Scalarizing Functions in Bayesian Multiobjective Optimization

Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving computationally expensive multi-and many-objective optimization problems using Bayesian multiobjective optimization is scarce. Scalarizing functions can play a crucial role on the quality and number of evaluations required when doing the optimization. In this article, we compare 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models on them. We use the expected improvement as infill criterion (or acquisition function) to update the models. In particular, we analyze the performance of different scalarizing functions on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights in using a scalarizing function, especially for problems with a large number of objectives.