Swarm-based optimization as stochastic training strategy for estimation of reference evapotranspiration using extreme learning machine

Reference evapotranspiration (ET0) is usually calculated as a pre-requisite to obtain the actual evapotranspiration (ET). Estimation of ET0 using extreme learning machine (ELM) is a new norm due to its excellent computation efficiency and its lower data dependency. However, the lack of stochastic tuning often results in the convergence to the local optima instead of the global optimum. This study attempts to address this issue by hybridizing the ELM with three swarm-based optimization algorithms, namely the particle swarm optimization (PSO), the moth-flame optimization (MFO) and the whale optimization algorithm (WOA) with different fitness functions. This study was conducted with three stations in Sabah and Sarawak (states in East Malaysia) as this region is to a very large extent covered with oil palm plantation. The water resources management is thus rather crucial for the area. The results showed that the WOA-ELM achieved a higher average rank score relative to the PSO-ELM and MFO-ELM, especially when the simple Taylor skill score was used as the fitness function. The application of different fitness functions did not show any significant effect. The reported standard deviations of the mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R2) for the three variations of the hybridized ELM were close to 0; thus reflecting their similarity in accuracy. However, in terms of computational efficiency, the simple Taylor skill score exhibited better stability where it could effectively reduce the number of required hidden neurons when the input meteorological parameters were decreased. The WOA was suggested as the best optimization algorithm for this study. For the three stations, respectively it achieved an average MAE, RMSE and R2 of 0.0007 to 0.1443, 0.0011 to 0.1927 and 1.0000 to 0.9486, from cases C1 to C6 with minimum time cost.