An improved whale optimization algorithm for locating critical slip surface of slopes

Locating a critical slip surface or calculating the minimum safety factor of a slope is important in geotechnical engineering, and also involves a complex optimization problem. A novel mathematical model considering linear and nonlinear failure criteria is developed to locate the critical slip surface. And an improved whale optimization algorithm (IWOA), which employs a nonlinear adjustment parameter and Gaussian perturbation operator in whale optimization algorithm (WOA), is proposed to examine this model. The parameter of IWOA is determined by numerical experiments. The performance of IWOA, WOA, salp swarm algorithm (SSA), and cuckoo search algorithm (CS) is investigated. Statistical analyses of twelve benchmark functions show that the four algorithms with high to low performances are IWOA, WOA, SSA and CS. Two multimodal functions for analyzing slope stability show that IWOA outperforms ant colony optimization algorithm (ACO), and imperialistic competitive algorithm (ICA). The time computational complexity of IWOA is same as WOA. Case studies of homogeneous and multilayer soil slopes indicate that the failure criterion has a significant effect on the minimum safety factor and the critical slip surface, and that IWOA can show better performance than WOA, SSA and CS. This study develops an efficient method to locate critical slip surfaces of soil slopes for engineers.