The flexure-based mechanism is a promising realization of fast tool servo (FTS), and the optimum determination of flexure hinge parameters is one of the most important elements in the FTS design. This paper presents a multi-objective optimization approach to optimizing the dimension and position parameters of the flexure-based mechanism, which is based on the improved differential evolution algorithm embedding chaos and nonlinear simulated anneal algorithm. The results of optimum design show that the proposed algorithm has excellent performance and a well-balanced compromise is made between two conflicting objectives, the stroke and natural frequency of the FTS mechanism. The validation tests based on finite element analysis (FEA) show good agreement with the results obtained by using the proposed theoretical algorithm of this paper. Finally, a series of experimental tests are conducted to validate the design process and assess the performance of the FTS mechanism. The designed FTS reaches up to a stroke of 10.25 ${mu}m$ with at least 2 kHz bandwidth. Both of the FEA and experimental results demonstrate that the parameters of the flexure-based mechanism determined by the proposed approaches can achieve the specified performance and the proposed approach is suitable for the optimum design of FTS mechanism and of excellent performances.