{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T18:28:39Z","timestamp":1775413719005,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2012,10,15]],"date-time":"2012-10-15T00:00:00Z","timestamp":1350259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Imperialist Competitive Algorithm (ICA) is a new population-based evolutionary algorithm. It divides its population of solutions into several sub-populations, and then searches for the optimal solution through two operations: assimilation and competition. The assimilation operation moves each non-best solution (called colony) in a sub-population toward the best solution (called imperialist) in the same sub-population. The competition operation removes a colony from the weakest sub-population and adds it to another sub-population. Previous work on ICA focuses mostly on improving the assimilation operation or replacing the assimilation operation with more powerful meta-heuristics, but none focuses on the improvement of the competition operation. Since the competition operation simply moves a colony (i.e., an inferior solution) from one sub-population to another sub-population, it incurs weak interaction among these sub-populations. This work proposes Interaction Enhanced ICA that strengthens the interaction among the imperialists of all sub-populations. The performance of Interaction Enhanced ICA is validated on a set of benchmark functions for global optimization. The results indicate that the performance of Interaction Enhanced ICA is superior to that of ICA and its existing variants.<\/jats:p>","DOI":"10.3390\/a5040433","type":"journal-article","created":{"date-parts":[[2012,10,16]],"date-time":"2012-10-16T03:33:50Z","timestamp":1350358430000},"page":"433-448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Interaction Enhanced Imperialist Competitive Algorithms"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6844-1182","authenticated-orcid":false,"given":"Jun-Lin","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chungli, Taoyuan 32003, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu-Hsiang","family":"Tsai","sequence":"additional","affiliation":[{"name":"Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chungli, Taoyuan 32003, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun-Ying","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chungli, Taoyuan 32003, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng-Shiou","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chungli, Taoyuan 32003, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems, MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.3390\/e13061152","article-title":"Ea\/g-ga for single machine scheduling problems with earliness\/tardiness costs","volume":"13","author":"Chen","year":"2011","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm\u2014Explosion, stability, and convergence in a multidimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1023\/A:1022452626305","article-title":"An electromagnetism-like mechanism for global optimization","volume":"25","author":"Birbil","year":"2003","journal-title":"J. Global Optim."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1016\/j.asoc.2010.08.024","article-title":"Recent advances in artificial immune systems: Models and applications","volume":"11","author":"Dasgupta","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2741","DOI":"10.1016\/j.cam.2012.01.013","article-title":"A global best artificial bee colony algorithm for global optimization","volume":"236","author":"Gao","year":"2012","journal-title":"J. Comput. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"841","DOI":"10.3390\/e13040841","article-title":"Optimal multi-level thresholding based on maximum tsallis entropy via an artificial bee colony approach","volume":"13","author":"Zhang","year":"2011","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Global Optim."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Atashpaz-Gargari, E., and Lucas, C. (2007, January 25\u201328). Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. Proceedings of IEEE Congress on Evolutionary Computation, Singapore.","DOI":"10.1109\/CEC.2007.4425083"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"14490","DOI":"10.1016\/j.eswa.2011.04.241","article-title":"A discrete colonial competitive algorithm for hybrid flowshop scheduling to minimize earliness and quadratic tardiness penalties","volume":"38","author":"Behnamian","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s00170-010-2676-5","article-title":"An imperialist competitive algorithm to schedule of receiving and shipping trucks in cross-docking systems","volume":"51","author":"Forouharfard","year":"2010","journal-title":"Int. J. Adv. Manuf. Tech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4965","DOI":"10.1080\/00207543.2010.481644","article-title":"Group scheduling in flexible flow shops: A hybridised approach of imperialist competitive algorithm and electromagnetic-like mechanism","volume":"49","author":"Karimi","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3087","DOI":"10.1080\/00207540903536155","article-title":"A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem","volume":"49","author":"Shokrollahpour","year":"2011","journal-title":"Int. J. Prod. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lian, K., Zhang, C., Gao, L., and Shao, X. (2012). A modified colonial competitive algorithm for the mixed-model u-line balancing and sequencing problem. Int. J. Prod. Res.","DOI":"10.1080\/00207543.2011.653453"},{"key":"ref_16","first-page":"41","article-title":"Application of imperialist competitive algorithm for feature selection: A case study on bulk rice classification","volume":"40","author":"MousaviRad","year":"2012","journal-title":"Int. J. Comput. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"137","DOI":"10.7763\/IJCTE.2012.V4.438","article-title":"Application of imperialist competitive algorithm for automated classification of remote sensing images","volume":"4","author":"Karami","year":"2012","journal-title":"Int. J. Comput. Theory Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s00170-010-2937-3","article-title":"Balancing of stochastic u-type assembly lines: An imperialist competitive algorithm","volume":"54","author":"Bagher","year":"2011","journal-title":"Int. J. Adv. Manuf. Tech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1109\/TMAG.2011.2172400","article-title":"A modified imperialist competitive algorithm for optimization in electromagnetics","volume":"48","author":"Coelho","year":"2012","journal-title":"IEEE Trans. Magn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1016\/j.compstruc.2010.06.011","article-title":"Optimum design of skeletal structures using imperialist competitive algorithm","volume":"88","author":"Kaveh","year":"2010","journal-title":"Comput.Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2048","DOI":"10.1587\/elex.8.2048","article-title":"Deployment of the meta heuristic colonial competitive algorithm in synthesis of unequally spaced linear antenna array","volume":"8","author":"Kazemi","year":"2011","journal-title":"IEICE Electron. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1016\/j.enconman.2010.01.014","article-title":"Application of an imperialist competitive algorithm to the design of a linear induction motor","volume":"51","author":"Lucas","year":"2010","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7615","DOI":"10.1016\/j.eswa.2010.04.081","article-title":"Solving the integrated product mix-outsourcing problem using the imperialist competitive algorithm","volume":"37","author":"Eivazy","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_24","first-page":"136","article-title":"Solving the graph bisection problem with imperialist competitive algorithm","volume":"34","author":"Soltanpoor","year":"2012","journal-title":"Int. Conf. Sys. Eng. Model."},{"key":"ref_25","first-page":"293","article-title":"The use of imperialist competitive algorithm for the optimization of heat transfer in an air cooler equipped with butterfly inserts","volume":"6","author":"Rezaei","year":"2012","journal-title":"Aust. J. Basic Appl. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lin, J.-L., Yu, C.-Y., and Tsai, Y.-H. (2012). PSO-based imperialist competitive algorithm. J. Phys. Conf. Ser., in press.","DOI":"10.3390\/a5040433"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/3-540-48873-1_45","article-title":"Analysis on the island model parallel genetic algorithms for the genetic drifts","volume":"1585","author":"Niwa","year":"1999","journal-title":"Simul. Evolut. Learn."},{"key":"ref_28","unstructured":"Atashpaz-Gargari, E. Imperialist competitive algorithm (ICA). Available online:http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/22046-imperialist-competitive-algorithm-ica."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1016\/j.patrec.2009.12.005","article-title":"Template matching using chaotic imperialist competitive algorithm","volume":"31","author":"Duan","year":"2010","journal-title":"Pattern Recogn. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.1016\/j.eswa.2009.11.055","article-title":"Synergy of evolutionary algorithm and socio-political process for global optimization","volume":"37","author":"Jain","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_31","unstructured":"Arabnia, H.R., de la Fuente, D., Kozerenko, E.B., Olivas, J.A., Chang, R., LaMonica, P.M., Liuzzi, R.A., and Solo, A.M.G. IC-AI, CSREA Press. 12\u201315 July 2010."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1016\/j.cnsns.2011.08.021","article-title":"Imperialist competitive algorithm combined with chaos for global optimization","volume":"17","author":"Talatahari","year":"2012","journal-title":"Commun. Nonlinear Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Bahrami, H., Faez, K., and Abdechiri, M. (2010, January 24\u201326). Imperialist competitive algorithm using chaos theory for optimization (cica). Proceedings of the 2010 12th International Conference on Computer Modelling and Simulation (UKSim), Cambridge, UK. IEEE Computer Society Conference Publishing Service.","DOI":"10.1109\/UKSIM.2010.26"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Wang, Y., and Peng, C. (2009, January 25\u201327). Improved imperialist competitive algorithm for constrained optimization. Proceedings of the International Forum on Computer Science-Technology and Applications, 2009, Chongqing, China.","DOI":"10.1109\/IFCSTA.2009.57"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Lin, J.-L., Cho, C.-W., and Chuan, H.-C. (2012). Imperialist competitive algorithms with perturbed moves for global optimization. Appl. Mech. Mater., in press.","DOI":"10.4028\/www.scientific.net\/AMM.284-287.3135"},{"key":"ref_36","first-page":"54","article-title":"A novel memetic algorithm with imperialist competition as local search","volume":"30","author":"Nozarian","year":"2012","journal-title":"IPCSIT"},{"key":"ref_37","first-page":"49","article-title":"Imperialist competitive algorithm with adaptive colonies movement","volume":"2","author":"Bahrami","year":"2012","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_38","first-page":"1","article-title":"Differential evolution using opposite point for global numerical optimization","volume":"4","author":"Ao","year":"2012","journal-title":"J. Intell. Learn. Syst. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Worasucheep, C. (2008, January 1\u20136). A particle swarm optimization with stagnation detection and dispersion. Proceedings of IEEE World Congress on Computational Intelligence, Hong Kong, China.","DOI":"10.1109\/CEC.2008.4630832"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/5\/4\/433\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:52:48Z","timestamp":1760219568000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/5\/4\/433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,15]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,12]]}},"alternative-id":["a5040433"],"URL":"https:\/\/doi.org\/10.3390\/a5040433","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,15]]}}}