume":"10","author":"PY Gubin","year":"2023","unstructured":"Gubin, P.Y., Kamel, S., Safaraliev, M., Senyuk, M., Hussien, A.G., Zawbaa, H.M.: Optimizing generating unit maintenance with the league championship method: a reliability-based approach. Energy Reports 10, 135\u2013152 (2023)","journal-title":"Energy Reports"},{"key":"385_CR7","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1016\/j.aej.2023.09.009","volume":"80","author":"D Izci","year":"2023","unstructured":"Izci, D., Rizk-Allah, R.M., Ekinci, S., Hussien, A.G.: Enhancing time-domain performance of vehicle cruise control system by using a multi-strategy improved run optimizer. Alexandria Eng. J. 80, 609\u2013622 (2023)","journal-title":"Alexandria Eng. J."},{"issue":"1","key":"385_CR8","doi-asserted-by":"publisher","first-page":"14591","DOI":"10.1038\/s41598-023-41608-1","volume":"13","author":"F Daqaq","year":"2023","unstructured":"Daqaq, F., Hassan, M.H., Kamel, S., Hussien, A.G.: A leader supply-demand-based optimization for large scale optimal power flow problem considering renewable energy generations. Sci. Rep. 13(1), 14591 (2023)","journal-title":"Sci. Rep."},{"key":"385_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.108320","volume":"242","author":"FA Hashim","year":"2022","unstructured":"Hashim, F.A., Hussien, A.G.: Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl. Based Syst. 242, 108320 (2022)","journal-title":"Knowl. Based Syst."},{"key":"385_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aei.2023.102004","volume":"57","author":"G Hu","year":"2023","unstructured":"Hu, G., Zheng, Y., Abualigah, L., Hussien, A.G.: Detdo: an adaptive hybrid dandelion optimizer for engineering optimization. Adv. Eng. Informat. 57, 102004 (2023)","journal-title":"Adv. Eng. Informat."},{"issue":"4","key":"385_CR11","doi-asserted-by":"publisher","first-page":"851","DOI":"10.3390\/math11040851","volume":"11","author":"G Hu","year":"2023","unstructured":"Hu, G., Wang, J., Li, M., Hussien, A.G., Abbas, M.: Ejs: multi-strategy enhanced jellyfish search algorithm for engineering applications. Mathematics 11(4), 851 (2023)","journal-title":"Mathematics"},{"issue":"12","key":"385_CR12","doi-asserted-by":"publisher","first-page":"14173","DOI":"10.3934\/mbe.2022660","volume":"19","author":"Yu Huangjing","year":"2022","unstructured":"Huangjing, Yu., Jia, H., Zhou, J., Hussien, A.: Enhanced aquila optimizer algorithm for global optimization and constrained engineering problems. Math. Biosci. Eng. 19(12), 14173\u201314211 (2022)","journal-title":"Math. Biosci. Eng."},{"key":"385_CR13","doi-asserted-by":"crossref","unstructured":"Sasmal, B., Hussien, A.G., Das, A., Dhal, K.G.: A comprehensive survey on aquila optimizer. Arch. Comput. Methods Eng., 1\u201328 (2023)","DOI":"10.1007\/s11831-023-09945-6"},{"key":"385_CR14","doi-asserted-by":"crossref","unstructured":"Sasmal, B., Hussien, A.G., Das, A., Dhal, K.G., Saha, R.: Reptile search algorithm: theory, variants, applications, and performance evaluation. Arch. Comput. Methods Eng., 1\u201329 (2023)","DOI":"10.1007\/s11831-023-09990-1"},{"key":"385_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2023.122054","volume":"353","author":"MA Elseify","year":"2024","unstructured":"Elseify, M.A., Hashim, F.A., Hussien, A.G., Kamel, S.: Single and multi-objectives based on an improved golden jackal optimization algorithm for simultaneous integration of multiple capacitors and multi-type dgs in distribution systems. Appl. Energy 353, 122054 (2024)","journal-title":"Appl. Energy"},{"key":"385_CR16","doi-asserted-by":"crossref","unstructured":"Wang, S., Hussien, A.G., Kumar, S., AlShourbaji, I., Hashim, F.A.: A modified smell agent optimization for global optimization and industrial engineering design problems. J. Comput. Des. Eng., qwad062 (2023)","DOI":"10.1093\/jcde\/qwad062"},{"issue":"3","key":"385_CR17","doi-asserted-by":"publisher","first-page":"294","DOI":"10.3390\/biomimetics8030294","volume":"8","author":"I Mir","year":"2023","unstructured":"Mir, I., Gul, F., Mir, S., Abualigah, L., Zitar, R.A., Hussien, A.G., Awwad, E.M., Sharaf, M.: Multi-agent variational approach for robotics: a bio-inspired perspective. Biomimetics 8(3), 294 (2023)","journal-title":"Biomimetics"},{"issue":"12","key":"385_CR18","doi-asserted-by":"publisher","first-page":"1919","DOI":"10.3390\/electronics11121919","volume":"11","author":"AG Hussien","year":"2022","unstructured":"Hussien, A.G., Abualigah, L., Abu Zitar, R., Hashim, F.A., Amin, M., Saber, A., Almotairi, K.H., Gandomi, A.H.: Recent advances in harris hawks optimization: a comparative study and applications. Electronics 11(12), 1919 (2022)","journal-title":"Electronics"},{"key":"385_CR19","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.aej.2022.12.045","volume":"68","author":"A Chhabra","year":"2023","unstructured":"Chhabra, A., Hussien, A.G., Hashim, F.A.: Improved bald eagle search algorithm for global optimization and feature selection. Alex. Eng. J. 68, 141\u2013180 (2023)","journal-title":"Alex. Eng. J."},{"key":"385_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00521-023-08936-9","volume":"35","author":"FA Hashim","year":"2023","unstructured":"Hashim, F.A., Neggaz, N., Mostafa, R.R., Abualigah, L., Damasevicius, R., Hussien, A.G.: Dimensionality reduction approach based on modified hunger games search: case study on Parkinson\u2019s disease phonation. Neural Comput. Appl. 35, 1\u201327 (2023)","journal-title":"Neural Comput. Appl."},{"issue":"3","key":"385_CR21","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1007\/s10586-021-03304-5","volume":"25","author":"FS Gharehchopogh","year":"2022","unstructured":"Gharehchopogh, F.S., Abdollahzadeh, B.: An efficient harris hawk optimization algorithm for solving the travelling salesman problem. Clust. Comput. 25(3), 1981\u20132005 (2022)","journal-title":"Clust. Comput."},{"key":"385_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.aei.2022.101623","volume":"52","author":"J Pasha","year":"2022","unstructured":"Pasha, J., Nwodu, A.L., Fathollahi-Fard, A.M., Tian, G., Li, Z., Wang, H., Dulebenets, M.: Exact and metaheuristic algorithms for the vehicle routing problem with a factory-in-a-box in multi-objective settings. Adv. Eng. Informat. 52, 101623 (2022)","journal-title":"Adv. Eng. Informat."},{"key":"385_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107298","volume":"105","author":"K Panwar","year":"2021","unstructured":"Panwar, K., Deep, K.: Discrete grey wolf optimizer for symmetric travelling salesman problem. Appl. Soft Comput. 105, 107298 (2021)","journal-title":"Appl. Soft Comput."},{"issue":"3","key":"385_CR24","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1080\/10798587.2000.10642829","volume":"8","author":"G \u00dc\u00e7oluk","year":"2002","unstructured":"\u00dc\u00e7oluk, G.: Genetic algorithm solution of the tsp avoiding special crossover and mutation. Intell. Automat. Soft Comput. 8(3), 265\u2013272 (2002)","journal-title":"Intell. Automat. Soft Comput."},{"key":"385_CR25","unstructured":"Wang, K.-P., Huang, L., Zhou, C.-G., Pang, W.: Particle swarm optimization for traveling salesman problem. In: Proceedings of the 2003 international conference on machine learning and cybernetics (IEEE cat. no. 03ex693), vol. 3, pp. 1583\u20131585. IEEE (2003)"},{"key":"385_CR26","unstructured":"Pang, W., Wang, K.-p., Zhou, C.-g., Dong, L.-j.: Fuzzy discrete particle swarm optimization for solving traveling salesman problem. In: The fourth international conference on computer and information technology, 2004. CIT\u201904., pp. 796\u2013800. IEEE (2004)"},{"issue":"5","key":"385_CR27","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.ipl.2007.03.010","volume":"103","author":"XH Shi","year":"2007","unstructured":"Shi, X.H., Liang, Y.C., Lee, H.P., Lu, C., Wang, Q.X.: Particle swarm optimization-based algorithms for tsp and generalized tsp. Inf. Process. Lett. 103(5), 169\u2013176 (2007)","journal-title":"Inf. Process. Lett."},{"issue":"12","key":"385_CR28","doi-asserted-by":"publisher","first-page":"14439","DOI":"10.1016\/j.eswa.2011.04.163","volume":"38","author":"S-M Chen","year":"2011","unstructured":"Chen, S.-M., Chien, C.-Y.: Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst. Appl. 38(12), 14439\u201314450 (2011)","journal-title":"Expert Syst. Appl."},{"issue":"10","key":"385_CR29","doi-asserted-by":"publisher","first-page":"2245","DOI":"10.1002\/j.1538-7305.1965.tb04146.x","volume":"44","author":"S Lin","year":"1965","unstructured":"Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44(10), 2245\u20132269 (1965)","journal-title":"Bell Syst. Tech. J."},{"key":"385_CR30","doi-asserted-by":"crossref","unstructured":"Karaboga, D., Gorkemli, B.: A combinatorial artificial bee colony algorithm for traveling salesman problem. In: 2011 International symposium on innovations in intelligent systems and applications, pp. 50\u201353. IEEE (2011)","DOI":"10.1109\/INISTA.2011.5946125"},{"issue":"1 and 2","key":"385_CR31","first-page":"158","volume":"6","author":"KI Rufai","year":"2021","unstructured":"Rufai, K.I., Usman, O.L., Olusanya, O.O., Adedeji, O.B.: Solving travelling salesman problem using an improved ant colony optimization algorithm. Univ. Ibadan J. Sci. Logics ICT Res. 6(1 and 2), 158\u2013170 (2021)","journal-title":"Univ. Ibadan J. Sci. Logics ICT Res."},{"key":"385_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107439","volume":"107","author":"Y Wang","year":"2021","unstructured":"Wang, Y., Han, Z.: Ant colony optimization for traveling salesman problem based on parameters optimization. Appl. Soft Comput. 107, 107439 (2021)","journal-title":"Appl. Soft Comput."},{"key":"385_CR33","doi-asserted-by":"crossref","unstructured":"Yadav, N., Pachung, P., Agrawal, V., Bansal, J.C.: Blended selection in ant colony optimization for solving travelling salesman problem. In: 2022 IEEE World Conference on Applied Intelligence and Computing (AIC), pp. 782\u2013787. IEEE (2022)","DOI":"10.1109\/AIC55036.2022.9848836"},{"key":"385_CR34","unstructured":"Raveendran, A.: Evaluation of a spark-enabled genetic algorithm applied to the travelling salesman problem (2020)"},{"key":"385_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106497","volume":"95","author":"H-C Lu","year":"2020","unstructured":"Lu, H.-C., Hwang, F.J., Huang, Y.-H.: Parallel and distributed architecture of genetic algorithm on apache hadoop and spark. Appl. Soft Comput. 95, 106497 (2020)","journal-title":"Appl. Soft Comput."},{"key":"385_CR36","doi-asserted-by":"crossref","unstructured":"Alanzi, E., Bennaceur, H.: Hadoop mapreduce for parallel genetic algorithm to solve traveling salesman problem. Int. J. Adv. Comput. Sci. Appl., 10(8) (2019)","DOI":"10.14569\/IJACSA.2019.0100814"},{"key":"385_CR37","unstructured":"Adewole, P., Akinwale, A.T, Otunbanowo, K.: A genetic algorithm for solving travelling salesman problem. Int. J. Adv. Comput. Sci. Appl. (2011)"},{"issue":"3","key":"385_CR38","first-page":"183","volume":"3","author":"M Asim","year":"2014","unstructured":"Asim, M., Gopalia, R., Swar, S.: Traveling salesman problem using genetic algorithm. Int. J. Latest Trends Eng. Technol. 3(3), 183\u2013190 (2014)","journal-title":"Int. J. Latest Trends Eng. Technol."},{"issue":"4","key":"385_CR39","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1504\/IJCAT.2022.129382","volume":"69","author":"A Jarrah","year":"2022","unstructured":"Jarrah, A., Bataineh, A.S., Al Almomany, A.: The optimisation of travelling salesman problem based on parallel ant colony algorithm. Int. J. Comput. Appl. Technol. 69(4), 309\u2013321 (2022)","journal-title":"Int. J. Comput. Appl. Technol."},{"issue":"2","key":"385_CR40","first-page":"1","volume":"27","author":"Y Rhee","year":"2022","unstructured":"Rhee, Y.: Gpu-based parallel ant colony system for traveling salesman problem. J. Korea Soc. Comput. Inf. 27(2), 1\u20138 (2022)","journal-title":"J. Korea Soc. Comput. Inf."},{"key":"385_CR41","doi-asserted-by":"crossref","unstructured":"Peng, C.: Parallel genetic algorithm for travelling salesman problem. In: International conference on automation control, algorithm, and intelligent bionics (ACAIB 2022), vol. 12253, pp. 259\u2013267. SPIE (2022)","DOI":"10.1117\/12.2639457"},{"issue":"5","key":"385_CR42","doi-asserted-by":"publisher","first-page":"4760","DOI":"10.1007\/s11227-022-04813-9","volume":"79","author":"Z Wang","year":"2023","unstructured":"Wang, Z., Shen, Y., Li, S., Wang, S.: A fine-grained fast parallel genetic algorithm based on a ternary optical computer for solving traveling salesman problem. J. Supercomput. 79(5), 4760\u20134790 (2023)","journal-title":"J. Supercomput."},{"key":"385_CR43","doi-asserted-by":"crossref","unstructured":"Mohan, A., Remya, G.: A parallel implementation of ant colony optimization for tsp based on mapreduce framework. Int. J. Comput. Appl., 88(8) (2014)","DOI":"10.5120\/15371-3900"},{"issue":"5","key":"385_CR44","first-page":"404","volume":"1","author":"ZCSS Hlaing","year":"2011","unstructured":"Hlaing, Z.C.S.S., Khine, M.A.: Solving traveling salesman problem by using improved ant colony optimization algorithm. Int. J. Inf. Educ. Technol. 1(5), 404 (2011)","journal-title":"Int. J. Inf. Educ. Technol."},{"key":"385_CR45","doi-asserted-by":"publisher","first-page":"1669","DOI":"10.1007\/s00500-016-2432-3","volume":"22","author":"\u015e G\u00fclc\u00fc","year":"2018","unstructured":"G\u00fclc\u00fc, \u015e, Mahi, M., Baykan, \u00d6.K., Kodaz, H.: A parallel cooperative hybrid method based on ant colony optimization and 3-opt algorithm for solving traveling salesman problem. Soft Comput. 22, 1669\u20131685 (2018)","journal-title":"Soft Comput."},{"key":"385_CR46","unstructured":"Li, L., Cheng, Y., Tan, L., Niu, B.: A discrete artificial bee colony algorithm for tsp problem. In: Bio-inspired computing and applications: 7th international conference on intelligent computing, ICIC 2011, Zhengzhou, China, August 11\u201314. 2011, revised selected papers 7. Springer, pp. 566\u2013573 (2012)"},{"key":"385_CR47","unstructured":"Er, H.R., Erdogan, N.: Parallel genetic algorithm to solve traveling salesman problem on mapreduce framework using hadoop cluster (2014). arXiv preprint arXiv:1401.6267"},{"issue":"2","key":"385_CR48","first-page":"108","volume":"15","author":"RB Erkartal","year":"2022","unstructured":"Erkartal, R.B., \u00c7etin, \u00d6., Y\u0131lmaz, A.: Data collection from wireless sensor networks: Openmp application on the solution of traveling salesman problem with parallel genetic algorithm and ant colony algorithm. J. Aeronaut. Sp. Technol. 15(2), 108\u2013124 (2022)","journal-title":"J. Aeronaut. Sp. Technol."},{"key":"385_CR49","unstructured":"Campus, A.K., Sel\u00e7uklu, K.: Solution of travelling salesman problem using intelligent water drops algorithm"},{"issue":"3","key":"385_CR50","first-page":"228","volume":"24","author":"S Halder","year":"2023","unstructured":"Halder, S., Sharma, H.K., Biswas, A., Prentkovskis, O., Majumder, S., Ska\u010dkauskas, P.: On enhanced intelligent water drops algorithm for travelling salesman problem under uncertain paradigm. Transp. Telecommun. 24(3), 228\u2013255 (2023)","journal-title":"Transp. Telecommun."},{"key":"385_CR51","doi-asserted-by":"crossref","unstructured":"Rabanal, P., Rodr\u00edguez, I., Rubio, F.: Solving dynamic tsp by using river formation dynamics. In: 2008 Fourth International Conference on Natural Computation, vol.\u00a01, pp. 246\u2013250. IEEE (2008)","DOI":"10.1109\/ICNC.2008.760"},{"key":"385_CR52","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.jocs.2017.08.002","volume":"22","author":"P Rabanal","year":"2017","unstructured":"Rabanal, P., Rodr\u00edguez, I., Rubio, F.: Applications of river formation dynamics. J. Comput. Sci. 22, 26\u201335 (2017)","journal-title":"J. Comput. Sci."},{"issue":"4","key":"385_CR53","first-page":"326","volume":"8","author":"H Afaq","year":"2011","unstructured":"Afaq, H., Saini, S.: On the solutions to the travelling salesman problem using nature inspired computing techniques. Int. J. Comput. Sci. Issues (IJCSI) 8(4), 326 (2011)","journal-title":"Int. J. Comput. Sci. Issues (IJCSI)"},{"key":"385_CR54","doi-asserted-by":"publisher","first-page":"6185","DOI":"10.1109\/ACCESS.2022.3233786","volume":"11","author":"E Alhenawi","year":"2023","unstructured":"Alhenawi, E., Khurma, R.A., Sharieh, A.A., Al-Adwan, O., Shorman, A., Al Shannaq, F.: Parallel ant colony optimization algorithm for finding the shortest path for mountain climbing. IEEE Access 11, 6185\u20136196 (2023)","journal-title":"IEEE Access"},{"issue":"3","key":"385_CR55","doi-asserted-by":"publisher","first-page":"407","DOI":"10.3390\/a8030407","volume":"8","author":"L Wang","year":"2015","unstructured":"Wang, L., Wang, Y., Xie, Y.: Implementation of a parallel algorithm based on a spark cloud computing platform. Algorithms 8(3), 407\u2013414 (2015)","journal-title":"Algorithms"},{"key":"385_CR56","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.compstruc.2012.07.010","volume":"110\u2013111","author":"H Eskandar","year":"2012","unstructured":"Eskandar, H., Sadollah, A., Bahreininejad, A., Hamdi, M.: Water cycle algorithm\u2014a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput. Struct. 110\u2013111, 151\u2013166 (2012)","journal-title":"Comput. Struct."},{"key":"385_CR57","doi-asserted-by":"crossref","unstructured":"Hosseini, H.S.: Problem solving by intelligent water drops. In: 2007 IEEE congress on evolutionary computation, pp. 3226\u20133231. IEEE (2007)","DOI":"10.1109\/CEC.2007.4424885"},{"issue":"6","key":"385_CR58","first-page":"475","volume":"24","author":"F-C Yang","year":"2007","unstructured":"Yang, F.-C., Wang, Y.-P.: Water flow-like algorithm for object grouping problems. J. Chin. Inst. Industr. Eng. 24(6), 475\u2013488 (2007)","journal-title":"J. Chin. Inst. Industr. Eng."},{"issue":"6","key":"385_CR59","first-page":"627","volume":"13","author":"S Selvarani","year":"2016","unstructured":"Selvarani, S., Sadhasivam, G.: An intelligent water drop algorithm for optimizing task scheduling in grid environment. Int. Arab J. Inf. Technol 13(6), 627\u2013634 (2016)","journal-title":"Int. Arab J. Inf. Technol"},{"key":"385_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiolchem.2022.107809","volume":"103","author":"E Alhenawi","year":"2023","unstructured":"Alhenawi, E., Al-Sayyed, R., Hudaib, A., Mirjalili, S.: Improved intelligent water drop-based hybrid feature selection method for microarray data processing. Comput. Biol. Chem. 103, 107809 (2023)","journal-title":"Comput. Biol. Chem."},{"issue":"4","key":"385_CR61","first-page":"73","volume":"22","author":"E Alhenawi","year":"2022","unstructured":"Alhenawi, E., Alazzam, H., Al-Sayyed, R., AbuAlghanam, O., Adwan, O.: Hybrid feature selection method for intrusion detection systems based on an improved intelligent water drop algorithm. Cybernet. Inf. Technol. 22(4), 73\u201390 (2022)","journal-title":"Cybernet. Inf. Technol."}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-023-00385-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-023-00385-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-023-00385-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T16:06:21Z","timestamp":1704297981000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-023-00385-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,3]]},"references-count":61,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["385"],"URL":"https:\/\/doi.org\/10.1007\/s44196-023-00385-5","relation":{},"ISSN":["1875-6883"],"issn-type":[{"value":"1875-6883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,3]]},"assertion":[{"value":"7 June 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 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":"Authors have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}},{"value":"(1) This material is the authors\u2019 own original work, which has not been previously published elsewhere. (2) The paper is not currently being considered for publication elsewhere. (3) The paper reflects the authors\u2019 own research and analysis in a truthful and complete manner.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"4"}}