# A Two-Stage Multi-Objective Optimization Algorithm for Solving Large-Scale Optimization Problems
###### Abstract  
For large-scale multi-objective optimization, it is particularly challenging for evolutionary algorithms to converge to the Pareto Front. Most existing multi-objective evolutionary algorithms (MOEAs) handle convergence and diversity in a mutually dependent manner during the evolution process. In this case, the performance degradation of one solution may lead to the deterioration of the performance of the other solution. This paper proposes a two-stage multi-objective optimization algorithm based on decision variable clustering (LSMOEA-VT) to solve large-scale optimization problems. In LSMOEA-VT, decision variables are divided into two categories and use dimensionality reduction methods to optimize the variables that affect evolutionary convergence. Following this, we performed an interdependence analysis to break down the convergence variables into multiple subcomponents that are more tractable. Furthermore, a non-dominated dynamic weight aggregation method is used to enhance the diversity of the population. To evaluate the performance of our proposed algorithm, we performed extensive comparative experiments against four optimization algorithms across a diverse set of benchmark problems, including eight multi-objective optimization problems and nine large-scale optimization problems. The experimental results show that our proposed algorithm performs well on some test functions and has certain competitiveness. l 1 (2025) 18 (  
computational complexity. The latter challenge stems from the sparse distribution of candidate solutions within the objective space, which undermines the efficacy of conventional diversity maintenance strategies. To address this category of problems, a \"divide and conquer\" strategy is commonly employed, which was first proposed in [10]. The core concept involves partitioning the large-scale decision variables in large-scale multi-objective problems (LSMOPs) into multiple lower-dimensional groups and subsequently optimizing each sub-problem independently following decomposition. In the context of coevolution, the selection of an appropriate decomposition strategy is of paramount importance. The most optimal strategy entails grouping variables that exhibit interactions while segregating independent variables into distinct groups. Currently, there are two predominant grouping strategies: one is the fixed grouping strategy [11; 12; 13], and the other is the dynamic grouping strategy [14; 15]. In a fixed grouping strategy, the composition of groups remains unchanged throughout the optimization process, as exemplified by the LMEA [16]. Conversely, in dynamic grouping strategies, the grouping configuration evolves continuously in tandem with the optimization process, as seen in the CCGDE3. The efficacy of grouping decision variables significantly influences the performance of the algorithm. For single-objective optimization problems [17; 18], due to the straightforward dependency relationships among variables, such issues are relatively more tractable. In contrast, multi-objective problems involve intricate dependencies [19; 20; 21] not only among variables but also across multiple objectives, thereby compounding the complexity of the solution process. Consequently, the judicious grouping of decision variables presents a formidable challenge. When addressing multi-objective optimization problems, it is imperative to account for the interrelationships among variables. Researchers have undertaken extensive work in this domain, with two of the most seminal algorithms being the multi-objective evolutionary algorithm based on decision variable analysis (MOEA/DVA) [22] and the evolutionary algorithm based on decision variable clustering (LMEA) [16]. Both algorithms categorize decision variables into convergence variables and diversity variables. Convergence variables are associated with the proximity of the population to the true Pareto front, whereas diversity variables govern the distribution of the population within the objective space.