Purpose-The aim of this paper is to reduce the evaluations number of the fine model within the output space mapping (OSM) technique in order to reduce their computing time. Design/methodology/approach-In this paper, n-level OSM is proposed and expected to be even faster than the conventional OSM. The proposed algorithm takes advantages of the availability of n models of the device to optimize, each of them representing an optimal trade-off between the model error and its computation time. Models with intermediate characteristics between the coarse and fine models are inserted within the proposed algorithm to reduce the number of evaluations of the consuming time model and then the computing time. The advantages of the algorithm are highlighted on the optimization problem of superconducting magnetic energy storage (SMES). Findings-A major computing time gain equals to three is achieved using the n-level OSM algorithm instead of the conventional OSM technique on the optimization problem of SMES. Originality/value-The originality of this paper is to investigate several models with different granularities within OSM algorithm in order to reduce its computing time without decreasing the performance of the conventional strategy.