Parameter optimization of support vector regression (SVR) plays a challenging role in improving the generalization ability of machine learning. Fruit fly optimization algorithm (FFOA) is a recently developed swarm optimization algorithm for complicated multi-objective optimization problems and is also suitable for optimizing SVR parameters. In this work, parameter optimization in SVR using FFOA is investigated. In view of problems of premature and local optimum in FFOA, an improved FFOA algorithm based on self-adaptive step update strategy (SSFFOA) is presented to obtain the optimal SVR model. Moreover, the proposed method is utilized to characterize magnetorheological elastomer (MRE) base isolator, a typical hysteresis device. In this application, the obtained displacement, velocity and current level are used as SVR inputs while the output is the shear force response of the device. Experimental testing of the isolator with two types of excitations is applied for model performance evaluation. The results demonstrate that the proposed SSFFOA-optimized SVR (SSFFOA_SVR) has perfect generalization ability and more accurate prediction accuracy than other machine learning models, and it is a suitable and effective method to predict the dynamic behaviour of MRE isolator. Keywords Support vector regression, fruit fly optimization algorithm, self-adaptive step, magnetorheological elastomer base isolator, dynamic response prediction Recently, the swarm intelligence optimization algorithms were proposed to tackle optimization problems, which were also applied to optimize the SVR parameters, such as particle swarm optimization (PSO), ant colony optimization (ACO), bee colony algorithm (BCA), firefly algorithm (FA) and artificial fish swarm algorithm (AFSA). In [14], Li et al. put forward a hybrid self-adaptive learning approach based on SVR