Multi-objective optimization (MOO) is a class of optimization problems where several objective functions must be simultaneously optimized. Traditional search methods are difficult to extend to MOO problems so many of these problems are solved using bio-inspired optimization algorithms. One of the famous optimization algorithms that have been applied to MOO is the nondominated sorting genetic algorithm II (NSGA-II). NSGA-II algorithm has been successfully used to solve MOO problems owing to its lower computational complexity compared with the other optimization algorithms. In this paper we use NSGA-II to solve a MOO problem of time series data mining. The problem in question is determining the optimal weights of a multi-metric distance that is used to perform several data mining tasks. NSGA-II is particularly appropriate to optimize data mining problems where fitness functions evaluation usually involves intensive computing resources. Whereas several previous papers have proposed different methods to optimize time series data mining problems, this paper is, to our knowledge, the first paper to optimize several time series data mining tasks simultaneously. The experiments we conducted show that the performance of the optimized combination of multi-metric distances we propose in executing time series data mining tasks is superior to that of the distance metrics that constitute the combination when they are applied separately.