{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T21:08:43Z","timestamp":1777064923248,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T00:00:00Z","timestamp":1612915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R009953\/1"],"award-info":[{"award-number":["EP\/R009953\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a Two-Dimensional Quantum Genetic Algorithm (2D-QGA), which is a new variety of QGA. This variety will allow the user to take the advantages of quantum computation while solving the problems which are suitable for two-dimensional (2D) representation or can be represented in tabular form. The performance of 2D-QGA is compared to two-dimensional GA (2D-GA), which is used to solve two-dimensional problems as well. The comparison study is performed by applying both the algorithm to the task allocation problem. The performance of 2D-QGA is better than 2D-GA while comparing execution time, convergence iteration, minimum cost generated, and population size.<\/jats:p>","DOI":"10.3390\/s21041251","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T16:12:10Z","timestamp":1613146330000},"page":"1251","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Two-Dimensional Quantum Genetic Algorithm: Application to Task Allocation Problem"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1109-5730","authenticated-orcid":false,"given":"Sabyasachi","family":"Mondal","sequence":"first","affiliation":[{"name":"School of Aerospace, Transport and Manufacturing (SATM), Cranfield University, Cranfield MK430AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3966-7633","authenticated-orcid":false,"given":"Antonios","family":"Tsourdos","sequence":"additional","affiliation":[{"name":"School of Aerospace, Transport and Manufacturing (SATM), Cranfield University, Cranfield MK430AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,10]]},"reference":[{"key":"ref_1","unstructured":"Davis, L. (1991). Handbook of Genetic Algorithms, Van Nostrand Reinhold."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Filipi\u010d, B., and Juri\u010di\u0107, D. (1993). An interactive genetic algorithm for controller parameter optimization. Artificial Neural Nets and Genetic Algorithms, Springer.","DOI":"10.1007\/978-3-7091-7533-0_66"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TSMC.1986.289288","article-title":"Optimization of control parameters for genetic algorithms","volume":"16","author":"Grefenstette","year":"1986","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_5","unstructured":"Goldberg, D.E., and Holland, J.H. (1988). Genetic Algorithms and Machine Learning, Kluwer Academic Publishers."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/S0166-1280(02)00619-X","article-title":"Artificial neural networks and genetic algorithms in QSAR","volume":"622","author":"Niculescu","year":"2003","journal-title":"J. Mol. Struct. THEOCHEM"},{"key":"ref_7","unstructured":"Karr, C.L. (1991, January 13\u201316). Design of an adaptive fuzzy logic controller using genetic algorithm. Proceedings of the 4th International Conference on Genetic Algorithms, San Diego, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/S0165-0114(02)00441-4","article-title":"Hybrid identification in fuzzy-neural networks","volume":"138","author":"Oh","year":"2003","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s11804-006-0064-1","article-title":"Nuclear power plant fault diagnosis based on genetic-RBF neural network","volume":"5","author":"Shi","year":"2006","journal-title":"J. Mar. Sci. Appl."},{"key":"ref_10","first-page":"103","article-title":"Neural network with genetically evolved algorithms for stocks prediction","volume":"18","author":"Phua","year":"2001","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_11","unstructured":"Shor, P.W. (1994, January 20\u201322). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th IEEE Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Grover, L.K. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA.","DOI":"10.1145\/237814.237866"},{"key":"ref_13","unstructured":"Narayanan, A., and Moore, M. (1996, January 20\u201322). Quantum-inspired genetic algorithms. Proceedings of the IEEE International Conference on Evolutionary Computation, Nagoya, Japan."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Miao, H., Wang, H., and Deng, Z. (2009, January 11\u201314). Quantum genetic algorithm and its application in power system reactive power optimization. Proceedings of the 2009 IEEE International Conference on Computational Intelligence and Security, Beijing, China.","DOI":"10.1109\/CIS.2009.133"},{"key":"ref_15","first-page":"243","article-title":"Comparison of genetic algorithm and quantum genetic algorithm","volume":"9","author":"Laboudi","year":"2012","journal-title":"Int. Arab J. Inf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/TEVC.2007.905006","article-title":"Quantum genetic optimization","volume":"12","author":"Malossini","year":"2008","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_17","unstructured":"Han, K.H., and Kim, J.H. (2000, January 16\u201319). Genetic quantum algorithm and its application to combinatorial optimization problem. Proceedings of the 2000 IEEE Congress on Evolutionary Computation, La Jolla, CA, USA."},{"key":"ref_18","unstructured":"Draa, A., Talbi, H., and Batouche, M. (2005, January 26\u201327). A quantum inspired genetic algorithm for solving the N-queens problem. Proceedings of the 7th International Symposium on Programming and Systems, Barcelona, Spain."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, G., and Rong, H. (2007, January 27\u201330). Real-observation quantum-inspired evolutionary algorithm for a class of numerical optimization problems. Proceedings of the International Conference on Computational Science, Beijing, China.","DOI":"10.1007\/978-3-540-72590-9_151"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, H., Liu, J., Zhi, J., and Fu, C. (2013). The improvement of quantum genetic algorithm and its application on function optimization. Math. Probl. Eng., 2013.","DOI":"10.1155\/2013\/730749"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhu, K., Gu, C., Qiu, J., Liu, W., Fang, C., and Li, B. (2016). Determining the optimal placement of sensors on a concrete arch dam using a quantum genetic algorithm. J. Sens., 2016.","DOI":"10.1155\/2016\/2567305"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10539","DOI":"10.1007\/s11042-017-4592-2","article-title":"Adaptive top-hat filter based on quantum genetic algorithm for infrared small target detection","volume":"77","author":"Deng","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1007\/s11280-018-0594-x","article-title":"IQGA: A route selection method based on quantum genetic algorithm-toward urban traffic management under big data environment","volume":"22","author":"Tian","year":"2019","journal-title":"World Wide Web"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1108\/WJE-02-2019-0032","article-title":"Quantum genetic algorithm to evolve controllers for self-reconfigurable modular robots","volume":"17","author":"Mezghiche","year":"2020","journal-title":"World J. Eng."},{"key":"ref_25","first-page":"327","article-title":"A two-dimensional genetic algorithm for the Ising problem","volume":"5","author":"Anderson","year":"1991","journal-title":"Complex Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1007\/BF01215974","article-title":"Two-dimensional packing problems using genetic algorithms","volume":"14","author":"Jain","year":"1998","journal-title":"Eng. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tsai, M.W., Hong, T.P., and Lin, W.T. (2015). A two-dimensional genetic algorithm and its application to aircraft scheduling problem. Math. Probl. Eng., 2015.","DOI":"10.1155\/2015\/906305"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, Q., and Xie, J. (2016, January 6\u20138). A two-dimensional genetic algorithm for identifying overlapping communities in dynamic networks. Proceedings of the 2016 IEEE 28th International Conference on Tools with Artificial Intelligence (ICTAI), San Jose, CA, USA.","DOI":"10.1109\/ICTAI.2016.0092"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.neucom.2020.04.107","article-title":"Optimal Topology for Consensus using Genetic Algorithm","volume":"404","author":"Mondal","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Mondal, S., and Tsourdos, A. (2020). Autonomous Addition of Agents to an Existing Group Using Genetic Algorithm. Sensors, 20.","DOI":"10.3390\/s20236953"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1251\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:22:21Z","timestamp":1760160141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/4\/1251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,10]]},"references-count":30,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["s21041251"],"URL":"https:\/\/doi.org\/10.3390\/s21041251","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,10]]}}}