Forecasting Different Types of Droughts Simultaneously Using Multivariate Standardized Precipitation Index (MSPI), MLP Neural Network, and Imperialistic Competitive Algorithm (ICA)

Precipitation deficit causes meteorological drought, and its continuation appears as other different types of droughts including hydrological, agricultural, economic, and social droughts. Multivariate Standardized Precipitation Index (MSPI) can show the drought status from the perspective of different drought types simultaneously. Forecasting multivariate droughts can provide good information about the future status of a region and will be applicable for the planners of different water divisions. In this study, the MLP model and its hybrid form with the Imperialistic Competitive Algorithm (MLP-ICA) have been investigated for the first time in multivariate drought studies. For this purpose, two semi-arid stations of western Iran were selected, and their precipitation data were provided from the Iranian Meteorological Organization (IRIMO), during the period of 1988–2017. MSPI was calculated in 5-time windows of the multivariate drought, including MSPI3–6 (drought in perspectives of soil moisture and surface hydrology simultaneously), MSPI6–12 (hydrological and agricultural droughts simultaneously), MSPI3–12 (soil moisture, surface hydrology, and agricultural droughts simultaneously), MSPI12–24 (drought in perspectives of agriculture and groundwater simultaneously), and MSPI24–48 (socio-economical droughts). The results showed acceptable performances in forecasting multivariate droughts. In both stations, the larger time windows (MSPI12–24 and MSPI24–48) had better predictions than the smaller ones (MSPI3–6, MSPI6–12, and MSPI3–12). Generally, it can be reported that, by decreasing the size of the time window, the gradual changes of the index give way to sudden jumps. This causes weaker autocorrelation and consequently weaker predictions, e.g., forecasting droughts from the perspective of soil moisture and surface hydrology simultaneously (MSPI3–6). The hybrid MLP-ICA shows stronger prediction results than the simple MLP model in all comparisons. The ICA optimizer could averagely improve MLP’s accuracy by 28.5%, which is a significant improvement. According to the evaluations (RMSE = 0.20; MAE = 0.15; R = 0.95), the results are hopeful for simultaneous forecasting of different drought types and can be tested for other similar areas.

Imperialist Competitive Algorithm with Updated Assimilation for the Solution of Real Valued Optimization Problems

In this paper, an improved imperialistic competitive algorithm is presented for real-valued optimization problems. A new method is introduced for the movement of colonies towards their imperialist, which is called assimilation. The proposed method uses Euclidean distance along with Pearson correlation coefficient as an operator for assimilating colonies with respect to their imperialists. Applications of the proposed algorithm to classical and recently published hard benchmark problems, and statistical analysis associated with the corresponding experimental results illustrated that the achieved success is significantly better than a number of state-of-the art methods.