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Bare Bones Particle Swarm Optimization (BBPSO) is a powerful algorithm, which has shown potential to solving multimodal optimization problems. Unfortunately, BBPSO may also get stuck into local optima when optimizing functions with many local optima in high dimensional search space. In previous attempts an approach was developed which consists of a jump strategy combined with PSO in order to escape from local optima and promising results have been obtained. In this paper, we combine BBPSO with a jump strategy when no fitness improvement is observed. The jump strategy is implemented based on the Gaussian or the Cauchy probability distribution. The algorithm was tested on a suite of well-known benchmark multimodal functions and the results were compared with those obtained by the standard BBPSO algorithm and with BBPSO with re-initialization. Simulation results show that the BBPSO with the jump strategy performs well in all functions investigated. We also notice that the improved performance is due to a successful number of Gaussian or Cauchy jumps.