In this study, multi-tracker optimization algorithm (MTOA), particle swarm optimization (PSO), and differential evolution (DE) algorithms were integrated with support vector regression (SVR) to predict energy dissipation downstream of labyrinth weirs (ΔE). In order to evaluate the performance of these methods, the results are compared with corresponding outcome obtained by applying two other methods, namely, multilayer perceptron neural network (MLPNN) and multiple linear regressions methods (MLR). The input parameters comprise the discharge, the upstream flow depth, the crest length of a single cycle of the labyrinth weir, the width of a single cycle of the labyrinth weir, the apex width, the number of labyrinth weir cycles, the sidewall angle, and the height of weir. The results indicate that the meta-heuristic algorithms substantially improve the performance of SVR. The results show that the integrative methods, SVR-MTOA, SVR-PSO, and SVR-DE, are more accurate than the MLPNN and the MLR. In average, the integrative methods provide 39.63% more accurate results than the MLPNN and 79.34% more accurate results than the MLR. The average RMSE and R² for the integrative methods are 0.0054 m and 0.977, respectively. Among all integrative methods, the SVR-MTOA yields the best results, with RMSE = 0.0044 m and R² = 0.986.

本研究将多跟踪器优化算法 (MTOA)、粒子群优化 (PSO) 和差分进化 (DE) 算法与支持向量回归 (SVR) 相结合，预测迷宫堰下游的能量耗散 (Δ E）。为了评估这些方法的性能，将结果与通过应用其他两种方法获得的相应结果进行比较，即多层感知器神经网络 (MLPNN) 和多元线性回归方法 (MLR)。输入参数包括流量、上游水流深度、迷宫堰单圈顶部长度、迷宫堰单圈宽度、顶点宽度、迷宫堰圈数、侧壁角度、和堰的高度。结果表明，元启发式算法显着提高了 SVR 的性能。结果表明，综合方法 SVR-MTOA、SVR-PSO 和 SVR-DE 比 MLPNN 和 MLR 更准确。平均而言，综合方法提供的结果比 MLPNN 和 79 的准确度高 39.63%。结果比 MLR 准确度高 34%。平均 RMSE 和综合方法的R ^{2 分别}为 0.0054 m 和 0.977。在所有综合方法中，SVR-MTOA 产生最好的结果，RMSE  = 0.0044 m 和R ²  = 0.986。