# Research on Multi-Objective Evolutionary Algorithms Based on Large-Scale Decision Variable Analysis
## 2 Related Work
### High-Dimensional Multi-Objective Optimization Algorithms  
Over the past decade, high-dimensional multi-objective evolutionary algorithms (MOEAs) have become a research hotspot [20]. Based on the evolutionary framework used, these algorithms can be divided into four categories: Pareto dominance-based multi-objective evolutionary framework, decomposition-based multi-objective evolutionary framework, indicator-based multi-objective evolutionary framework, and other high-dimensional multi-objective evolutionary algorithms. In Pareto dominance-based MOEAs, the dominance relationship between individuals is determined by the rank and density function value of their positions in the population. The former is considered the primary selection criterion, while the latter is used to maintain population diversity. When rank cannot distinguish between individuals, those with lower density are preferred. To address this challenge, researchers typically optimize in two ways: modifying traditional Pareto dominance definitions (e.g., \(\epsilon\)-dominance [21], angle-dominance [22], Ra-dominance [23]) or introducing new diversity selection criteria (e.g., SDE [24], KnEA [25], L-norm [24]). For example, [PERSON] et al. [22] proposed a novel angle-dominance strategy that transforms the objective space into an angular space to determine the dominance relationship between individuals. [PERSON] et al. [24] proposed an environmental selection mechanism based on space partitioning and angle pruning to maintain selection pressure. Decomposition-based MOEAs transform multi-objective optimization problems into multiple single-objective subproblems through aggregation functions [11]. However, the performance of these algorithms heavily depends on whether the distribution of weight vectors matches the shape of the Pareto front. To improve this framework, researchers optimize weight vector generation, aggregation function construction, and computational resource allocation strategies. For example, [PERSON] et al. [26] proposed a two-layer weight vector generation method that combines a single-row lattice design and coordinate transformation to generate the final weight vector set. [PERSON] et al. [27] introduced two adaptive aggregation functions to adapt to different Pareto surfaces and combined them with a new population update strategy to build a new MOEA/D framework. Additionally, [PERSON] et al. [19] proposed an adaptive decomposition evolutionary algorithm based on objective space partitioning, which allocates evolutionary opportunities adaptively according to the advancement distance of each subspace. In 2022, [PERSON] et al. [28] proposed an adaptive algorithm, LSMOEA/D, which incorporates reference vectors into the analysis of control variables and combines adaptive strategies to optimize decision variables. In an indicator-based multi-objective evolutionary framework, the environmental selection process distinguishes non-dominated solutions based on user-preferred indicators (e.g., Hyper-volume [29], IGD [30], \(\epsilon\)+ [31]). The main drawback of this framework is that the computational complexity of the algorithm increases exponentially with the number of objective variables. To reduce the computational complexity in high-dimensional objective environments, [PERSON] et al. [29] improved the calculation efficiency of Hyper-volume using space partitioning and Monte Carlo approximation. [PERSON] et al. [32] used a variant of the R2 indicator to approximate the Hyper-volume value. [PERSON] et al. [31] adopted a lightweight convergence indicator as the primary criterion for evaluating individual dominance relationships and combined it with boundary protection strategies to maintain population diversity. Besides the three evolutionary frameworks mentioned above, there are unique high-dimensional MOEAs. For example, study [33] utilized individual convergence and divergence to convert high-dimensional multi-objective optimization problems into two-objective optimization problems, which are then solved using traditional MOEAs.