## 1 Introduction
Multi-objective Cellular Automata Optimization is another approach that applies cellular automata. Potential solutions are cells in a network that evolve based on local rules and interaction with their neighbors. This approach seeks to reach a balance by facilitating the identification of solutions [44]. Cellular Multi-objective Particle Swarm Optimization (CMPSO) is a variant of PSO in which particles are arranged in a cellular structure and only interact with their close neighbors. This promotes solution diversity by limiting global influences and encourages better exploration, and it is beneficial in applications that require simultaneous optimization of several criteria [45]. Cellular Teaching-Learning-Based Optimization (CTLBO) is a teaching-learning-based approach to optimization. In this method, solutions are organized in a cellular structure, where each cell represents an individual who learns from its neighbors and a virtual teacher who guides the process. This approach enhances the algorithm's ability to adapt to dynamic changes for multiple objectives that may vary over time [46]. Following this trend, a recent single-objective optimization algorithm is the Majority-=minority Cellular Automata Algorithm (MmCAA), which was tested on several test problems in multiple dimensions and for various applications in engineering, obtaining satisfactory results against other well-recognized algorithms [47]. This paper presents a multi-objective version of this algorithm called MOMmCAA. This algorithm is inspired by the local behavior of cellular automata, particularly the majority and minority rules, which are intermixed and able to generate complex behaviors in order to perform the tasks of exploration and exploitation in the search space. The problem to be addressed in this work is the optimization of multi-objective problems using a modification of the MmCAA to obtain an adequate approximation of its PS. Although multi-objective algorithms are continuously proposed in the specialized literature, they have yet to fully exploit the advantages offered by the different cellular automata rules, such as the diversities and richness of their dynamic behaviors and their easy implementation. Thus, this work aims to test and demonstrate the feasibility of modifying the MmCAA to deal with multi-objective problems in a manner comparable to current well-recognized algorithms for performing this task. The manuscript's originality lies in the fact that it is the first to propose an algorithm for multi-objective optimization inspired by cellular automata using majority and minority rules, and is complemented by managing a repository to control the density of solutions in the FP. To test the performance of the MOMmCAA, we used the DLTZ benchmark, ten quadratic problems, and ten CEC2020 problems. The proposed algorithm was also tested on two practical engineering problems, obtaining satisfactory results. In these cases, five other algorithms were also considered for comparison: Multi-Objective Lightning Attachment Procedure Optimization (MOLAPO) [48], Grid Search (GS) [49], Multi-Objective Particle Swarm Optimization (MOPSO) [13], the Non-dominated Sorting Genetic Algorithm (NSGA-II) [10], and the Multi-objective Nelder-Mead Algorithm (MNMA) [50]. Non-parametric Wilcoxon statistical tests were performed to show the statistical significance of the experiments. The results indicate that the proposed algorithm ranks among the best with respect to the other methods used in this work. The rest of this article is organized as follows.