Imperialist competitive algorithm combined with chaos for global optimization. (English) Zbl 1241.90193
Summary: A novel chaotic improved imperialist competitive algorithm (CICA) is presented for global optimization. The ICA is a new meta-heuristic optimization developed based on a socio-politically motivated strategy and contains two main steps: the movement of the colonies and the imperialistic competition. Here different chaotic maps are utilized to improve the movement step of the algorithm. Seven different chaotic maps are investigated and the Logistic and Sinusoidal maps are found as the best choices. Comparing the new algorithm with the other ICA-based methods demonstrates the superiority of the CICA for the benchmark functions.
MSC:
| 90C59 | Approximation methods and heuristics in mathematical programming |
| 90C29 | Multi-objective and goal programming |
References:
| [1] | Kaveh, A.; Talatahari, S., Optimum design of skeletal structures using imperialist competitive algorithm, Comput Struct, 88, 1220-1229 (2010) |
| [2] | Atashpaz-Gargari, E.; Lucas, C., Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition, IEE Cong Evol Comput, 4661-4667 (2007) |
| [3] | Atashpaz-Gargari, E.; Hashemzadeh, F.; Rajabioun, R.; Lucas, C., Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process, Int J Intell Comput Cybernet, 3, 1, 337-355 (2008) · Zbl 1151.90586 |
| [4] | Kaveh, A.; Talatahari, S., Imperialist competitive algorithm for engineering design problems, Asian J Civil Eng, 11, 6, 675-697 (2010) · Zbl 1223.90082 |
| [5] | Ott, E.; Grebogi, C.; Yorke, J., Controlling chaos, Phys Rev Lett, 64, 11, 1196-1199 (1990) · Zbl 0964.37501 |
| [6] | Pecora, L.; Carroll, T., Synchronization in chaotic system, Phys Rev Lett, 64, 8, 821-824 (1990) · Zbl 0938.37019 |
| [7] | Yang, D.; Li, G.; Cheng, G., On the efficiency of chaos optimization algorithms for global optimization, Chaos Soliton Fract, 34, 1366-1375 (2007) |
| [8] | Alatas, B.; Akin, E.; Ozer, A., Chaos embedded particle swarm optimization algorithms, Chaos Soliton Fract, 40, 1715-1734 (2009) · Zbl 1198.90400 |
| [9] | Alatas, B., Chaotic harmony search algorithm, Appl Math Comput, 29, 4, 2687-2699 (2010) · Zbl 1193.65094 |
| [10] | Alatas, B., Chaotic bee colony algorithms for global numerical optimization, Expert Syst Appl, 37, 5682-5687 (2010) |
| [11] | Alatas, B., Uniform big bang-chaotic big crunch optimization, Commun Nonlinear Sci Numer Simul, 16, 9, 3696-3703 (2011) · Zbl 1222.65054 |
| [12] | Tavazoei, M. S.; Haeri, M., An optimization algorithm based on chaotic behavior and fractal nature, Comput Appl Math, 206, 1070-1081 (2007) · Zbl 1151.90555 |
| [13] | Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan; 1995.; Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan; 1995. |
| [14] | Dorigo, M.; Maniezzo, V.; Colorni, A., The ant system: optimization by a colony of cooperating agents, IEEE Trans Systems Man Cybernet B, 26, 1, 29-41 (1996) |
| [15] | Geem, Z. W.; Kim, J. H.; Loganathan, G. V., A new heuristic optimization algorithm; harmony search, Simulation, 76, 60-68 (2001) |
| [16] | Kaveh, A.; Talatahari, S., A novel heuristic optimization method: Charged system search, Acta Mech, 213, 3-4, 267-289 (2010) · Zbl 1397.65094 |
| [17] | He, Y.; Zhou, J.; Xiang, X.; Chen, H.; Qin, H., Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling, Chaos Solitons Fract, 42, 3169-3176 (2009) · Zbl 1198.90184 |
| [18] | Coelho, L.; Mariani, V., Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization, Expert Syst Appl, 34, 1905-1913 (2008) |
| [19] | Ott, E., Chaos in dynamical systems (2002), Cambridge University Press: Cambridge University Press Cambridge UK · Zbl 1006.37001 |
| [20] | May, R. M., Simple mathematical models with very complicated dynamics, Nature, 261, 459-474 (1976) · Zbl 1369.37088 |
| [21] | He, D.; He, C.; Jiang, L.; Zhu, L.; Hu, G., Chaotic characteristic of a one-dimensional iterative map with infinite collapses, IEEE Trans Circuits Syst, 48, 7, 900-906 (2001) · Zbl 0993.37033 |
| [22] | Zheng, W. M., Kneading plane of the circle map, Chaos Soliton Fract, 1221-1233 (1994) · Zbl 0817.58030 |
| [23] | Bucolo, M.; Caponetto, R.; Fortuna, L.; Frasca, M.; Rizzo, A., Does chaos work better than noise?, IEEE Circuits Syst Mag, 2, 3, 4-19 (2002) |
| [24] | Yang J. A chaos algorithm based on progressive optimality and Tabu search algorithm. In: Proceedings of the fourth conference on machine learning and cybernetics; 2005. p. 2977-81.; Yang J. A chaos algorithm based on progressive optimality and Tabu search algorithm. In: Proceedings of the fourth conference on machine learning and cybernetics; 2005. p. 2977-81. |
| [25] | Xu, H.; Zhu, H.; Zhang, T.; Wang, Z., Application of mutation scale chaos algorithm in power plant and units economics dispatch, J Harbin Inst Tech, 32, 4, 55-58 (2000) |
| [26] | Xu, L.; Zhou, S.; Zhang, H., A hybrid chaos optimization method and its application, System Eng Electron, 25, 2, 226-228 (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
