Surrogate Models are not Necessary for Black-Box Expensive Optimization

For black-box expensive optimization problems, the limitation in the number of function evaluations prevents evolutionary algorithms (EAs) from achieving convergence. To date, surrogate models have emerged as the predominant technique to accelerate the convergence of EAs by offering numerous virtual evaluations. However, surrogate models are often criticized for their low accuracy in fitting complex objective functions and low generalizability in handling heterogeneous decision variables. In this work, we propose an alternative idea that abandons surrogate models, focusing instead on the customization of simple EAs for expensive optimization. We construct EAs by incorporating the translation, scale, and rotation invariant variation operators, which have robust generalization capabilities due to their space independent properties, and have outstanding convergence performance due to their learnable parameterized representation. Through a series of comparative experiments, this work answers two questions: Can an EA without surrogate models outperform those with surrogate models for expensive optimization? If so, can surrogate models further accelerate the convergence of such an EA?