{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:33Z","timestamp":1760243253965,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2014,12,12]],"date-time":"2014-12-12T00:00:00Z","timestamp":1418342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61272283","61304082","61305083"],"award-info":[{"award-number":["61272283","61304082","61305083"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we propose a novel definition of opposite path. Its core feature is that the sequence of candidate paths and the distances between adjacent nodes in the tour are considered simultaneously. In a sense, the candidate path and its corresponding opposite path have the same (or similar at least) distance to the optimal path in the current population. Based on an accepted framework for employing opposition-based learning, Oppositional Biogeography-Based Optimization using the Current Optimum, called COOBBO algorithm, is introduced to solve traveling salesman problems. We demonstrate its performance on eight benchmark problems and compare it with other optimization algorithms. Simulation results illustrate that the excellent performance of our proposed algorithm is attributed to the distinct definition of opposite path. In addition, its great strength lies in exploitation for enhancing the solution accuracy, not exploration for improving the population diversity. Finally, by comparing different version of COOBBO, another conclusion is that each successful opposition-based soft computing algorithm needs to adjust and remain a good balance between backward adjacent node and forward adjacent node.<\/jats:p>","DOI":"10.3390\/a7040663","type":"journal-article","created":{"date-parts":[[2014,12,12]],"date-time":"2014-12-12T10:06:43Z","timestamp":1418378803000},"page":"663-684","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["COOBBO: A Novel Opposition-Based Soft Computing Algorithm for TSP Problems"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8212-1073","authenticated-orcid":false,"given":"Qingzheng","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Information Service, Xi'an Communications Institute, No. 8, Zhangba East Road, Xi'an 710106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lemeng","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Information Service, Xi'an Communications Institute, No. 8, Zhangba East Road, Xi'an 710106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Basic Courses, Xi'an Communications Institute, No. 8, Zhangba East Road,  Xi'an 710106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjian","family":"He","sequence":"additional","affiliation":[{"name":"Department of Information Service, Xi'an Communications Institute, No. 8, Zhangba East Road, Xi'an 710106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Tizhoosh, H.R., and Ventresca, M. (2008). Studies in Computational Intelligence: Oppositional Concepts in Computational Intelligence, Springer-Verlag.","DOI":"10.1007\/978-3-540-70829-2"},{"key":"ref_2","unstructured":"Tizhoosh, H.R. (2005, January 28\u201330). Opposition-based learning: A new scheme for machine intelligence. Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation, and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, Vienna, Austria."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rahnamayan, S., Tizhoosh, H.R., and Salama, M.M.A. (2007, January 25\u201328). Quasi-oppositional differential evolution. Proceedings of IEEE Congress on Evolutionary Computation, Singapore.","DOI":"10.1109\/CEC.2007.4424748"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ergezer, M., Simon, D., and Du, D.W. (2009, January 11\u201314). Oppositional biogeography-based optimization. Proceedings of IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, USA.","DOI":"10.1109\/ICSMC.2009.5346043"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rahnamayan, S., and Wang, G.G. (2009, January 18\u201321). Center-based sampling for population-based algorithms. Proceedings of IEEE Congress on Evolutionary Computation, Trondheim, Norway.","DOI":"10.1109\/CEC.2009.4983045"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, H., Wu, Z.J., Liu, Y., Wang, J., Jiang, D.Z., and Chen, L.L. (2009, January 12\u201314). Space transformation search: A new evolutionary technique. Proceedings of ACM\/SIGEVO Summit on Genetic and Evolutionary Computation, Shanghai, China.","DOI":"10.1145\/1543834.1543907"},{"key":"ref_7","first-page":"308","article-title":"Opposition-based differential evolution using the current optimum for function optimization","volume":"29","author":"Xu","year":"2011","journal-title":"J. Appl. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.asoc.2007.07.010","article-title":"Opposition versus randomness in soft computing techniques","volume":"8","author":"Rahnamayan","year":"2008","journal-title":"Appl. Soft Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2828","DOI":"10.1016\/j.asoc.2012.03.034","article-title":"An intuitive distance-based explanation of opposition-based sampling","volume":"12","author":"Rahnamayan","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.asoc.2014.10.038","article-title":"Opposition versus randomness in binary spaces","volume":"27","author":"Seif","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Rahnamayan, S., Tizhoosh, H.R., and Salama, M.M.A. (2006, January 16\u201321). Oposition-based differential evolution algorithms. Proceedings of IEEE Congress on Evolutionary Computation, Vancouver, Canada.","DOI":"10.1109\/CEC.2007.4424748"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/TEVC.2007.894200","article-title":"Opposition-based differential evolution","volume":"12","author":"Rahnamayan","year":"2008","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Han, L., and He, X.S. (2007, January 24\u201327). A novel opposition-based particle swarm optimization for noisy problems. Proceedings of International Conference on Natural Computation, Haikou, China.","DOI":"10.1109\/ICNC.2007.119"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Omran, M.G.H., and Al-Sharhan, S. (2008, January 21\u201323). Using opposition-based learning to improve the performance of particle swarm optimization. Proceedings of IEEE Swarm Intelligence Symposium, St. Louis, MO, USA.","DOI":"10.1109\/SIS.2008.4668288"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10898-012-9913-4","article-title":"A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization","volume":"55","author":"Kaucic","year":"2013","journal-title":"J. Glob. Optim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4097","DOI":"10.1016\/j.asoc.2011.01.045","article-title":"Knowledge of opposite actions for reinforcement learning","volume":"11","author":"Shokri","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ergezer, M., and Sikder, I. (2011, January 22\u201324). Survey of oppositional algorithms. Proceedings of International Conference on Computer and Information Technology, Dhaka, Bangladesh.","DOI":"10.1109\/ICCITechn.2011.6164863"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ventresca, M., and Tizhoosh, H.R. (2006, January 16\u201321). Improving the convergence of backpropagation by opposite transfer functions. Proceedings of International Joint Conference on Neural Networks, Vancouver, Canada.","DOI":"10.1109\/IJCNN.2006.247153"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ventresca, M., and Tizhoosh, H.R. (2009, January 14\u201319). Improving gradient-based learning algorithms for large scale feedforward networks. Proceedings of International Joint Conference on Neural Networks, Atlanta, USA.","DOI":"10.1109\/IJCNN.2009.5178798"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gao, X.Z., Wang, X., and Ovaska, S.J. (2010, January 11\u201313). A hybrid harmony search method based on OBL. Proceedings of IEEE International Conference on Computational Science and Engineering, Hong Kong, China.","DOI":"10.1109\/CSE.2010.26"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Qin, A.K., and Forbes, F. (2011, January 12\u201316). Dynamic regional harmony search with opposition and local learning. Proceedings of 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Ireland.","DOI":"10.1145\/2001858.2001890"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Malisia, A.R., and Tizhoosh, H.R. (2007, January 1\u20135). Applying opposition-based ideas to the ant colony system. Proceedings of IEEE Swarm Intelligence Symposium, Honolulu, USA.","DOI":"10.1109\/SIS.2007.368044"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Banerjee, S., and Tizhoosh, H.R. (2010, January 18\u201323). Visualization of hidden structures in corporate failure prediction using opposite pheromone per node model. Proceedings of IEEE Congress on Evolutionary Computation, Barcelona, Spain.","DOI":"10.1109\/CEC.2010.5586399"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"El-Abd, M. (2011, January 12\u201316). Opposition-based artificial bee colony algorithm. Proceedings of 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Ireland.","DOI":"10.1145\/2001576.2001592"},{"key":"ref_25","first-page":"56","article-title":"Opposition-based artificial bee colony with dynamic cauchy mutation for function optimization","volume":"4","author":"Yang","year":"2012","journal-title":"Int. J. Adv. Comput. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engappai.2013.12.004","article-title":"A review of opposition-based learning from 2005 to 2012","volume":"29","author":"Xu","year":"2014","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4038","DOI":"10.1016\/j.ins.2008.07.005","article-title":"A diversity maintaining population-based incremental learning algorithm","volume":"178","author":"Ventresca","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ergezer, M., and Simon, D. (2011, January 5\u20138). Oppositional biogeography-based optimization for combinatorial problems. Proceedings of IEEE Congress on Evolutionary Computation, New Orleans.","DOI":"10.1109\/CEC.2011.5949792"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xu, Q.Z., Guo, L.M., Wang, N., Pan, J., and Wang, L. (2014, January 19\u201321). A novel oppositional biogeography-based optimization for combinatorial problems. Proceedings of International Conference on Natural Computation, Xiamen, China.","DOI":"10.1109\/ICNC.2014.6975871"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/TEVC.2008.919004","article-title":"Biogeography-based optimization","volume":"12","author":"Simon","year":"2008","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_31","unstructured":"Wikipedia Website, Travelling Salesman Problem. Available online:http:\/\/en.wikipedia.org\/wiki\/Travelling_salesman_problem."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Igelnik, B., and Zurada, J.M. (2013). Efficiency and Scalability Methods for Computational Intellect, IGI Global.","DOI":"10.4018\/978-1-4666-3942-3"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1287\/ijoc.3.4.376","article-title":"TSPLIB\u2014A traveling salesman problem library","volume":"3","author":"Reinelt","year":"1991","journal-title":"ORSA J. Comput."},{"key":"ref_34","first-page":"1582","article-title":"Modified opposition-based differential evolution for function optimization","volume":"7","author":"Xu","year":"2011","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_35","unstructured":"Maekawa, K., Mori, N., Kita, H., and Nishikawa, H. (1996, January 20\u201322). A genetic solution for the traveling salesman problem by means of a thermodynamical selection rule. Proceedings of IEEE International Conference on Evolutionary Computation, Nagoya, Japan."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1145\/2480741.2480752","article-title":"Exploration and exploitation in evolutionary algorithms: A survey","volume":"45","author":"Crepinsek","year":"2013","journal-title":"ACM Comput. 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