###### Abstract
Today, CFD tools are no longer used just for theoretical analysis; they have become reliable optimization tools for hydraulic machinery. In their work, [PERSON] and [PERSON] [10] proposed a Pelton runner design methodology based on the application of non-uniform rational B-splines during the bucket modeling process, coupled with the usage of the CFD commercial software CFX. The methodology resulted in a maximum hydraulic efficiency of 84% for the Pelton runner design. [PERSON] developed an optimization methodology taking into account 12 Pelton runner design parameters, and numerical simulation results showed an efficiency increase of 2.5% after reducing the number of buckets and the exit angle to the lowest possible [16; 17]. [PERSON] et al. presented an optimization strategy to enhance Pelton turbine efficiency based on a 21-parameter parametric model of the bucket geometry and FVPM numerical simulations. Due to the complexity of managing 21 parameters, a dimension reduction was performed showing that the exit angle, tilt angle, length-to-width ratio, depth-to-width ratio, and pitch diameter are the design parameters with a higher impact on the turbine performance [11]. Due to efficiency in terms of both time and money, cut-out edge optimization techniques are widely used in all the design processes. The design and optimization of hydraulic machinery have seen extensive use of evolutionary algorithms, which are the most representative of global optimization techniques. A Francis turbine runner was optimized by [PERSON] [PERSON] et al. using the EASY optimization program and a hierarchical approach in conjunction with CFD, leading to a 0.15% gain in hydraulic efficiency [18]. When designing the Pelton bucket, [PERSON], and [PERSON] used the EASY software and CFD simulations to boost efficiency by 6.8% [19]. In a similar vein, [PERSON] et al. developed a method to improve the hydraulic efficiency of the runner by 13.21%, by optimizing the design of a Pelton bucket using a genetic algorithm linked with the Smoothed Particle Hydrodynamics (SPH) method [20]. This study aims to provide a novel methodology for the Pelton bucket's design and optimization, using metaheuristic optimization techniques such as evolutionary algorithms coupled with CFD numerical simulations. As described above, almost all the numerical simulations available in the literature were performed using commercial software. This research is focused on the use of open-source software, such as OpenFOAM 9 and the multi-objective, elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) available in the Python optimization library \"pyMOO\". To demonstrate the validity of the methodology, an operating Pelton turbine has been selected as a case study. _Case Study: \"Illuchi N\({}^{\circ}\) 2\" Hydropower Center_  
The \"Illuchi N\({}^{\circ}\)2\" is a small-scale hydrocenter. It is property of the public company ELEPCO S.A and is located in the Ecuadorian North Andean region, specifically in Latacunga city. This plant is powered by two Theodore Bell and Cia Pelton-type generation units described in Table 1, and has an installed capacity of 5.523 [kW] and 6.5 [MVA]. It is worth mentioning that the \"Illuchi N\({}^{\circ}\)2\" power plant works with turbinated water from the \"Illuchi N\({}^{\circ}\)1\" center and trees the water to the Illuchi River. Generation unit number two has been chosen as the subject of study. This turbine operates with a head of 327 m, a nominal water flow of 0.95 [m\({}^{3}\)/s], an output power of 2675 [kW], and a rotational speed of 720 [RPM]; these conditions are the ones used for the design of the Pelton bucket and the numerical analysis.