In this paper, we proposed the Levy flights to replace the random numbers whether it was in Gauss distribution or uniform distribution in the standard slime mould algorithm (SMA). Three kinds of classical benchmark functions such as the unimodal, multimodal benchmark functions and those who have basins which we could see clearly from their three dimensional profiles. Comparisons were made through the average results over 100 Monte Carlo simulation experiments in order to eliminate the influence of randomness. Results showed that the improved SMA with Levy flight might not always perform better. The improved SMA replacing the uniform distributed parameter achieved better performance whereas the improved SMA replacing the Gauss distributed parameter gained nothing in performance, even worse sometimes than the standard SMA.

In this paper, we hybridize the grey wolf optimization (GWO) algorithm with the newly proposed slime mould algorithm (SMA). Comparisons had been made and three kinds of benchmark functions were introduced to verify the capability. 100 Monte Carlo simulation experiments had been carried on to reduce the influence of randomness as less as possible. Results showed that the performance of hybrid GWO-SMA would base on the given characteristics of problems themselves because of the random threshold parameter p and the multiple branches in the updating equation. The hybridization of the GWO and SMA might be not recommended for steady applications and engineering problems.