This work investigates different Bayesian network structure learning techniques by thoroughly studying several variants of Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm (HMOBEDA), applied to the MNK Landscape combinatorial problem. In the experiments, we evaluate the performance considering three different aspects: optimization abilities, robustness and learning efficiency. Results for instances of multi- and many-objective MNK-landscape show that, score-based structure learning algorithms appear to be the best choice. In particular, HMOBEDA\(_{k2}\) was capable of producing results comparable with the other variants in terms of the runtime of convergence and the coverage of the final Pareto front, with the additional advantage of providing solutions that are less sensible to noise while the variability of the corresponding Bayesian network models is reduced.

这项工作通过彻底研究混合多目标贝叶斯分布算法（HMOBEDA）的几种变体，研究了不同的贝叶斯网络结构学习技术，并将其应用于MNK景观组合问题。在实验中，我们考虑了三个不同方面来评估性能：优化能力，鲁棒性和学习效率。多目标和多目标MNK景观实例的结果表明，基于得分的结构学习算法似乎是最佳选择。特别是HMOBEDA \（_ {k2} \） 在收敛的运行时间和最终Pareto前沿的覆盖范围方面，能够产生与其他变体可比的结果，并具有提供对噪声较不敏感的解决方案，同时减少了相应贝叶斯网络模型的可变性的附加优势。 。