## 4 Analysis of Single Objective Algorithms Overview
### Learner Performance-Based Behavior
Unfortunately, finding a single solution capable of optimizing all the target functions at the same time is a difficult undertaking [39] ([PERSON]). If and only if solution \(A\) achieves a higher value in at least one of the objective functions, whereas the values of other objectives stay the same, then solution \(A\) is deemed superior or dominant to solution \(B\) in the context of MOP. Given that it denotes the perfect balance between the objectives, the Pareto-optimal solution is the best possible solution for a multi-objective problem [15,69,70]. ### Multi-Objective Methods

Evolutionary algorithms are used in the MOO paradigm. The research topic of evolutionary MOO [67,71,72] encompasses the theoretical framework, real-world applications, and computational techniques. A variety of multi-objective evolutionary algorithms that were particularly created to solve MOO problems are described in the literature. Several characteristics allow for the classification of these algorithms. The following groups make up one often-used classification for multi-objective evolutionary algorithms [73,74]:

1. Pareto-dominance-based algorithms: NSGA has been used to find the Pareto front for MOO problems since its invention in 1994. Following this, several intelligent optimization algorithms that relied on Pareto-dominated methods surfaced. Non-convex optimization problems were handled through intelligent algorithms that preserved each goal's distinctive qualities on their own, without relying on the others. A growing number of studies on intelligent optimization algorithms have been carried out by researchers to offer Pareto-dominated solutions for MOO problems. The Pareto dominance relationship is applied, which entails choosing a partner from the population of individuals that it dominates for non-dominated individuals. Amongst well-known algorithms of this kind are Pareto Envelope-based Selection Algorithm II (PESA-II) [25,74], Strength Pareto Evolutionary Algorithm 2 (SPEA-2) [75], and Non-Dominated Sorting Genetic Algorithm II (NSGA-II) [42,76]. 2. Decomposition-based algorithms transform MOP into a set of SOPs utilizing the scalarizing functions: After that, concurrent solutions are found for these resultant single-objective problems. MOGLS (i.e., multi-objective genetic local search algorithm) [77], the cellular multi-objective genetic algorithm (C-MOGA), and the multiobjective evolutionary algorithm based on decomposition (MOEA/D) [2] are a few examples of algorithms of that method. 3. Indicator-based algorithms utilize indicator function for the assessment of a set of solutions' quality through utilizing a measure that takes into account the objective function space's convergence and diversity. Those algorithms' objective is to determine, depending on the performance indicator, the optimal subset of the Pareto non-dominated solution. There are other variations of such algorithms, including the Fast Hypervolume MOO Algorithm, S-Metric Selection Evolutionary MOO Algorithm (SMS-EMOA), and Indicator Based-Selection Evolutionary Algorithm (IBEA) [78]. ### Multi-Objective Algorithms Overview

There are several objective functions in a MOO problem that need to either be maximized or minimized. Similar to a single-objective optimization problem, any conceivable solution--including all of the optimal solutions--must fulfil several constraints in the MOO problem. Objectives could be maximized or minimized, respectively. The extremist concept of seeking an optimum solution cannot be applied to a single objective in the context of MOO when other objectives are significant as well. Trade-offs--conflicting consequences between aims--between various objectives might result from different solutions. A compromise must be made about other objectives to achieve an extreme (in a better sense) solution for one goal. One cannot select a solution that is ideal for only one objective as a result. This indicates two optimal MOO goals [8]:

1. Find a set of solutions lying on the Pareto-optimal front;
2.