## 4 Analysis of Single Objective Algorithms Overview
### Learner Performance-Based Behavior
Find a set of solutions diverse enough to represent the whole Pareto-optimal front range. #### 5.3.1 Evolutionary MOO

The aforementioned concepts are what evolutionary MOO approaches seek to uphold. From a practical standpoint, an optimization issue, whether multi- or single-objective, only needs one solution, even though multiple- and single-objective optimizations differ in the cardinality of the optimum set. Finding a set of ideal solutions that successfully balance each objective is the aim of MOO. When a user finds several trade-off options, they can employ more sophisticated qualitative factors to help them decide. To identify a group of non-dominated solutions in MOO, EMO approaches are appropriate since they manage a population of solutions in every one of the iterations [8; 25]. When handling MOO problems, an evolutionary multi-objective technique functions based on the following notion [25]:

Step 1: Identify many non-dominated places along the Pareto-optimal front that exhibit broad trade-offs across the objectives. Step 2: Select one of the acquired points based on more advanced data. Figure 7 roughly illustrates the ideas used in an EMO approach. EMO processes, being heuristic, do not ensure the discovery of Pareto-optimal points, unlike theoretically proven optimization methods designed for situations that are linear or convex. Significant operators are employed by EMO approaches for improving evolving non-dominated points, emphasizing both convergence and variety, much like how artificial and natural evolving systems constantly enhance their solutions. Given that, one of the recent simulation studies [1; 8] showed that starting from random non-optimal solutions, a specific EMO method could iteratively progress toward the theoretical Karush-Kuhn-Tucker (KKT) points in real-value MOO problems. Finding many trade-off solutions in a single simulation is one benefit of using an evolutionary MOO technique. Figure 6 shows the identification of many non-dominated points reflecting trade-offs vertically downward during Step 1 of the EMO-based MOO method. In Step 2, one of the trade-off points resulting from the task displayed horizontally to the right is chosen using higher-level information. In this case, when applying this dual-tasking capability to single-objective optimization tasks, it becomes intriguing. According to detailed explanations in other studies, a single-objective optimization is a degenerate version of MMO [8]. Ideally, Step 1 should find the unique globally optimal solution in single-objective optimization, such that Step 2 is not necessary. It is crucial to first identify all or a few global optima in single-objective optimization with numerous global optima before choosing a solution based on more in-depth knowledge of the issue. Although it seems specifically designed for MOO, Figure 7's framework can be thought of as a universal principle that applies to both single- and MOO. By concentrating on many non-dominated and unique solutions, an EMO seeks to find multiple Pareto-optimal solutions inside a single simulation. Later, we will look at a few EMO techniques that clarify how this dual emphasis is accomplished. The NSGA-II approach is a popular EMO method which finds many Pareto-optimal solutions to an MOO problem [42]. It has the following three characteristics:

1. It employs an elitist concept. 2. It employs a specific strategy to maintain diversity. 3. It highlights non-dominated solutions. Applying crowded sorting on the points in the final front yields the points with the largest diversity. Points are selected starting at the top of the list and going down in descending order based on their crowding distance values. The unoccupied objective space surrounding point i in the population is measured by the crowding distance di of point i. We compute di by estimating the crowding distance, which is the perimeter of the cuboid formed with the use of the closest neighbors as vertices in the objective space.