A relation learning-assisted algorithm with knee point transfer for expensive dynamic multi-objective optimization

Expensive dynamic multi-objective optimization problems (EDMOPs) involve multiple objective functions that change over time steps, and only a limited number of function evaluations are allowed at each time step. Existing methods typically treat EDMOPs as multiple independent static expensive multi-objective optimization problems and track the evolving pareto optimal set (POS) through Gaussian Process (GP)-assisted optimization. However, the dynamic nature of the environment results in a severe scarcity of training samples at each time step, which may impact the fitting accuracy of the GP model and prevent the accurate prediction of the POS. Taking this cue, in this paper, we propose a relation learning-assisted expensive dynamic multi-objective optimization algorithm. Unlike existing methods, the proposed approach simultaneously constructs relation models based on category criteria and fitness criteria. These two types of models work collaboratively in a two-stage filtering mechanism to precisely select the optimized population, enhancing the exploration of the search space while maintaining good fitting accuracy. Additionally, to accelerate the convergence of the optimization process, we predict the knee point set at the current time step using the center points and manifolds of knee points from historical time steps, effectively guiding the search direction of the population. To evaluate the performance of the proposed method, we conduct an extensive empirical study utilizing commonly used EXDMOP benchmarks and a real-world case study on gradient material machining. Experimental results demonstrate the effectiveness of the proposed method in solving EDMOPs.