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Due to inherent randomness and fluctuation of wind speeds, it is very challenging to develop an effective and practical model to achieve accurate wind speed forecasting, especially over large forecasting horizons. This paper presents a new decomposition-optimization model created by integrating Variational Mode Decomposition (VMD), Backtracking Search Algorithm (BSA), and Regularized Extreme Learning Machine (RELM) to enhance forecasting accuracy. The observed wind speed time series is firstly decomposed by VMD into several relative stable subsequences. Then, an emerging optimization algorithm, BSA, is utilized to search the optimal parameters of the RELM. Subsequently, the well-trained RELM is constructed to do multi-step (1-, 2-, 4-, and 6-step) wind speed forecasting. Experiments have been executed with the proposed method as well as several benchmark models using several datasets from a widely-studied wind farm, Sotavento Galicia in Spain. Additionally, the effects of decomposition and optimization methods on the final forecasting results are analyzed quantitatively, whereby the importance of decomposition technique is emphasized. Results reveal that the proposed VMD-BSA-RELM model achieves significantly better performance than its rivals both on single-and multi-step forecasting with at least 50% average improvement, which indicates it is a powerful tool for short-term wind speed forecasting.

Reservoir optimal operation (ROO) needs to coordinate various profit-making objectives, which is a typical multiobjective optimization problem (MOP) with complex constraints. With the development of multiobjective evolutionary algorithms (MOEAs) in the past decades, more and more research has focused on MOEAs to solve MOP. Considering that multiobjective ROO is also a typical multi-stage Markov decision-making problem, this paper introduces the application of multiobjective dynamic programming (MODP) for multiobjective ROO in detail. On this basis, an improved MODP with selection mechanism of non-dominated solutions based on reference lines (MODP-BRL) is proposed to improve the convergence efficiency of MODP. The experimental results show that the proposed MODP-BRL is a reliable and effective tool in solving multiobjective ROO. In addition, MODP-BRL has better performance in convergence effect and efficiency in comparison experiments with NSGAII, NSGAIII, and SPEA2. It is noteworthy that MODP and MODP-BRL are very sensitive to the discrete step. With the decrease of the discrete step (the higher the discrete precision), the computing time increases nonlinearly. The appropriate discrete step of the state variable is key presets to balance the superiority and computational efficiency of non-dominated solutions with the application of MODP and MODP-BRL.

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