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
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