## 3 Optimization
### Algorithms
#### 3.3.2 Multi-Objective Optimization Algorithms  
The Non-dominated Sorting Genetic Algorithm II (NSGA-II), developed by [PERSON] et al. [23] in 2002, is characterized by non-dominated sorting, crowding distance calculation, elitism, fast computation, and genetic operations such as crossover and mutation to generate new solutions.  
In 2006, [PERSON] et al. [38] introduced R-NSGA-II, incorporating decision-maker preferences through reference points to more effectively guide the search for desirable solutions.  
[PERSON] and [PERSON] developed NSGA-III [39] in 2013. This algorithm modifies specific selection mechanisms of NSGA-II to enhance the diversity of the resulting solutions.  
The Unified NSGA-III (UNSGA-III) algorithm [40], an extension of NSGA-III developed by [PERSON] and [PERSON] in 2015, aims to improve performance and broaden applicability in multi-objective optimization. It integrates several techniques and concepts for more efficient handling of multi-objective problems, including a unified approach for diversity maintenance, reference-point management, and solution selection, thereby enhancing its versatility.  
The Reference point-based NSGA-III (R-NSGA-III) algorithm [41], designed by [PERSON] et al. in 2018, builds upon NSGA-III by incorporating user-defined reference points. This allows users to specify preferred regions within the objective space, guiding the search towards solutions of interest.  
A distinct approach to multi-objective optimization was introduced by [PERSON] and [PERSON] in 2007, with the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) [42]. This method decomposes a multi-objective optimization problem intoa set of scalar optimization subproblems, then solves them concurrently by integrating evolutionary algorithms with a decomposition strategy.  
In 2019, [PERSON] introduced the Adaptive Geometry Estimation-based MOEA (AGE-MOEA) [43], an adaptive, generalized, multi-objective evolutionary algorithm. While it follows the general structure of NSGA-II, it employs a modified crowding distance calculation. This algorithm incorporates an adaptive framework that adjusts parameters or strategies based on the evolving optimization process.  
Also in 2019, [PERSON] et al. introduced the Convergence and Trade-off-based Multi-objective Evolutionary Algorithm (C-TAEA) [44] for solving multi-objective problems. This algorithm emphasizes both convergence to the Pareto front and the maintenance of a well-distributed set of solutions.  
The S-Metric Selection Evolutionary Multi-objective Optimization Algorithm (SMSEMOA), introduced by [PERSON] et al. [45] in 2007, is specifically designed to maximize the dominated hypervolume during the optimization process. It employs the s-metric (referring to the hypervolume measure) as a central component in its selection process, effectively guiding the population of solutions toward a diverse and high-quality representation of the Pareto front.  
The Reference Vector Guided Evolutionary Algorithm (RVEA), presented by [PERSON] et al. [46] in 2016, utilizes reference vectors in the objective space to guide the population toward the Pareto front while maintaining diversity. It incorporates an angle penalty function to dynamically balance convergence and diversity.