A difference vector angle dominance relation for expensive multi-objective optimization

For the latest two years, relation classification-based surrogate assisted evolutionary algorithms show good potential for solving expensive multi-objective optimization problems (EMOPs). However, the existing studies are still at the initial stage and lack specific research on the dominance relation. This paper proposes a difference vector angle dominance relation for EMOPs, which uses an angle threshold $\phi$ to control the selection pressure and is called DVAD-$\phi$. The proposed DVAD-$\phi$ 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-$\phi$ that measures the superiority from one solution to another solution according to the angle threshold $\phi$. Then, we deduce that there is monotonicity between the angle threshold $\phi$ and the number of non-dominated solutions in the sense of DVAD-$\phi$. At last, 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 23 test functions from two benchmark sets and one real-world problem. The experimental results have verified the effectiveness of DVAD-$\phi$.