In this paper, a new meta-heuristic algorithm, called beetle swarm optimization (BSO) algorithm, is proposed by enhancing the performance of swarm optimization through beetle foraging principles. The performance of 23 benchmark functions is tested and compared with widely used algorithms, including particle swarm optimization (PSO) algorithm, genetic algorithm (GA) and grasshopper optimization algorithm (GOA). Numerical experiments show that the BSO algorithm outperforms its counterparts. Besides, to demonstrate the practical impact of the proposed algorithm, two classic engineering design problems, namely, pressure vessel design problem and himmelblau?s optimization problem, are also considered and the proposed BSO algorithm is shown to be competitive in those applications.

The adjoint tidal model based on the theory of inverse problem has been applied to investigate the effect of bottom friction coefficient (BFC) on the tidal simulation. Using different schemes of BFC containing the constant, different constant in different subdomain, depth‐dependent form, and spatial distribution obtained from data assimilation, the M₂ constituent in the Bohai, Yellow, and East China Sea (BYECS) is simulated by assimilating TOPEX/Poseidon altimeter data, respectively. The simulated result with spatially varying BFC obtained from data assimilation is better than others. Results and analysis of BFC in BYECS indicate that spatially varying BFC obtained from data assimilation is the best fitted one; meanwhile it could improve the accuracy in the simulation of M₂ constituent. Through the analysis of the best fitted one, new empirical formulas of BFC in BYECS are developed with which the commendable simulated results of M₂ constituent in BYECS are obtained.

As a link for energy transfer between the land and atmosphere in the terrestrial ecosystem, karst vegetation plays an important role. Karst vegetation is not only affected by environmental factors but also by intense human activities. The nonlinear characteristics of vegetation growth are induced by the interaction mechanism of these factors. Previous studies of this relationship were not comprehensive, and it is necessary to further explore it using a suitable method. In this study, we selected climate, human activities, topography, and soil texture as the response factors; a nonlinear relationship model between the karst normalized difference vegetation index (NDVI) and these factors was established by applying a back propagation neural network (BPNN), a radial basis function neural network (RBFNN), the random forest (RF) algorithm, and support vector regression (SVR); and then, the karst NDVI was predicted. The coefficient of determination (R²), mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the obtained results were calculated, and the mean R² values of the BPNN, RBFNN, RF, and SVR models were determined to be 0.77, 0.86, 0.89, and 0.91, respectively. Compared with the BPNN, RBFNN, and RF models, the SVR model had the lowest errors, with mean MSE, RMSE, and MAPE values of 0.001, 0.02, and 2.77, respectively. The results show that the BPNN, RBFNN, RF, and SVR models are within acceptable ranges for karst NDVI prediction, but the overall performance of the SVR model is the best, and it is more suitable for karst vegetation prediction.