A new approach to estimating the expected first hitting time of evolutionary algorithms

AbstractEvolutionary algorithms (EA) have been shown to be very effective in solving practical problems, yet many important theoretical issues of them are not clear. The expected first hitting time is one of the most important theoretical issues of evolutionary algorithms, since it implies the average computational time complexity. In this paper, we establish a bridge between the expected first hitting time and another important theoretical issue, i.e., convergence rate. Through this bridge, we propose a new general approach to estimating the expected first hitting time. Using this approach, we analyze EAs with different configurations, including three mutation operators, with/without population, a recombination operator and a time variant mutation operator, on a hard problem. The results show that the proposed approach is helpful for analyzing a broad range of evolutionary algorithms. Moreover, we give an explanation of what makes a problem hard to EAs, and based on the recognition, we prove the hardness of a general problem

An improved method to test the Distance--Duality relation

Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ