Analysis of Noisy Evolutionary Optimization When Sampling Fails

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Previous studies on sampling are mainly empirical. In this paper, we first investigate the effect of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the noisy LeadingOnes problem, we show that as the sample size increases, the running time can reduce from exponential to polynomial, but then return to exponential. This suggests that a proper sample size is crucial in practice. Then, we investigate what strategies can work when sampling with any fixed sample size fails. By two illustrative examples, we prove that using parent or offspring populations can be better. Finally, we construct an artificial noisy example to show that when using neither sampling nor populations is effective, adaptive sampling (i.e., sampling with an adaptive sample size) can work. This, for the first time, provides a theoretical support for the use of adaptive sampling

Exploring the deviation of cosmological constant by a generalized pressure dark energy model

We bring forward a generalized pressure dark energy (GPDE) model to explore the evolution of the universe. This model has covered three common pressure parameterization types and can be reconstructed as quintessence and phantom scalar fields, respectively. We adopt the cosmic chronometer (CC) datasets to constrain the parameters. The results show that the inferred late-universe parameters of the GPDE model are (within $1\sigma$): The present value of Hubble constant $H_{0}=(72.30^{+1.26}_{-1.37})$km s$^{-1}$ Mpc$^{-1}$; Matter density parameter $\Omega_{\text{m0}}=0.302^{+0.046}_{-0.047}$, and the universe bias towards quintessence. While when we combine CC data and the $H_0$ data from Planck, the constraint implies that our model matches the $\Lambda$CDM model nicely. Then we perform dynamic analysis on the GPDE model and find that there is an attractor or a saddle point in the system corresponding to the different values of parameters. Finally, we discuss the ultimate fate of the universe under the phantom scenario in the GPDE model. It is demonstrated that three cases of pseudo rip, little rip, and big rip are all possible.Comment: 11 pages, 5 figures, 5 table

Is Cosmological Constant Needed in Higgs Inflation?

The detection of B-mode shows a very powerful constraint to theoretical inflation models through the measurement of the tensor-to-scalar ratio $r$. Higgs boson is the most likely candidate of the inflaton field. But usually, Higgs inflation models predict a small value of $r$, which is not quite consistent with the recent results from BICEP2. In this paper, we explored whether a cosmological constant energy component is needed to improve the situation. And we found the answer is yes. For the so-called Higgs chaotic inflation model with a quadratic potential, it predicts $r\approx 0.2$, $n_s\approx0.96$ with e-folds number $N\approx 56$, which is large enough to overcome the problems such as the horizon problem in the Big Bang cosmology. The required energy scale of the cosmological constant is roughly $\Lambda \sim (10^{14} \text{GeV})^2$, which means a mechanism is still needed to solve the fine-tuning problem in the later time evolution of the universe, e.g. by introducing some dark energy component.Comment: 4 pages, 2 figure