Difference Vector Angle Dominance with an Angle Threshold for Expensive Multi-objective Optimization

For the latest two years, relation classification-based surrogate-assisted algorithms show good potential for solving expensive multi-objective optimization problems (EMOPs). In this category of methods, the used dominance relation that is vital for building training dataset and selecting promising solutions to reduce expensive real function evaluations (FEs). However, the existing studies are still at the initial stage and lack specific research on the dominance relation. This paper proposes a novel dominance relation called Difference Vector Angle Dominance with an angle threshold for EMOPs (called as DVAD- \(\varphi \) ). The proposed DVAD- \(\varphi \) has adaptive selection pressure and considers the convergence and diversity of solutions when picking out superior solutions, which makes it beneficial to pick out promising solutions for expensive real FEs and reduce expensive real FEs. To be specific, we firstly give the definition of DVAD- \(\varphi \) that measures the superiority from one solution to another solution, where the angle threshold \(\varphi \) controls the selection pressure. Then, we propose an adaptive determination strategy of angle threshold based on bisection to set proper pressure for picking out promising solutions for expensive real FEs. Experiments have been conducted on 7 test functions from one benchmark set. The experimental results have verified the effectiveness of DVAD- \(\varphi \) .