A large-scale multi-objective optimization framework based on a dual-space attention mechanism

Existing attention-based methods for large-scale multi-objective optimization (LMOAM) focus only on decision variables, using their variance to guide search behavior. However, single-space strategies ignore critical information in the objective space and the diversity and search efficiency are often degraded for solving multimodal multi-objective optimization problems (MOPs). To address this problem, a novel large-scale optimization framework that integrates a dual-space attention mechanism is proposed in this paper. Different from building attention only with information in decision space, a dual-space Key matrix that quantifies variable importance by combining decision-variable and objective-space distributions is first designed in the framework to refine the precision of the attention. Subsequently, a cross-space clustering method is adopted to select the representative solutions by analyzing the characteristics of individuals in both spaces to construct the Query matrix. The accuracy of attention allocation is improved. Finally, A linear inverse mapping strategy is used to enhance the diversity of the population by translating promising objective-space solutions back to the decision space. Unlike existing approaches, the characteristics of decision and objective space are linked with a new attention mechanism, and the exploration and exploitation of the population are well balanced. Three types of experiments are designed on two benchmark test sets with 500-dimensional and 1000-dimensional decision variables and the voltage transformer optimization problem to demonstrate the efficacy of the AIDF framework, experimental results indicate that AIDF surpasses comparative algorithms in terms of the average performance of IGD and HV.