This paper introduces DEEM (Differential Evolution with Elitism and Multi-populations), a novel heuristic optimisation algorithm of the Differential Evolution family. DEEM integrates elitism and multi-population strategies to improve convergence speed and accuracy. Additionally, a diversity-based restart strategy is employed to significantly reduce the algorithm's susceptibility to being trapped in local minima. The influence of algorithm parameter choices on optimisation success is demonstrated through a sensitivity study. The algorithm's effectiveness is validated against benchmark functions from CEC 2015, 2017, 2020, and 2022, showing superior performance compared to state-of-the-art DE algorithms. Additionally, DEEM's application is showcased through a complex optimisation problem in the field of geotechnical engineering: the calibration of advanced constitutive models for predicting the stress-strain behaviour of soils under monotonic and cyclic loading. This calibration process is notably time-consuming. DEEM not only achieves better objective values but also does so in fewer iterations, thus significantly reducing computational time.

Aiming to address the problem of selecting the parameters of a soil constitutive model in the calculation of foundation pit stability, this paper proposes a hybrid genetic differential evolution algorithm (GADE) which performs by jumping out of local optima with fast convergence based on the hybrid optimization algorithm strategy and compares the advantages and disadvantages of genetic algorithms (GAs) and differential evolution algorithms (DEs). Three typical test functions were used to evaluate the search efficiency and convergence speed of GAs, DEs, and GADE, respectively. It was found that GADE has the fastest convergence speed and can search for the global optimal solution to the problem, which highlights its excellent optimization performance. At the same time, taking the Shimao Binjiang deep foundation pit as an example, GADE was used to invert the soil modulus parameters of a CX1 measuring point and construct a finite-element model for calculation. The results showed that the simulated calculation curve and the measured displacement curve were in good agreement and the curve fitting reached 95.05%, indicating the applicability and feasibility of applying GADE to identify soil parameters.

Slopes have a significant impact on the ground motion characteristics, which can aggravate the damage degree of building structures during a strong earthquake. However, many studies have focused on the design response spectra under flat site conditions and fewer researchers have investigated the impact of slope topography on the design response spectra. In this study, the numerical simulation is used to obtain the seismic response of slopes and the differential evolution algorithm is used to obtain the standardized response spectra of the acceleration time histories along the ground surface behind the slope crest. The impacts of slope height (H), slope gradient (i), average shear wave velocity in the top 30 m (VS30) and distance from the slope crest (x) on the characteristic parameters of the design response spectra are then investigated. The results show that H, i, VS30 and x have a little influence on the normalized second inflection point period (mean(Tg/Tg,ff)) but a great influence on the normalized plateau value (mean(alpha max/alpha max,ff)). Specifically, both mean(Tg/Tg,ff) and mean(alpha max/alpha max,ff) show a trend from increasing first to decreasing and stabilizing finally as x increases; the mean(alpha max/alpha max,ff) shows an increasing trend as H increases, but a decreasing trend as i or VS30 increases. Finally, to provide some guidance for the seismic design of building structures near slopes, two approximate relationships are proposed: (1) between mean(Tg/Tg,ff) and x, and (2) between mean(alpha max/alpha max,ff) and H, i, VS30, x. The main innovation of this paper is that the relationship between the characteristic parameters of the design response spectra and the slope site characteristic parameters is clearly summarized and quantified for the first time.