Dynamic search in fireworks algorithm

We propose an improved version of the recently developed Enhanced Fireworks Algorithm (EFWA) based on an adaptive dynamic local search mechanism. In EFWA, the explosion amplitude (i.e., search area around the current location) of each firework is computed based on the quality of the firework's current location. This explosion amplitude is limited by a lower bound which decreases with the number of iterations in order to avoid the explosion amplitude to be [close to] zero, and in order to enhance global search abilities at the beginning and local search abilities towards the later phase of the algorithm. As the explosion amplitude in EFWA depends solely on the fireworks' fitness and the current number of iterations, this procedure does not allow for an adaptive optimization process. To deal with these limitations, we propose the Dynamic Search Fireworks Algorithm (dynFWA) which uses a dynamic explosion amplitude for the firework at the currently best position. If the fitness of the best firework could be improved, the explosion amplitude will increase in order to speed up convergence. On the contrary, if the current position of the best firework could not be improved, the explosion amplitude will decrease in order to narrow the search area. In addition, we show that one of the EFWA operators can be removed in dynFWA without a loss in accuracy - this makes dynFWA computationally more efficient than EFWA. Experiments on 28 benchmark functions indicate that dynFWA is able to significantly outperform EFWA, and achieves better performance than the latest SPSO version SPSO2011.