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To improve Bat Algorithm's global converging capability and speed, this paper presents a novel time-varying-Morlet-Wavelet-Mutation-based Bat Algorithm (TVMWMBA). It first builds a Morlet wavelet distribution function to describe the probability density of the wavelet mutation factor distribution. Afterwards, it takes advantage of the waving property and periodicity of Morlet wavelet to carry out wavelet mutation on each member of the bat population in each iteration to avoid localized optimization. Finally, it uses time-varying coefficient to dynamically contract the mutation space of the wavelet mutation factor to improve the algorithm's converging speed and converging precision. Simulated experiment for function optimization shows that the improved algorithm has effectively maintained the diversity of the population and significantly raised the optimization stability. It has also achieved strong global converging capability, excellent optimum-searching precision, and fast converging speed.