A new adaptive Kriging-based optimization (AKBO) framework for constrained optimization problems: A case study on shared autonomous electric vehicle system design

Abstract

Adaptive Kriging-based optimization (AKBO) efficiently performs optimization by employing adaptive sampling methods that sequentially update Kriging model. To solve constrained optimization problems, existing adaptive sampling methods add samples based on probability of feasibility (PoF) representing the probability that all constraints are satisfied. However, these methods have the limitation that samples are added inefficiently when the PoF is inaccurate. Therefore, this study proposes a new AKBO framework that is robust to instability of PoF in adaptive sampling. To this end, a near constraint boundary region that is expected to be close to the constraint boundary is defined based on a probability measure. Then, a near constraint boundary search (NCBS) algorithm, which explores the sample point that minimizes the objective function within the near constraint boundary region, is developed for global search, whereas a near optimum search (NOS) algorithm, which searches for better solutions that may exist near the current optimum candidate, is developed for local search. To alleviate the distortions of the Kriging model that may occur due to the highly nonlinear response, a truncated constraint function (TCF) method that limits the extremely violated constraint values used in the design of experiment (DoE) of the Kriging model is also proposed. This study verifies the performance of the proposed AKBO framework through the shared autonomous electric vehicle (SAEV) system design optimization problem. Comparison of optimum designs derived from various optimization methods shows that the proposed AKBO framework derives the feasible global optimum with high accuracy and efficiency.