Over previous decades, many nature-inspired optimization algorithms (NIOAs) have been proposed and applied due to their importance and significance. Some survey studies have also been made to investigate NIOAs and their variants and applications. However, these comparative studies mainly focus on one single NIOA, and there lacks a comprehensive comparative and contrastive study of the existing NIOAs. To fill this gap, we spent a great effort to conduct this comprehensive survey. In this survey, more than 120 meta-heuristic algorithms have been collected and, among them, the most popular and common 11 NIOAs are selected. Their accuracy, stability, efficiency and parameter sensitivity are evaluated based on the 30 black-box optimization benchmarking (BBOB) functions. Furthermore, we apply the Friedman test and Nemenyi test to analyze the performance of the compared NIOAs. In this survey, we provide a unified formal description of the 11 NIOAs in order to compare their similarities and differences in depth and a systematic summarization of the challenging problems and research directions for the whole NIOAs field. This comparative study attempts to provide a broader perspective and meaningful enlightenment to understand NIOAs.

The chicken swarm optimization (CSO) algorithm is a new swarm intelligence optimization (SIO) algorithm and has been widely used in many engineering domains. However, there are two apparent problems with the CSO algorithm, i.e., slow convergence speed and difficult to achieve global optimal solutions. Aiming at attacking these two problems of CSO, in this paper, we propose an adaptive fuzzy chicken swarm optimization (FCSO) algorithm. The proposed FCSO uses the fuzzy system to adaptively adjust the number of chickens and random factors of the CSO algorithm and achieves an optimal balance of exploitation and exploration capabilities of the algorithm. We integrate the cosine function into the FCSO to compute the position update of roosters and improve the convergence speed. We compare the FCSO with eight commonly used, state-of-the-art SIO algorithms in terms of performance in both low- and high-dimensional spaces. We also verify the FCSO algorithm with the nonparametric statistical Friedman test. The results of the experiments on the 30 black-box optimization benchmarking (BBOB) functions demonstrate that our FCSO outperforms the other SIO algorithms in both convergence speed and optimization accuracy. In order to further test the applicability of the FCSO algorithm, we apply it to four typical engineering problems with constraints on the optimization processes. The results show that the FCSO achieves better optimization accuracy over the standard CSO algorithm.

We consider best arm identification in the multi-armed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization (Lai, 1987), the leading term in the Bayesian simple regret derives from the region where the gap between optimal and suboptimal arms is smaller than $\sqrt{\frac{\log T}{T}}$. We propose a simple and easy-to-compute algorithm with its leading term matching with the lower bound up to a constant factor; simulation results support our theoretical findings.