## 1 Introduction
Another work that is an extension of a recent metaheuristic algorithm is the Multi-objective Salp Swarm Algorithm (MSSA) [21]. Inspired by the swarming behavior of sea salps, the MSSA splits the population into a leader and followers, using an external file to store the non-dominated solutions. This approach shows adequate convergence and coverage of the PS. The interplay of several PSO algorithms for simultaneous optimization of single objectives in a multi-objective problem (MPMO) is described in [22] using multiple populations. In discrete problems, the MPMOGA is a new algorithm inspired by the GA which uses multiple populations to solve problems with multiple objectives. It was used in [23] to address the job-shop scheduling problems, obtaining satisfactory results. Multi-Objective Heat Transfer Search (MOHTS) based on Heat Transfer Search was proposed in [24] to optimize structural multi-objective problems, obtaining better results compared with other algorithms based on ant colonies and symbolic organisms. In related research, a multi-objective version of the symbolic organism algorithm was presented in [25] for optimal reinforcement design. Multi-Objective Teaching-Learning-based Optimization (MOTLBO) is an extension of the Teaching-Learning-based Optimization (TLBO) algorithm. This approach uses two main phases: the teacher phase, where solutions are improved based on the best individual, and the learner phase, where solutions are optimized through knowledge sharing between individuals [26]. Multi-Objective Thermal Exchange Optimization (MOTEO), inspired by the principles of thermodynamics and heat exchange, seeks to solve optimization problems by considering multiple criteria simultaneously [27]. Multi-objective Plasma GenerationOptimization (MOPGO) is inspired by the generation and behavior of plasmas, where charged particles interact and move towards lower energy states [28]. the Multi-Objective Crystal Structure Algorithm (MOCSA) is motivated by the formation and organization of crystalline structures; solutions resemble atoms that organize themselves into configurations that minimize the energy of the system [29]. The Multi-Objective Forest Optimization Algorithm (MOPOA) follows the dynamics and ecology of forests; solutions resemble trees competing for resources, allowing the solutions (trees) to evolve and adapt in a competitive and cooperative environment [30]. The Competitive Mechanism Integrated Multi-Objective While Optimization Algorithm with Differential Evolution (CMI-MOWOA-DE) combines whale social behavior and differential evolution; the solutions simulate whale movement and hunting strategy, while differential evolution introduces variation and diversification to achieve a balance between multiple conflicting objectives. The Multi-Objective Harris Hawks Optimizer (MOHHO) is an extension of the Harris Hawks Optimizer (HHO) algorithm, which evokes the cooperative hunting strategies of [PERSON] [31]. The Marine Predators Algorithm (MPA) emulates the behavior of species such as sharks and dolphins for multi-objective optimization, using search tactics and solution space exploitation to optimize multiple objectives [32]. The Multi-Objective Sine-Cosine Algorithm (MOSCA) is a variant of the Sine-Cosine Algorithm (SCA) that uses sine and cosine functions to guide the exploration and exploitation of the search space, dynamically adjusting the positions of candidate solutions to maintain diversity and ensure convergence to the FP [33]. The Multi-objective Atomic Orbital Search (MAOS) algorithm is based on the concept of atomic orbitals from quantum chemistry; the potential solutions are treated as electrons in different orbitals, and the search process resembles the movement of these electrons to reach lower energy configurations [34]. In the branch-and-bound framework for continuous global multi-objective optimization, the search space is recursively divided into smaller subregions, then lower and upper bounds are computed for the objective functions in these subregions.