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This problem was called the photo-gravitational restricted three-body problem by Radzievskii [19]. In a later work [20], Radzievskii performed a complete treatment of the behavior of the equilibrium points. In both papers, however, Radzievskii, who was primarily interested in the solar problem, only treated a limited range of radiation pressure parameters (in

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Coagulation is the most sensitive step in drinking water treatment. Underdosing may not yield the required water quality, whereas overdosing may result in higher costs and excess sludge. Traditionally, the coagulant dosage is set based on bath experiments performed manually, known as jar tests. Therefore, this test does not allow real-time dosing control, and its accuracy is subject to operator experience. Alternatively, solutions based on machine learning (ML) have been evaluated as computer-aided alternatives. Despite these advances, there is open debate on the most suitable ML method applied to the coagulation process, capable of the most highly accurate prediction. This study addresses this gap, where a comparative analysis between ML methods was performed. As a research hypothesis, a data-driven (D2) fuzzy inference system (FIS) should provide the best performance due to its ability to deal with uncertainties inherent to complex processes. Although ML methods have been widely investigated, only a few studies report hybrid neuro-fuzzy systems applied to coagulation. Thus, to the best of our knowledge, this is the first study thus far to address the accuracy of this non-hybrid data-driven FIS (D2FIS) for such an application. The D2FIS provided the smallest error (0.69 mg/L), overcoming the adaptive neuro-fuzzy inference system (1.09), cascade-correlation network (1.18), gene expression programming (1.15), polynomial neural network (1.20), probabilistic network (1.17), random forest (1.26), radial basis function network (1.28), stochastic gradient tree boost (1.25), and support vector machine (1.17). This finding points to the D2FIS as a promising alternative tool for accurate real-time coagulant dosage in drinking water treatment. In conclusion, the D2FIS can help WTPs to reduce operating costs, prevent errors associated with manual processes and operator experience, and standardize the efficacy with real-time and highly accurate predictions, and enhance safety for the water industry. Moreover, the evidence from this study can assist in filling the gap with the most suitable ML method and identifying a promising alternative for computer-aided coagulant dosing. For further advances, future studies should address the potential of the D2FIS for the control and optimization of other unit operations in drinking water treatment.