A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization

The theory of evolutionary computation for discrete search spaces has made significant progress since the early 2010s. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models of runtime analysis of evolutionary algorithms, highlights recent theoretical insights on parameter tuning and parameter control, and summarizes the latest advances for stochastic and dynamic problems. We regard how evolutionary algorithms optimize submodular functions, and we give an overview over the large body of recent results on estimation of distribution algorithms. Finally, we present the state of the art of drift analysis, one of the most powerful analysis technique developed in this field.

One-Pot Synthesis of Ni0.05Ce0.95O2−δ Catalysts with Nanocubes and Nanorods Morphology for CO2 Methanation Reaction and in Operando DRIFT Analysis of Intermediate Species

The valorization of CO2 via renewable energy sources allows one to obtain carbon-neutral fuels through its hydrogenation, like methane. In this study, Ni0.05Ce0.95O2−δ catalysts were prepared using a simple one-pot hydrothermal method yielding nanorod and nanocube particles to be used for the methanation reaction. Samples were characterized by XRD, BET, TEM, H2-TPR, and H2-TPD experiments. The catalytic activity tests revealed that the best performing catalyst was Ni0.05Ce0.95O2−δ, with nanorod morphology, which gave a CO2 conversion of 40% with a selectivity of CH4 as high as 93%, operating at 325 °C and a GHSV of 240,000 cm3 h−1 g−1. However, the lower activation energy was found for Ni0.05Ce0.95O2−δ catalysts with nanocube morphology. Furthermore, an in operando diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) analysis was performed flowing CO2:H2 or CO:H2 mixture, showing that the main reaction pathway, for the CO2 methanation, is the direct hydrogenation of formate intermediate.

Tail bounds on hitting times of randomized search heuristics using variable drift analysis

Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing, etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, for example the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. On all these problems, the probability of deviating by an r-factor in lower-order terms of the expected time decreases exponentially with r. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Finally, user-friendly specializations of the general drift theorem are given.