Document Type : Original Research Paper

**Author**

Department of Computer Engineering, Safashahr Branch, Islamic Azad University, Safashahr, Iran

**Abstract**

Meta-heuristic algorithms inspired by the natural processes are part of the optimization algorithms that they have been considered in recent years, such as genetic algorithm, particle swarm optimization, ant colony optimization, Firefly algorithm. Recently, a new kind of evolutionary algorithm has been proposed that it is inspired by the human sociopolitical evolution process. This new algorithm has been called Imperialist Competitive Algorithm (ICA). The ICA is a population-based algorithm where the populations are represented by countries that are classified as colonies or imperialists. This paper is going to present a modified ICA with considerable accuracy, referred to here as ICA2. The ICA2 is tested with six well-known benchmark functions. Results show high accuracy and avoidance of local optimum traps to reach the minimum global optimal.

Three important policies are in the ICA, and assimilation policy is the most important of them. This research focuses on an assimilation policy in the ICA to propose a meta-heuristic optimization algorithm for optimizing function with high accuracy and avoiding to trap in local optima rather than using original ICA by a new assimilation strategy.

**Keywords**

**Main Subjects**

[2] Holland, J. H. (1975). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press.

[3] Kennedy, J., & Eberhart, R. (1995, November). Particle swarm optimization. In Proceedings of IEEE international conference on neural networks (Vol. 4, No. 2, pp. 1942-1948).

[4] Dorigo, M., & Gambardella, L. M. (1997). Ant colony system: a cooperative learning approach to the traveling salesman problem. Evolutionary Computation, IEEE Transactions on, 1(1), 53-66.

[5] Storn, R., & Price, K. (1995). Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley: ICSI.

[6] Webster, B., & Bernhard, P. J. (2003). A local search optimization algorithm based on natural principles of gravitation. http://hdl.handle.net/11141/117

[7] Yang, X. S. (2009). Firefly algorithms for multimodal optimization. In Stochastic algorithms: foundations and applications (pp. 169-178). Springer Berlin Heidelberg. doi : 10.1007/978-3-642-04944-6_14

[8] Atashpaz-Gargari, E., & Lucas, C. (2007, September). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In Evolutionary Computation, 2007. CEC 2007. IEEE Congress on (pp. 4661-4667). IEEE. doi : 10.1109/CEC.2007.4425083

[9] Kaveh, A. (2014). Advances in Metaheuristic Algorithms for Optimal Design of Structures.(page 349-355, ch 11) Springer International Pu. doi: 10.1007/978-3-319-05549-7

[10] Esmaeilzadeh, M. (2013). A modified colonial competitive algorithm for optimizing convex functions. International Journal of Intelligent Computing and Cybernetics, 6(4), 370-385. doi : 10.1108/IJICC-02-2013-0006

[11] Atashpaz-Gargari, E., Hashemzadeh, F., & Lucas, C. (2008, June). Designing MIMO PID controller using colonial competitive algorithm: applied to distillation column process. In Evolutionary Computation, 2008. CEC 2008.(IEEE World Congress on Computational Intelligence). IEEE Congress on (pp. 1929-1934). IEEE. doi: 10.1109/CEC.2008.4631052

[12] Nemati, K., Shamsuddin, S. M., & Darus, M. (2014). An optimization technique based on imperialist competition algorithm to measurement of error for solving initial and boundary value problems. Measurement, 48, 96-108. doi: 10.1016/j.measurement.2013.10.043

[13] Zarandi, M. H., Zarinbal, M., Ghanbari, N., & Turksen, I. B. (2013). A new fuzzy functions model tuned by hybridizing imperialist competitive algorithm and simulated annealing. Application: Stock price prediction. Information Sciences, 222, 213-228. doi: 10.1016/j.ins.2012.08.002

[14] Niknam, T., Taherian Fard, E., Pourjafarian, N., & Rousta, A. (2011). An efficient hybrid algorithm based on modified imperialist competitive algorithm and K-means for data clustering. Engineering Applications of Artificial Intelligence, 24(2), 306-317. doi : 10.1016/j.engappai.2010.10.001

[15] Kayvanfar, V., & Zandieh, M. (2012). The economic lot scheduling problem with deteriorating items and shortage: an imperialist competitive algorithm. The International Journal of Advanced Manufacturing Technology, 62(5-8), 759-773. doi: 10.1007/s00170-011-3820-6

[16] Karimi, N., Zandieh, M., & Najafi, A. A. (2011). Group scheduling in flexible flow shops: a hybridised approach of imperialist competitive algorithm and electromagnetic-like mechanism. International Journal of Production Research, 49(16), 4965-4977. doi : 10.1080/00207543.2010.481644

[17] Mohammadi-ivatloo, B., Rabiee, A., Soroudi, A., & Ehsan, M. (2012). Imperialist competitive algorithm for solving non-convex dynamic economic power dispatch. Energy, 44(1), 228-240. doi : 10.1016/j.energy.2012.06.034

[18] Ahmadi, M. A., Ebadi, M., Shokrollahi, A., & Majidi, S. M. J. (2013). Evolving artificial neural network and imperialist competitive algorithm for prediction oil flow rate of the reservoir. Applied Soft Computing, 13(2), 1085-1098. doi: 10.1016/j.asoc.2012.10.009

[19] Meysam Mousavi, S., Tavakkoli-Moghaddam, R., Vahdani, B., Hashemi, H., & Sanjari, M. J. (2013). A new support vector model-based imperialist competitive algorithm for time estimation in new product development projects. Robotics and Computer-Integrated Manufacturing, 29(1), 157-168. doi : 10.1016/j.rcim.2012.04.006

[20] Coelho, L. D. S., Afonso, L. D., & Alotto, P. (2012). A modified imperialist competitive algorithm for optimization in electromagnetics. Magnetics, IEEE Transactions on, 48(2), 579-582. doi: 10.1109/TMAG.2011.2172400

[21] Lucas, C., Nasiri-Gheidari, Z., & Tootoonchian, F. (2010). Application of an imperialist competitive algorithm to the design of a linear induction motor. Energy Conversion and Management, 51(7), 1407-1411. doi: 10.1016/j.enconman.2010.01.014

[22] Liu, J. Y. C., Su, C., & Chiu, C. T. (2013, July). On the Convergence of Imperialist Competitive Algorithm. In Modelling Symposium (AMS), 2013 7th Asia (pp. 16-20). IEEE. doi: 10.1109/AMS.2013.9

[23] Xing, B., & Gao, W. J. (2014). Imperialist Competitive Algorithm. In Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms (pp. 203-209). Springer International Publishing. doi: 10.1007/978-3-319-03404-1_15

[24] Afonso, L. D., Mariani, V. C., & Dos Santos Coelho, L. (2013). Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization. Expert Systems with Applications, 40(9), 3794-3802. doi: 10.1016/j.eswa.2012.12.093

[25]Naimi Sadigh, A., Mozafari, M., & Karimi, B. (2012). Manufacturer–retailer supply chain coordination: A bi-level programming approach. Advances in Engineering Software, 45(1), 144-152. doi: 10.1016/j.advengsoft.2011.09.008

[26] Duan, H., Xu, C., Liu, S., & Shao, S. (2010). Template matching using chaotic imperialist competitive algorithm. Pattern recognition letters, 31(13), 1868-1875. doi: 10.1016/j.patrec.2009.12.005

[27] Behnamian, J., & Zandieh, M. (2011). A discrete colonial competitive algorithm for hybrid flowshop scheduling to minimize earliness and quadratic tardiness penalties. Expert Systems with Applications, 38(12), 14490-14498. doi: 10.1016/j.eswa.2011.04.241

[28]Ramezani, F., Lotfi, S., & Soltani-Sarvestani, M. A. (2012). A hybrid evolutionary imperialist competitive algorithm (HEICA). In Intelligent Information and Database Systems (pp. 359-368). Springer Berlin Heidelberg. doi: 10.1007/978-3-642-28487-8_37

[29] Lepagnot, J., Idoumghar, L., & Fodorean, D. (2013, October). Hybrid Imperialist Competitive Algorithm with Simplex Approach: Application to Electric Motor Design. In Systems, Man, and Cybernetics (SMC), 2013 IEEE International Conference on (pp. 2454-2459). IEEE. doi: 10.1109/SMC.2013.419

[30] Goldansaz, S. M., Jolai, F., & Zahedi Anaraki, A. H. (2013). A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop. Applied Mathematical Modelling, 37(23), 9603-9616. doi: 10.1016/j.apm.2013.05.002

[31] Jula, A., Othman, Z., & Sundararajan, E. (2013, April). A hybrid imperialist competitive-gravitational attraction search algorithm to optimize cloud service composition. In Memetic Computing (MC), 2013 IEEE Workshop on (pp. 37-43). IEEE. doi : 10.1109/MC.2013.6608205

[32] Yao, X., Liu, Y., & Lin, G. (1999). Evolutionary programming made faster. Evolutionary Computation, IEEE Transactions on, 3(2), 82-102.

[33] Kundu, R., Das, S., Mukherjee, R., & Debchoudhury, S. (2014). An improved particle swarm optimizer with difference mean based perturbation. Neurocomputing, 129, 315-333. doi : 10.1016/j.neucom.2013.09.026

[34] Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics bulletin, 80-83.

[35] Zhang, J., & Sanderson, A. C. (2009). JADE: adaptive differential evolution with optional external archive. Evolutionary Computation, IEEE Transactions on, 13(5), 945-958. doi: 10.1109/TEVC.2009.2014613

[36] Gao, W., & Liu, S. (2011). Improved artificial bee colony algorithm for global optimization. Information Processing Letters, 111(17), 871-882. doi: 10.1016/j.ipl.2011.06.002

[37] Kaveh, A., & Talatahari, S. (2010). Optimum design of skeletal structures using imperialist competitive algorithm. Computers & structures, 88(21), 1220-1229.

[38] Xu, J., He, H., & Man, H. (2012). DCPE co-training for classification. Neurocomputing, 86, 75-85.

[39] Xu, J., & Man, H. (2011). Dictionary learning based on laplacian score in sparse coding. In Machine Learning and Data Mining in Pattern Recognition (pp. 253-264). Springer Berlin Heidelberg.