Bi-direction multi-surrogate surrogate assisted global optimization

For global optimization, an important issue is a trade-off between exploration and exploitation within limited number of evaluations. Efficient Global Optimization (EGO) is an important algorithm considering such condition termed as Expected Improvement (EI). One of major bottlenecks of EGO is to keep the diversity of samples. Recently, Multi-Surrogate EGO (MSEGO) uses more samples generated by multiple surrogates to improve the efficiency. However, the total number of samples is commonly large. To overcome this bottleneck, a bi-direction multi-surrogate global optimization is suggested.

As the name implies, two different ways are used. The first way is to EI criterion to find better samples similar to EGO. The second way is to use the second term of EI to find accurate regions. Sequentially, the samples in these regions should be evaluated by multiple surrogates instead of exact function evaluations. To enhance the accuracy of these samples, Bayesian inference is employed to predicted the performance of each surrogate in each iteration and obtain the corresponding weight coefficients. The predicted response value of a cheap sample is evaluated by the weighted multiple surrogates combination. Therefore, both accuracy and efficiency can be guaranteed based on such frame.

According to the test functions, it empirically shows that the proposed algorithm is a potentially feasible method for complicated underlying problems.

A bi-direction sampling strategy is suggested. The first way is to use EI criterion to generate samples similar to the EGO. In this way, new samples should be evaluated by real functions or simulations called expensive samples. Another way is to search accurate region according to the second term of EI. To guarantee the reliability of samples, a sample selection scenario based on Bayesian theorem is suggested to select the cheap samples. We hope this strategy help us to construct more accurate model without increasing computational cost.