## 1 Introduction
It is renowned for being reasonably study and quick. DE was developed in the 1990s and was used in practice to address problems with scientific optimization [15]. Its application was extended to various problem areas, such as MOO, due to its established achievements [16]. DE was applied to address problems in multi-objective domains in several recent studies. The literature has described this research [16; 17; 18; 19]. [PERSON] and [PERSON] (2019) state that the fitness dependent optimizer (FDO) is a computational program that takes its cues from bee swarm reproduction. This algorithm simulates a swarm of bees going through their reproductive behavior. The core idea of the algorithm comes from the way scout bees search among several possible hives for a new, ideal colony. This program views each one of the scout bees that visit new hives as a possible solution. Furthermore, selecting the best hive from a collection of quality hives is thought to be convergent toward optimality [20]. In the year (2021), [PERSON] and [PERSON] introduced the idea of learner performance-based behavior (LPB). The learner performance behavior-based algorithm, a new optimization technique, was proposed. The LPB technique mimics the procedures used by different institutions to admit high school graduates and the actions taken by these students that affect their academic performance in college. It also looks at the elements that could help students change their high school study routines that do not work for college-level coursework. To accomplish this, multiple populations may be used to present students with different GPAs. This ultimately results in a beneficial balance between exploitation and exploration [21]. The need for efficient and effective optimization approaches that can handle multi-objective decision-making problems in the actual world is what motivated this study. Researchers want to take advantage of current algorithmic advances while addressing the inherent difficulties in MOO tasks by extending single-objective algorithms to multi-objective frameworks. By expanding upon proven single-objective optimization methods,this approach not only increases the adaptability of optimization algorithms but simplifies the development process. This study provides a thorough overview of single and MOO algorithms, including DE, EO, FDO, PSO, and LPB, as well as a concise description of each algorithm. These algorithms can be extended to solve multi-objective world problems. This study's primary contribution is a review of multi-and single-objective algorithms, which aims to provide academics studying optimization algorithms with up-to-date, comprehensive knowledge. The main contributions are as described below:  
1. The presented work consolidates the current state-of-the-art approaches in multi- and single-objective optimization algorithms, offering a holistic understanding of both classical methodologies and modern metaheuristic approaches. 2. By conducting a detailed examination of various algorithms, and their conceptual underpinnings, strengths, and limitations, this paper provides valuable insights into their applicability across various problem domains. 3. The review identifies recent advancements, comparative studies, and emerging trends in optimization research, shedding light on novel techniques and methodologies that are shaping the field's future trajectory. 4. By emphasizing the importance of collaboration between academia and industry, as well as the need for innovative approaches to address real-world challenges, the paper aims to stimulate further research and development in optimization. 5. The study offers a roadmap for future research endeavors by identifying important research gaps and highlighting prospects. It encourages the investigation of hybridization techniques, domain-specific optimizations, and scalability advances in MOO.