Shuffled Complex Evolution algorithm

In arid and semi-arid regions particularly vulnerable to climate change, optimizing the long-term operation of multipurpose reservoirs is paramount. This study derived an optimum two-dimensional rule curve to jointly operate the parallel reservoirs of Mosul and Dukan, Northern Iraq. A hybridized optimization technique combining conventional dynamic programming with the shuffled complex evolution algorithm (SCE-UA) was developed to solve this problem. The results showed that the proportion of normal water supply areas increased from the beginning of the flood season (October) to its highest levels in April (58.77% of the total water supply area). The proportion decreased to its lowest in September (25.04% of the total water supply area). The newly derived 2D rule cure was compared with the current operation policy and was found to optimize the amount of water shortage by 21.1% during the operational period. It also reduced the shortage period and avoided catastrophic water shortages during droughts. In addition, the developed model optimized the amounts of water more than the joint water requirements, suffering from a significant deficit in meeting the demand during some months of the operational years. As a result, the storage in each reservoir was improved and thence can be adapted to face water shortages during future climate changes. This study proved the new hybridized model's applicability and can serve as a tool for sustainable water management.

Frictional drag coefficients for spheres are critical in Chemical Engineering. The falling-sphere problem provides an example of evolving solution strategies. Solutions include analytical approaches, asymptotic expansions, and curve-fitting.

An accurate correlation for the smooth sphere drag coefficient with wide range of applicability is a useful tool in the field of particle technology. The present study focuses on the development of high accurate drag coefficient correlations from low to very high Reynolds numbers (up to 10 6) using a multi-gene Genetic Programming (GP) procedure. A clear superiority of GP over other methods is that GP is able to determine the structure and parameters of the model, simultaneously, while the structure of the model is imposed by the user in traditional regression analysis, and only the parameters of the model are assigned. In other words, in addition to the parameters of the model, the structure of it can be optimized using GP approach. Among two new and high accurate models of the present study, one of them is acceptable for the region before drag dip, and the other is applicable for the whole range of Reynolds numbers up to 10 6 including the transient region from laminar to turbulent. The performances of the developed models are examined and compared with other reported models. The results indicate that these models respectively give 16.2% and 69.4% better results than the best existing correlations in terms of the sum of squared of logarithmic deviations (SSLD). On the other hand, the proposed models are validated with experimental data. The validation results show that all of the estimated drag coefficients are within the bounds of ±7% of experimental values.

An accurate correlation for the smooth sphere drag coefficient with wide range of applicability is a useful tool in the field of particle technology. The present study focuses on the development of high accurate drag coefficient correlations from low to very high Reynolds numbers (up to 10 6) using a multi-gene Genetic Programming (GP) procedure. A clear superiority of GP over other methods is that GP is able to determine the structure and parameters of the model, simultaneously, while the structure of the model is imposed by the user in traditional regression analysis, and only the parameters of the model are assigned. In other words, in addition to the parameters of the model, the structure of it can be optimized using GP approach. Among two new and high accurate models of the present study, one of them is acceptable for the region before drag dip, and the other is applicable for the whole range of Reynolds numbers up to 10 6 including the transient region from laminar to turbulent. The performances of the developed models are examined and compared with other reported models. The results indicate that these models respectively give 16.2% and 69.4% better results than the best existing correlations in terms of the sum of squared of logarithmic deviations (SSLD). On the other hand, the proposed models are validated with experimental data. The validation results show that all of the estimated drag coefficients are within the bounds of ±7% of experimental values.

The present study aims to the improvement of the accuracy of the empirical drag coef¬ ficient correlations using global optimization. Sixteen popular models are considered in two groups based on the range of applicability. The first group covers subcritical region while the second covers Reynolds numbers up to 10®. Shuffled Complex Evolution (SCE) algorithm is used to improve the parameters of the equations through a direct fit to the 486 reliable experimental data points. Furthermore, some parameters are added to drag equations forgiving more degrees of freedom in fitting experimental data. By using this procedure, ten new equations which were improved both in range and in accuracy were developed with the same or different forms of the existing drag correlations. The proposed equations in comparison with the existing correlations substantially (up to almost 96%) improve the fit to experimental data in terms of the Sum of Squared of Logarithmic Deviations (SSLD).

An accurate model for the estimation of the drag coefficient of a falling sphere is essential for different theoretical analyses and engineering applications. Ramírez (2017) summarized relationships of the frictional drag coefficient and presented the historical chronological sequence of the coefficient. While the author’s intention is laudable, this note discuss some important points in the subject matter, which is useful for the chemical engineers.

An accurate model for the drag coefficient (CD) of a falling sphere is presented in terms of a non-linear rational fractional transform of the series of Goldstein (Proc. Roy. Soc. London A, 123, 225-235, 1929) to Oseen's equation. The coefficients of the six polynomial terms are improved through a direct fit to the experimental data of Roos and Willmarth (AIAA J., 9:285-290, 1971). The model predicts CD up to Reynolds number 100,000 with a standard deviation of 0.04. Results are compared with eight different formulations of other authors.

The present study aims to the improvement of the accuracy of the empirical drag coef¬ ficient correlations using global optimization. Sixteen popular models are considered in two groups based on the range of applicability. The first group covers subcritical region while the second covers Reynolds numbers up to 10®. Shuffled Complex Evolution (SCE) algorithm is used to improve the parameters of the equations through a direct fit to the 486 reliable experimental data points. Furthermore, some parameters are added to drag equations forgiving more degrees of freedom in fitting experimental data. By using this procedure, ten new equations which were improved both in range and in accuracy were developed with the same or different forms of the existing drag correlations. The proposed equations in comparison with the existing correlations substantially (up to almost 96%) improve the fit to experimental data in terms of the Sum of Squared of Logarithmic Deviations (SSLD).

An accurate correlation for the smooth sphere drag coefficient with wide range of applicability is a useful tool in the field of particle technology. The present study focuses on the development of high accurate drag coefficient correlations from low to very high Reynolds numbers (up to 106) using a multi-gene Genetic Programming (GP) procedure. A clear superiority of GP over other methods is that GP is able to determine the structure and parameters of the model, simultaneously, while the structure of the model is imposed by the user in traditional regression analysis, and only the parameters of the model are assigned. In other words, in addition to the parameters of the model, the structure of it can be optimized using GP approach. Among two new and high accurate models of the present study, one of them is acceptable for the region before drag dip, and other is applicable for the whole range of Reynolds numbers up to 106 including the transient region from laminar to turbulent. The performances of the developed models are examined and compared with other reported models. The results indicate that these models respectively give 16.2% and 69.4% better results than the best existing correlations in terms of the sum of squared of logarithmic deviations (SSLD).  On the other hand, the proposed models are validated with experimental data. The validation results show that all of the estimated drag coefficients are within the bounds of ± 7% of experimental values.

Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 105.Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 105