The research work on optimization has witnessed significant growth in the past few years, particularly within multi- and single-objective optimization algorithm areas. This study provides a comprehensive overview and critical evaluation of a wide range of optimization algorithms from conventional methods to innovative metaheuristic techniques. The methods used for analysis include bibliometric analysis, keyword analysis, and content analysis, focusing on studies from the period 2000–2023. Databases such as IEEE Xplore, SpringerLink, and ScienceDirect were extensively utilized. Our analysis reveals that while traditional algorithms like evolutionary optimization (EO) and particle swarm optimization (PSO) remain popular, newer methods like the fitness-dependent optimizer (FDO) and learner performance-based behavior (LPBB) are gaining attraction due to their adaptability and efficiency. The main conclusion emphasizes the importance of algorithmic diversity, benchmarking standards, and performance evaluation metrics, highlighting future research paths including the exploration of hybrid algorithms, use of domain-specific knowledge, and addressing scalability issues in multi-objective optimization.

This paper presents the Multi-Objective Ant Nesting Algorithm (MOANA), a novel extension of the Ant Nesting Algorithm (ANA), specifically designed to address multi-objective optimization problems (MOPs). MOANA incorporates adaptive mechanisms, such as deposition weight parameters, to balance exploration and exploitation, while a polynomial mutation strategy ensures diverse and high-quality solutions. The algorithm is evaluated on standard benchmark datasets, including ZDT functions and the IEEE Congress on Evolutionary Computation (CEC) 2019 multi-modal benchmarks. Comparative analysis against state-of-the-art algorithms like MOPSO, MOFDO, MODA, and NSGA-III demonstrates MOANA's superior performance in terms of convergence speed and Pareto front coverage. Furthermore, MOANA's applicability to real-world engineering optimization, such as welded beam design, showcases its ability to generate a broad range of optimal solutions, making it a practical tool for decision-makers. MOANA addresses key limitations of traditional evolutionary algorithms by improving scalability and diversity in multi-objective scenarios, positioning it as a robust solution for complex optimization tasks.

Multi-Objective Optimization (MOO) techniques have become increasingly popular in recent years due to their potential for solving real-world problems in various fields, such as logistics, finance, environmental management, and engineering. These techniques offer comprehensive solutions that traditional single-objective approaches fail to provide. Due to the many innovative algorithms, it has been challenging for researchers to choose the optimal algorithms for solving their problems. This paper examines recently developed MOO-based algorithms. MOO is introduced along with Pareto optimality and trade-off analysis. In real-world case studies, MOO algorithms address complicated decision-making challenges. This paper examines algorithmic methods, applications, trends, and issues in multi-objective optimization research. This exhaustive review explains MOO algorithms, their methods, and their applications to real-world problems. This paper aims to contribute further advancements in MOO research. No singular strategy is superior; instead, selecting a particular method depends on the natural optimization problem, the computational resources available, and the specific objectives of the optimization tasks.