New evaluation criteria for the convergence of continuous evolutionary algorithms

The first hitting time (FHT) plays an important role in convergence evaluation for evolutionary algorithms. However, the current criteria of the FHT are mostly under a hypothesis that never has been testified: the FHT subjects to the normal distribution. Aiming at more convincible evaluations, this paper investigates the distribution of the FHT through a goodness-of-fit test and discovers an unexpected result. Based on this result, this paper proposes a new set of criteria, which utilizes two types of relative frequency histograms. This paper validates the proposed criteria on the optimization problem of benchmark functions by the standard genetic algorithm (SGA) and the particle swarm optimization (PSO). The experiments show that the proposed criteria are effective to evaluate the convergent speed and the convergent stability of the evolutionary algorithms.