Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto optimal solutions. In many real-world problems, a decision-maker has some preferences on the objective functions. One approach to incorporate the preferences in multi-objective BO is to use a scalarising function and build a single surrogate model (mono-surrogate approach) on it. This approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of an acquisition function e.g., expected improvement can be used. We overcome these limitations by building independent surrogate models (multi-surrogate approach) on each objective function and show that the distribution of the scalarising function is not Gaussian. We approximate the distribution using Generalised value distribution. We present an a-priori multi-surrogate approach to incorporate the desirable objective function values (or reference point) as the preferences of a decision-maker in multi-objective BO. The results and comparison with the existing mono-surrogate approach on benchmark and real-world optimisation problems show the potential of the proposed approach.
翻译:许多现实世界的多目标优化问题依赖于计算成本高昂的功能评估。 多重目标贝耶斯优化( BO) 可用于缩短计算时间, 以找到一套大致的帕雷托最佳解决方案。 在许多现实世界的问题中, 决策者对目标功能有一些偏好。 将偏好纳入多目标BO 的方法之一是使用一个缩放功能, 并据此建立一个单一的替代模型( 多边覆盖方法) 。 这种方法有两个主要限制。 首先, 倍增功能和客观功能的适合性景观可能并不相似。 第二, 这种方法假定, 缩放功能分布是高斯的, 从而对获取功能的封闭形式表示, 例如, 可以利用预期的改进。 我们克服这些局限性的方法是在每个目标功能上建立独立的替代模型( 多重覆盖方法), 并表明, 缩放功能的分布不是高估。 我们用通用的参照值分布来比较分布。 我们用一个最优先的多目标选项分配方式, 将当前选择性目标的定位方法与当前目标对比结果结合起来。