Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space. 1. Introduction Nowadays, since the evolutionary algorithm can solve some problem that the traditional optimization algorithm cannot do easy, the evolutionary algorithms are widely applied in different fields, such as the management science, engineering optimization, scientific computing. More and more modern metaheuristic algorithms inspired by nature or social phenomenon are emerging and they become increasingly popular, for example, particles swarms optimization (PSO) [1], firefly algorithm (FA) [2, 3], artificial chemical reaction optimization algorithm (ACROA) [4], glowworm swarms optimization (GSO) [5], invasive weed optimization (IWO) [6], differential evolution (DE) [7–9], bat algorithm (BA) [2, 10], and so on [11–15]. Some researchers have proposed their hybrid versions by combining two or more algorithms. Bat Algorithm (BA) is a novel metaheuristic optimization algorithm based on the echolocation behaviour of microbats, which was proposed by Yang in 2010 [2, 10]. This algorithm gradually aroused people’s close attention, and which is increasingly applied to different areas. Tsai et al. (2011) proposed an improved EBA to solve numerical optimization problems [16]. A multiobjective bat algorithm (MOBA) is proposed by Yang (2011) [17], which is first validated against a subset of test functions, and then applied to solve multiobjective design problems such as welded beam design. In 2012, Bora et al. applied BA to solve the Brushless DC Wheel Motor Problem [18]. Although the basic BA has remarkable property compared against several traditional optimization methods, the phenomenon of slow convergence rate and low accuracy still exists. Therefore, in this paper, we put forward an improved bat algorithm based on differential operator and Lévy
J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks (ICNN '95), vol. 4, pp. 1942–1948, December 1995.
X.-S. Yang, “Firefly algorithms for multimodal optimization,” in Proceedings of the 5th International Conference on Stochastic Algorithms: Foundations and Applications (SAGA '09), pp. 169–178, 2009.
B. Alatas, “ACROA: artificial chemical reaction optimization algorithm for global optimization,” Expert Systems with Applications, vol. 38, no. 10, pp. 13170–13180, 2011.
K. N. Krishnanand and D. Ghose, “Glowworm warm optimization for searching higher dimensional spaces,” Studies in Computational Intelligence, vol. 248, pp. 61–75, 2009.
A. R. Mehrabian and C. Lucas, “A novel numerical optimization algorithm inspired from weed colonization,” Ecological Informatics, vol. 1, no. 4, pp. 355–366, 2006.
R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
A. Mucherino and O. Seref, “Monkey search: a novel metaheuristic search for global optimization,” in Proceedings of the Conference on Data Mining, Systems Analysis, and Optimization in Biomedicine, vol. 953, pp. 162–173, March 2007.
K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control,” IEEE Control Systems Magazine, vol. 22, no. 3, pp. 52–67, 2002.
G. R. Reynolds, “Cultural algorithms: theory and application,” in New Iders in Optimization, D. Corne, M. Dorigo, and F. Glover, Eds., pp. 367–378, McGraw-Hill, New York, NY, USA, 1999.
R. Oftadeh, M. J. Mahjoob, and M. Shariatpanahi, “A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search,” Computers and Mathematics with Applications, vol. 60, no. 7, pp. 2087–2098, 2010.
P. W. Tsai, J. S. Pan, B. Y. Liao, M. J. Tsai, and V. Istanda, “Bat algorithm inspired algorithm for solving numerical optimization problems,” Applied Mechanics and Materials, vol. 148-149, pp. 134–137, 2011.
T. C. Bora, L. S. Coelho, and L. Lebensztajn, “Bat-Inspired optimization approach for the brushless DC wheel motor problem,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 947–950, 2012.
V. A. Chechkin, R. Metzler, J. Klafter, and V. Y. Gonchar, “Introduction to the theory of Lévy flights,” in Anomalous Transport: Foundations and Applications, pp. 129–162, Wiley-VCH, Cambridge, UK, 2008.
A. M. Reynolds and M. A. Frye, “Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search,” PLoS ONE, vol. 2, no. 4, p. e354, 2007.
N. Mercadier, W. Guerin, M. Chevrollier, and R. Kaiser, “Lévy flights of photons in hot atomic vapours,” Nature Physics, vol. 5, no. 8, pp. 602–605, 2009.
C. Grosan and A. Abraham, “A new approach for solving nonlinear equations systems,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 38, no. 3, pp. 698–714, 2008.