Directional crossover slime mould algorithm with adaptive Lévy diversity for the optimal design of real-world problems

Abstract

The slime mould algorithm (SMA) has become a classical algorithm applied in many fields since it was presented. Nevertheless, when faced with complex tasks, the algorithm converges slowly and tends to fall into the local optimum. So, there is still room for improvement in the performance of SMA. This work proposes a novel SMA variant (SDSMA), combining the adaptive Lévy diversity mechanism and directional crossover mechanism. Firstly, the adaptive Lévy diversity mechanism can improve population diversity. Then, the directional crossover mechanism can enhance the balance of exploration and exploitation, thus helping SDSMA to increase the convergence speed and accuracy. SDSMA is compared with SMA variants, original algorithms, improved algorithms, improved-SMAs, and others on the benchmark function set to verify its performance. Meanwhile, the Wilcoxon signed-rank test, the Friedman test, and other analytical methods are considered to analyze the experimental results. The analysis results show that SDSMA with two strategies significantly improves the performance of SMA. Meanwhile, the computational cost of SDSMA is smaller than that of SMA on benchmark function. Finally, the proposed algorithm is applied to three real-world engineering design problems. The experiments prove that SDSMA is an effective aid tool for computationally complex practical tasks.