## 7 Conclusions  
This paper explored the feasibility of the 4-zero texture model using the most recent experimental values. To gather data that can inform decisions on the model's viability, we employed a chi-square fit to compare the theoretical expressions of the model with the experimental values of well-measured physical observables. We developed a single-objective optimization model by defining a \(\chi^{2}(X)\) function to identify the allowed regions for the free parameters of the 4-zero texture model that are consistent with the experimental data. To address the challenge of optimizing the \(\chi^{2}(X)\) function within the chi-square fit, we proposed a new DEPSO algorithm variant, HE-DEPSO. The proposed algorithm has demonstrated its ability to efficiently optimize different functions, particularly those from the CEC 2017 single-objective benchmark functions set. The convergence properties of HE-DEPSO show a good balance between solution precision and convergence speed in most cases. Regarding optimizing the \(\chi^{2}(X)\) function, our findings indicate that HE-DEPSO and DEPSO are more than adequate for solving the optimization problem, with HE-DEPSO providing the best solution quality and consistency. At the same time, DEPSO maintains a faster convergence rate. This part of the investigation also highlights the difficulty that some algorithms can face when optimizing the \(\chi^{2}(X)\) function, such as algorithms like SHADE and CoDE, despite exhibiting good performance on the CEC 2017 test set. We can also conclude that optimization algorithms such as SHADE, CoDE, and DE would be worth considering for optimization problems in high-energy physics. Finally, with the use of the HE-DEPSO algorithm we show that the 4-zero texture model is compatible with current experimental data, and thus we can affirm that this model is physically feasible. Importantly, our proposed approach, with the help of HE-DEPSO, allows a more accurate exploration of the full parameter space of the elements of the 4-zero texture quark mass matrix, an aspect that is often overlooked in analytical approaches. While aligning with the latest experimental data, this approach could enhance the structural features of 4-zero quark mass matrices. It may serve as a valuable starting point for future model building. Future work will focus on enhancing the convergence speed of the HE-DEPSO algorithm and evaluating its effectiveness across diverse problem domains, exploring its ability to tackle more complex optimization challenges. An extended comparative analysis against other bio-inspired algorithms or other advanced DE variants could also be conducted. Furthermore, this research could be expanded by analyzing additional texture models like 2- and 5-zero texture models and determining their validity based on current experimental data. Additionally, the use of this method could have potential applications in any phenomenological fermion mass model SM extension, for example, nearest-neighbor textures [59], neutrino mass models [60], and discrete flavor symmetries models [14; 15]. Conceptualization, P.M.-R. and R.N.-P.; methodology, P.L.-E., P.M.-R. and R.N.-P.; software, E.M.-G.; validation, E.M.-G. and P.L.-E.; formal analysis, P.L.-E. and P.M.-R.; investigation, E.M.-G. and P.L.-E; resources, P.M.-R. and P.L.-E.; writing--original draft preparation, E.M.-G., P.M.-R. and [PERSON]-P.; writing--review and editing, P.M.-R. and J.C.S.-T.-M.; visualization, [PERSON]-[PERSON] and [PERSON]-T.-M.; supervision, [PERSON]-[PERSON] and [PERSON]-T.-M.; funding acquisition, J.C.S.-T.-M. All authors have read and agreed to the published version of the manuscript. This study was supported by the Autonomous University of Hidalgo (UAEH) and the National Council for Humanities, Science, and Technology (CONAHCYT) with project number F003-320109.