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

The dependence of the IR-radio correlation on the metallicity

We have compiled a sample of 26 metal-poor galaxies with 12 + log(O/H) < 8.1 with both infrared continuum and 1.4 GHz radio continuum data. By comparing to galaxies at higher metallicity, we have investigated the dependence on the metallicity of the IR-radio relationship at 24 um, 70 um, 100 um and 160 um bands as well as the integrated FIR luminosity. It is found that metal-poor galaxies have on average lower qIR than metal-rich ones with larger offsets at longer IR wavelengths, from -0.06 dex in q24um to -0.6 dex in q160um. The qIR of all galaxies as a whole at 160 um show positive trends with the metallicity and IR-to-FUV ratio, and negative trends with the IR color, while those at lower IR wavelengths show weaker correlations. We proposed a mechanism that invokes combined effects of low obscured-SFR/total-SFR fraction and warm dust temperature at low metallicity to interpret the above behavior of qIR, with the former reducing the IR radiation and the latter further reducing the IR emission at longer IR wavelength. Other mechanisms that are related to the radio emission including the enhanced magnetic field strength and increased thermal radio contribution are unable to reconcile the IR-wavelength-dependent differences of qIR between metal-poor and metal- rich galaxies. In contrast to qIR, the mean total-SFR/radio ratio of metal-poor galaxies is the same as the metal-rich one, indicating the 1.4 GHz radio emission is still an effective tracer of SFRs at low metallicity.Comment: 25 pages, 11 figures, 4 tables. ApJ in pres