Nature-inspired optimization algorithms are widely used in various mathematical and engineering problems because of their usability and applicability. However, these optimization algorithms show different performances depending on the characteristics of the problem applied. There have been various effort to solve this problem by developing a new algorithm, applying other heuristics, changing parameters, etc. The deep learning-based self-adaptive harmony search (DLSaHS) developed in this study is another effort to tackle the problem by controlling the probability of heuristics by using recurrent neural network (RNN) and the parameter called checkpoint (CP). DLSaHS contains the heuristics obtained from harmony search (HS), genetic algorithm (GA), particle swarm optimization (PSO), and copycat harmony search (CcHS). DLSaHS was applied to the ten mathematical benchmark problems obtained from IEEE CEC 2021. The performance of DLSaHS is compared to the HS which showed better performance. Also, the optimal CP value obtained when applied to low-dimensional problems and the probability of heuristics according to the CP were derived to efficiently apply the DLSaHS, and it is confirmed that the error and standard deviation of the result, and computation time can be considerably reduced by applying them to high-dimensional problems.