We propose an acceleration method for the fireworks algorithms which uses a convergence point for the population estimated from moving vectors between parent individuals and their sparks. To improve the accuracy of the estimated convergence point, we propose a new type of firework, the synthetic firework, to obtain the correct of the local/global optimum in its local area’s fitness landscape. The synthetic firework is calculated by the weighting moving vectors between a firework and each of its sparks. Then, they are used to estimate a convergence point which may replace the worst firework individual in the next generation. We design a controlled experiment for evaluating the proposed strategy and apply it to 20 CEC2013 benchmark functions of 2-dimensions (2-D), 10-D and 30-D with 30 trial runs each. The experimental results and the Wilcoxon signed-rank test confirm that the proposed method can significantly improve the performance of the canonical firework algorithm.