Multi-Objective Optimization with Surrogate Trees

Multi-objective optimization problems are usually solved with evolutionary algorithms when the objective functions are cheap to compute, or with surrogate-based optimizers otherwise. In the latter case, the objective functions are modeled with powerful non-linear model learners such as Gaussian Processes or Support Vector Machines, for which the training time can be prohibitively large when dealing with optimization problems with moderately expensive objective functions. In this paper, we investigate the use of model trees as an alternative kind of model, providing a good compromise between high expressiveness and low training time. We propose a fast surrogate-based optimizer exploiting the structure of model trees for candidate selection. The empirical results show the promise of the approach for problems on which classical surrogate-based optimizers are painfully slow.