Solving Highly Expensive Optimization Problems via Evolutionary Expected Improvement

Although many methods have been proposed to solve expensive optimization problems (EOPs), they often consume hundreds of function evaluations (FEs) to find the optimal solution, which is unacceptable when facing highly EOPs. To reduce the number of FEs, we incorporate the population distribution into the well-known expected improvement (EI); thus, a new infill criterion called evolutionary EI (EEI) is proposed. In EEI, the covariance matrix adaptation evolution strategy is used to provide the population distribution. Compared with the original EI, EEI focuses more on promising regions provided by the population distribution, thus, reducing the FEs wasted in unpromising regions. By employing EEI as the infill criterion of Bayesian optimization, a new algorithm called EEI-BO is designed. Moreover, we also introduce an extended version of EEI-BO, called EEI-BO ⁺ , to handle multitask EOPs. To verify the effectiveness of EEI-BO, it is used to solve 10−, 20−, and 30-D test problems by using only 40, 50, and 60 FEs, respectively. The results show that EEI-BO is able to obtain high-quality solutions by consuming limited FEs. In addition, we apply EEI-BO to deal with the lightweight and crashworthiness design of the side body of an automobile. The results demonstrate that EEI-BO performs well on solving it. Furthermore, the performance of EEI-BO ⁺ is investigated by nine test problems. The results show that it has the capability to solve multitask EOPs with fast convergence speed.