Abstract
In order to overcome the poor exploitation of the krill herd (KH) algorithm, a hybrid differential evolution KH (DEKH) method has been developed for function optimization. The improvement involves adding a new hybrid differential evolution (HDE) operator into the krill, updating process for the purpose of dealing with optimization problems more efficiently. The introduced HDE operator inspires the intensification and lets the krill perform local search within the defined region. DEKH is validated by 26 functions. From the results, the proposed methods are able to find more accurate solution than the KH and other methods. In addition, the robustness of the DEKH algorithm and the influence of the initial population size on convergence and performance are investigated by a series of experiments.






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Lévano M, Nowak H (2011) New aspects of the elastic net algorithm for cluster analysis. Neural Comput Appl 20(6):835–850. doi:10.1007/s00521-010-0498-x
Talatahari S, Kheirollahi M, Farahmandpour C, Gandomi A (2012) A multi-stage particle swarm for optimum design of truss structures. Neural Comput Appl. doi:10.1007/s00521-012-1072-5
Wang G, Guo L, Duan H, Liu L, Wang H (2012) Path planning for UCAV using bat algorithm with mutation. Sci World J 2012:1–15. doi:10.1100/2012/418946
Li X, Yin M (2013) An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure. Adv Eng Softw 55:10–31. doi:10.1016/j.advengsoft.2012.09.003
Zou D, Gao L, Li S, Wu J (2011) Solving 0-1 knapsack problem by a novel global harmony search algorithm. Appl Soft Comput 11(2):1556–1564. doi:10.1016/j.asoc.2010.07.019
Zou D, Liu H, Gao L, Li S (2011) An improved differential evolution algorithm for the task assignment problem. Eng Appl Artif Intell 24(4):616–624. doi:10.1016/j.engappai.2010.12.002
Yang XS, Gandomi AH, Talatahari S, Alavi AH (2013) Metaheuristics in water. Geotechnical and Transport Engineering, Elsevier
Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Metaheuristic applications in structures and infrastructures. Elsevier, Waltham
Goldberg DE (1998) Genetic algorithms in search. Optimization and machine learning. Addison-Wesley, New York
Zhao M, Ren J, Ji L, Fu C, Li J, Zhou M (2012) Parameter selection of support vector machines and genetic algorithm based on change area search. Neural Comput Appl 21(1):1–8. doi:10.1007/s00521-011-0603-9
Loghmanian S, Jamaluddin H, Ahmad R, Yusof R, Khalid M (2012) Structure optimization of neural network for dynamic system modeling using multi-objective genetic algorithm. Neural Comput Appl 21(6):1281–1295. doi:10.1007/s00521-011-0560-3
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359
Gandomi AH, Yang X-S, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200. doi:10.1016/j.camwa.2011.11.010
Khazraee S, Jahanmiri A, Ghorayshi S (2011) Model reduction and optimization of reactive batch distillation based on the adaptive neuro-fuzzy inference system and differential evolution. Neural Comput Appl 20(2):239–248. doi:10.1007/s00521-010-0364-x
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. doi:10.1177/003754970107600201
Wang H, Yuan X, Wang Y, Yang Y (2013) Harmony search algorithm-based fuzzy-PID controller for electronic throttle valve. Neural Comput Appl 22(2):329–336. doi:10.1007/s00521-011-0678-3
Gholizadeh S, Barzegar A (2013) Shape optimization of structures for frequency constraints by sequential harmony search algorithm. Eng Optim 45(6):627–646. doi:10.1080/0305215x.2012.704028
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471. doi:10.1007/s10898-007-9149-x
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Paper presented at the proceeding of the IEEE international conference on neural networks, Perth, Australia, 27 Nov–1 Dec
Chen D, Zhao C, Zhang H (2011) An improved cooperative particle swarm optimization and its application. Neural Comput Appl 20(2):171–182. doi:10.1007/s00521-010-0503-4
Gandomi AH, Yun GJ, Yang XS, Talatahari S (2013) Chaos-enhanced accelerated particle swarm algorithm. Commun Nonlinear Sci Numer Simul 18(2):327–340. doi:10.1016/j.cnsns.2012.07.017
Back T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, Oxford
Beyer H (2001) The theory of evolution strategies. Springer, New York
Dorigo M, Stutzle T (2004) Ant colony optimization. MIT Press, Cambridge
Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using Firefly Algorithm. Comput Struct 89(23–24):2325–2336. doi:10.1016/j.compstruc.2011.08.002
Cai X, Fan S, Tan Y (2012) Light responsive curve selection for photosynthesis operator of APOA. Int J Bio-Inspired Comput 4(6):373–379
Xie L, Zeng J, Formato RA (2012) Selection strategies for gravitational constant G in artificial physics optimisation based on analysis of convergence properties. Int J Bio-Inspired Comput 4(6):380–391
Simon D (2008) Biogeography-based optimization. IEEE T Evol Comput 12(6):702–713. doi:10.1109/TEVC.2008.919004
Gandomi AH, Alavi AH (2011) Multi-stage genetic programming: a new strategy to nonlinear system modeling. Inf Sci 181(23):5227–5239. doi:10.1016/j.ins.2011.07.026
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceeding of World congress on nature & biologically inspired computing (NaBIC 2009), Coimbatore, India, Dec 2009. IEEE Publications, USA, pp 210–214
Gandomi AH, Talatahari S, Yang XS, Deb S (2012) Design optimization of truss structures using cuckoo search algorithm. Struct Des Tall Spec. doi:10.1002/tal.1033
Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35. doi:10.1007/s00366-011-0241-y
Li X, Zhang J, Yin M (2013) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 1–11. doi:10.1007/s00521-013-1433-8
Shumeet B (1994) Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Carnegie Mellon University, Pittsburgh
Erol OK, Eksin I (2006) A new optimization method: Big Bang-Big Crunch. Adv Eng Softw 37(2):106–111. doi:10.1016/j.advengsoft.2005.04.005
Kaveh A, Talatahari S (2009) Size optimization of space trusses using Big Bang-Big Crunch algorithm. Comput Struct 87(17–18):1129–1140. doi:10.1016/j.compstruc.2009.04.011
Kaveh A, Talatahari S (2010) Optimal design of Schwedler and ribbed domes via hybrid Big Bang-Big Crunch algorithm. J Constr Steel Res 66(3):412–419. doi:10.1016/j.jcsr.2009.10.013
Kaveh A, Talatahari S (2010) A discrete big bang-big crunch algorithm for optimal design of skeletal structures. Asian J Civil Eng 11(1):103–122
Gandomi AH, Yang X-S, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255. doi:10.1007/s00521-012-1028-9
Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483. doi:10.1108/02644401211235834
Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4):267–289. doi:10.1007/s00707-009-0270-4
Gandomi AH, Alavi AH (2012) Krill Herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simulat 17(12):4831–4845. doi:10.1016/j.cnsns.2012.05.010
El-Abd M (2011) A hybrid ABC-SPSO algorithm for continuous function optimization. In: Swarm intelligence (SIS), 2011 IEEE symposium on, Paris, 11–15 Apr 2011. IEEE, pp 1–6. doi:10.1109/SIS.2011.5952576
Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math 2013:21. doi:10.1155/2013/696491
Duan H, Zhao W, Wang G, Feng X (2012) Test-sheet composition using analytic hierarchy process and hybrid metaheuristic algorithm TS/BBO. Math Probl Eng 2012:1–22. doi:10.1155/2012/712752
Gao X, Wang X, Jokinen T, Ovaska S, Arkkio A, Zenger K (2012) A hybrid PBIL-based harmony search method. Neural Comput Appl 21(5):1071–1083. doi:10.1007/s00521-011-0675-6
Geem ZW (2009) Particle-swarm harmony search for water network design. Eng Optim 41(4):297–311. doi:10.1080/03052150802449227
Gong W, Cai Z, Ling C (2010) DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput 15(4):645–665. doi:10.1007/s00500-010-0591-1
Kuo RJ, Syu YJ, Chen Z-Y, Tien FC (2012) Integration of particle swarm optimization and genetic algorithm for dynamic clustering. Inf Sci 195:124–140. doi:10.1016/j.ins.2012.01.021
Sun Y, Zhang L, Gu X (2012) A hybrid co-evolutionary cultural algorithm based on particle swarm optimization for solving global optimization problems. Neurocomputing 98:76–89. doi:10.1016/j.neucom.2011.08.043
Sheikhan M, Mohammadi N (2012) Neural-based electricity load forecasting using hybrid of GA and ACO for feature selection. Neural Comput Appl 21(8):1961–1970. doi:10.1007/s00521-011-0599-1
Marichelvam M (2012) An improved hybrid Cuckoo Search (IHCS) metaheuristics algorithm for permutation flow shop scheduling problems. Int J Bio-Inspired Comput 4(4):200–205. doi:10.1504/IJBIC.2012.048061
Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2013) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl. doi:10.1007/s00521-012-1304-8
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE T Evol Comput 3(2):82–102
Yang X-S, Cui Z, Xiao R, Gandomi AH, Karamanoglu M (2013) Swarm intelligence and bio-inspired computation. Elsevier, Waltham
Arslan M, Çunkaş M, Sağ T (2012) Determination of induction motor parameters with differential evolution algorithm. Neural Comput Appl 21(8):1995–2004. doi:10.1007/s00521-011-0612-8
Li X, Yin M (2012) Application of differential evolution algorithm on self-potential data. PLoS ONE 7(12):e51199. doi:10.1371/journal.pone.0051199
Jia L, Cheng D, Chiu M-S (2012) Pareto-optimal solutions based multi-objective particle swarm optimization control for batch processes. Neural Comput Appl 21(6):1107–1116. doi:10.1007/s00521-011-0659-6
Zhang Y, Huang D, Ji M, Xie F (2011) Image segmentation using PSO and PCM with Mahalanobis distance. Expert Syst Appl 38(7):9036–9040. doi:10.1016/j.eswa.2011.01.041
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Wang, GG., Gandomi, A.H., Alavi, A.H. et al. Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput & Applic 25, 297–308 (2014). https://doi.org/10.1007/s00521-013-1485-9
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DOI: https://doi.org/10.1007/s00521-013-1485-9