## 5 Conclusions and Further Work  
This paper presents a new multi-objective optimization algorithm called the MOMmCAA inspired by the neighborhood and local interaction rules of majority and minority cellular automata. The randomness, concurrency, and information exchange generated between the smart-cells by applying different rules produce an appropriate balance between exploration and exploitation actions.  
Comparative computational testing was carried out on 27 test functions with various characteristics, including convex, concave, mixed, disconnected, and degenerated PFs. These test functions were used to challenge the MOMmCAA, and its performance was compared against five other algorithms recognized for their efficiency. The experiments showed satisfactory performance on the part of the MOMmCAA.  
In addition, two multi-objective engineering problems from the recent literature were used to test the MOMmCAA against the results obtained by the other algorithms. The MOMmCAA again demonstrated its high quality in finding solutions to these problems, proving its competitiveness against other recent metaheuristics.  
Compared to classical techniques, the MOMmCAA provides improved flexibility. It can explore large search spaces and adapt to problems with multiple objectives and complex constraints. These features make the MOMmCAA especially useful for solving multi-objective optimization problems, where traditional methods may be inefficient due to assumptions about the problem's nature, the need for derivatives, or the complexity of the objective functions.  
As further work, the MOMmCAA has to be proven effective in solving real-world problems such as power grid design, vehicle routing optimization, industrial systems control, and feature selection in bioinformatics. Its ability to balance multiple conflicting criteria makes it suitable for multi-objective situations.  
However, the MOMmCAA has limitations in scalability for high-dimensional problems, where managing the repository of non-dominated solutions and correctly selecting the algorithm parameters are critical aspects affecting its performance. Its computational cost can also be high when dealing with complex problems, especially when requiring many iterations or accurate PF estimation.  
These limitations provide opportunities for future algorithm refinement, including testing improvements with fewer parameters, dynamic parameter control, or other solution control mechanisms such as niche strategy, clustering, rank dominance, or FP maintenance methods. The richness of cellular automata behaviors also presents new opportunities for proposing new multi-objective optimization algorithms, such as the utilization of periodic, chaotic, universal, complex, or surjective and reversible cellular automata.  
Conceptualization, J.C.S.-T.-M. and [PERSON]; methodology, [PERSON] and [PERSON]; validation, [PERSON] and [PERSON]; formal analysis, [PERSON], [PERSON] and [PERSON]; investigation, [PERSON], [PERSON] and [PERSON]; resources, [PERSON] and [PERSON]; writing--original draft preparation, [PERSON]-[PERSON], [PERSON] and [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, [PERSON] and [PERSON]; funding acquisition, [PERSON]. 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.  
Not applicable.  
The MOMmCAA source code is available on Github [[https://github.com/juanseck/MOMmCAA](https://github.com/juanseck/MOMmCAA)]([https://github.com/juanseck/MOMmCAA](https://github.com/juanseck/MOMmCAA)) (accessed on 23 August 2024).  
The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.