## 1 Introduction  
Multi-objective optimization (MOO) has gained attention and become a topic of application and study in recent times [1]. Those who practice and research have attempted to tackle numerous kinds of optimization and search problems faced in practical situations. They did this by presenting computationally efficient as well as novel optimization algorithms that were aimed at addressing these issues. Real-world problems of optimization are not simple to solve because they can be found in many types or forms. There might be just one goal to be achieved in certain optimization problems, several competing objectives in others, severe constraints in some, and multiple optimal solutions in others. To solve these problems, a user first evaluates the underlying problem and selects an appropriate algorithm [2]. This is because a single-objective optimization problem's lone optimum cannot be effectively found by an algorithm that is designed to identify several optimal solutions to another optimization problem. To address a variety of issues, a user must be knowledgeable about a variety of algorithms, each of which is focused on resolving a specific class of optimization problems [3], whether they include maximizing or minimizing values, or employing a single objective or several objectives [4]. The optimization problems typically include multiple objectives that conflict with one another, making a single solution unfeasible. Rather, our goal is to identify optimal \"trade-off\" solutions that optimally balance the various objectives [5]. MOO refers to problems with multiple objectives. Various fields, including engineering, mathematics, economics, social studies, aviation, agriculture, and automobiles, encounter this kind of issue daily [6; 7]. EO algorithms use a population of solutions approach, where various solutions are involved in each iteration and aid in the creation of a new population of solutions [8; 9]. Their broad appeal is a result of several reasons, including (i) no derivative information being required for executive orders (EOs); (ii) EOs are quite simple to execute; and (iii) EOs have a wide range of applications and are adaptable. While it might not seem necessary to use a population of solutions to find the single best solution for single-objective optimization problems, doing so is a great way to solve MOO problems. The inventors of PSO classify their heuristic search method as an evolutionary algorithm [6] Scholars are now investigating the use of the PSO method in different disciplines due to its success as a single-objective optimizer, especially in continuous search spaces. The multi-objective particle swarm optimizer (MOPSO) was first proposed [10; 11], and the first PSO technique modification for solving multi-objective problems was presented in a 1999 paper [12]. The field of optimization algorithms has seen significant advancements, with evolutionary, swarm, and behavior-based methods playing a pivotal role in solving complex computational problems. Despite extensive research, the integration of multi-objective optimization into behavior-based algorithms remains underexplored. This paper addresses this gap by introducing a novel framework that enhances computational efficiency and solution quality. Our comprehensive review of the literature from 2000 to 2023, utilizing sources like IEEE Xplore, ScienceDirect, and Web of Science, uncovers emerging trends and identifies key contributors shaping the future of optimization algorithms. After this first attempt, researchers were highly interested in expanding PSO; nevertheless, strongly, the next suggestion was not published until 2002. Nonetheless, around twenty-five different MOPSO concepts are already documented in the specialized literature. The authors offer a comprehensive analysis of the many MOPSO algorithms that have been published in academic journals [11; 13; 14]. Differential evolution (DE) is a stochastic optimization approach that makes use of the direct search evolution technique.