Scalarizing Functions in Bayesian Multiobjective Optimization
This work provides incremental insights for researchers and practitioners in optimization by comparing scalarizing functions to improve efficiency in computationally expensive multiobjective scenarios.
The authors studied 15 scalarizing functions within Bayesian multiobjective optimization to address expensive optimization problems, finding that the choice of function significantly impacts evaluation quality and efficiency, with specific functions performing better on benchmarks across varying objective counts.
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 in 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 study and review 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models (as surrogates, metamodels or emulators) on them. We use expected improvement as infill criterion (or acquisition function) to update the models. In particular, we compare different scalarizing functions and analyze their performance on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights when using and selecting a scalarizing function when using a Bayesian multiobjective optimization method.