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Abstract: This paper presents a nonlinear piecewise smooth dynamical system of the trajectory of deviated wells according to engineering background. An optimal control model is established and the necessary conditions for optimality are proved via maximum principle. The optimal control problem is solved by a revised Hooke–Jeeves algorithm. The uniform design technique has been incorporated into the revised Hooke–Jeeves algorithm to handle the multimodal function. Computer simulation is used for this paper, and the numerical example illustrates the validity and efficiency of the algorithm. The procedure demonstrates its advantages in practical applications in Liaohe Oil Field. [Copyright &y& Elsevier]

Abstract: Grey theory is one approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. Generally, the GM (1,1) and Discrete GM (1,1) models are two typical grey forecasting models in grey theory. However, there are two shortcomings in the above grey models respectively, i.e., the homogeneous-exponent simulative deviation in GM (1,1) model, and the unequal conversion between the original and white equations in DGM (1,1) model. In this paper, we firstly propose a novel Generalized GM (1,1) model termed GGM (1,1) model, based on GM (1,1) and DGM (1,1) models, to overcome the above shortcomings. Then, we detailedly study four important properties in this new grey model. Four estimative approaches of stepwise ratio in GGM (1,1) model context is also covered. In the end, we simulate and forecast the fuel production in China during the period 2003–2010 using three GM (1,1) models. The empirical results show that GGM (1,1) model has higher simulative and predictive accuracy than GM (1,1) and DGM (1,1) models. This work contributes significantly to improve grey forecasting theory and proposes a optimized GM (1,1) model. [Copyright &y& Elsevier]