## 1 Introduction
subregions that cannot contain optimal solutions are discarded, which reduces the overall search space. Multi-Objective Differential Evolution (MODE) uses a population of candidate solutions that evolve through mutation operators. The multi-objective optimization method based on adaptive parameter harmony search algorithm simulates the improvisation process of musicians searching for the best harmony, dynamically adapting its parameters using memory and tuning operators to explore new solutions and preserve the best ones [35]. The Guided Population Archive Whale Optimization Algorithm (GPA-WOA) is a variant of the Whale Optimization Algorithm (WOA) that simulates the hunting behavior of humpback whales and uses guides or benchmark solutions to direct the search and improve convergence to the FP; a population file is dynamically updated to preserve diversity and ensure that solutions are optimal and well-distributed [36]. The quantum-inspired Decomposition-based Quantum Salp Swarm Algorithm (DQSSA) combines quantum mechanical principles with the swarming behavior of salps to divide multi-objective problems into more tractable subproblems, allowing a set of well-distributed optimal solutions to be found at the FP [37]. The above works are just a sample of the many single-objective algorithms that have recently been extended in various ways to deal with multi-objective problems. Single-objective optimization algorithms inspired by cellular automata are practical and have competitive results on these types of problems compared to more recent metaheuristics. For instance, Cellular Particle Swarm Optimization (CPSO) is a variant of the classical PSO algorithm that organizes particles into a cellular lattice structure in which each particle only interacts with its nearest neighbors, thereby improving exploration and reducing the probability of premature convergence [38]. Island Cellular Model Differential Evolution combines the principles of Differential Evolution (DE) with a distributed population structure; a cellular scheme divides the population into subpopulations, which promotes genetic diversity, reduces premature convergence, and enhances exploration capability [39]. The Continuous-State Cellular Automata Algorithm (CCAA) is inspired by cellular automata but adapted to work with continuous rather than discrete variables. In this algorithm,individuals (or smart-cells) are organized in a spatial grid; each cell updates its state (candidate solution) based on the solutions of its local neighbors. Continuous states allow for finer exploration of the search space, while the restricted neighborhood structure favors a balance between local exploitation and global exploration [40]. The Cellular Learning Automata and Reinforcement Learning (CLARL) approach combines the principles of learning automata and reinforcement learning. In this method, learning automata are organized in a cellular mesh, where each automaton represents a potential solution and adapts its behavior through local interactions and reward-based feedback. This scheme allows for learning strategies that improve the system's dynamic adaptability [41]. The Reversible Elementary Cellular Automata Algorithm (RECAA) uses reversible rules, meaning that the system can return to previous states without losing information. In this algorithm, each potential solution follows simple local rules to update its state but with the property of reversibility, enabling a more controlled and efficient search space exploration [42]. However, only a few works have applied the concept of cellular automata for general multi-objective optimization. One of the most representative examples is the Cellular Ant Algorithm (CAA) for multi-objective optimization, which combines the ant colony structure with a cellular mesh in which ants only interact with their close neighbors. This mechanism simultaneously optimizes several objective functions, achieving balanced solutions to complex problems with multiple criteria [43].