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.

翻译：我们建议一种代用辅助参考矢量适应(SRVA)方法,以解决各种Pareto前形的昂贵的多目标和许多目标优化问题。SRVA与一种多目标贝叶西亚优化(MBO)算法相结合,采用参考矢量优化(MBO)算法,利用参考矢量优化(MBO)使客观功能升级。MBO的Kriging代孕模型用来估计Pareto前形,产生适应性参考矢量在估计的Pareto前端上统一分布。我们把SRVA与预期改进以惩罚为基础的边界交叉点作为MBO的填充标准结合起来。提议的算法与另外两种MBO算法相比,采用这些算法,将之与各种Pareto前形的基准问题进行比较。实验结果显示,拟议的算法超越了另外两种问题中的其他两个,其客观功能被Kriging模型合理地近似。SRVA用连续的、不连续的和退化的Pareto前线改进了这些问题的非主要解决办法的多样性。此外,提议的算法从最初的优化阶段,特别是许多目标问题中获得了更好的解决办法。