Time series clustering is a challenging problem due to the large-volume, high-dimensional, and warping characteristics of time series data. Traditional clustering methods often use a single criterion or distance measure, which may not capture all the features of the data. This paper proposes a novel method for time series clustering based on evolutionary multi-tasking optimization, termed i-MFEA, which uses an improved multifactorial evolutionary algorithm to optimize multiple clustering tasks simultaneously, each with a different validity index or distance measure. Therefore, i-MFEA can produce diverse and robust clustering solutions that satisfy various preferences of decision-makers. Experiments on two artificial datasets show that i-MFEA outperforms single-objective evolutionary algorithms and traditional clustering methods in terms of convergence speed and clustering quality. The paper also discusses how i-MFEA can address two long-standing issues in time series clustering: the choice of appropriate similarity measure and the number of clusters.