Hypervolume Gradient Subspace Approximation

Kenneth Zhang, Angel E. Rodriguez-Fernandez, Ke Shang, Hisao Ishibuchi, Oliver Schütze

Abstract: Multi-objective evolutionary algorithms (MOEAs) are powerful optimizers that are capable of solving black-box multi-objective optimization problems. Due to their stochastic nature, local search methods, including directed search algorithms, have been proposed to guide search directions in the decision variable space. In particular, recent studies have shown that the inclusion of local hypervolume-based gradient methods can lead to better convergence rates. In this paper, a set-based method of estimating hypervolume gradients without additional function evaluations or Jacobian information is proposed and integrated with SMS-EMOA to form a steady-state MOEA. The proposed algorithm is compared to some widely-used MOEAs on two- and three-objective benchmark suites, outperforming all other algorithms on all 6/6 two-objective problems and 12/17 three-objective problems.