  We propose a surrogate-assisted reference vector adaptation (SRVA) method to
solve expensive multi- and many-objective optimization problems with various
Pareto front shapes. SRVA is coupled with a multi-objective Bayesian
optimization (MBO) algorithm using reference vectors for scalarization of
objective functions. The Kriging surrogate models for MBO is used to estimate
the Pareto front shape and generate adaptive reference vectors uniformly
distributed on the estimated Pareto front. We combine SRVA with expected
improvement of penalty-based boundary intersection as an infill criterion for
MBO. The proposed algorithm is compared with two other MBO algorithms by
applying them to benchmark problems with various Pareto front shapes.
Experimental results show that the proposed algorithm outperforms the other two
in the problems whose objective functions are reasonably approximated by the
Kriging models. SRVA improves diversity of non-dominated solutions for these
problems with continuous, discontinuous, and degenerated Pareto fronts.
Besides, the proposed algorithm obtains much better solutions from early stages
of optimization especially in many-objective problems.
