The RBF Hyperparameter in Metamodel-Assisted Evolutionary Search

RBF metamodels, which are commonly used in expensive optimization problems, rely on a hyperparameter which affects their prediction. The optimal hyperparameter value is typically unknown and hence needs to be estimated by additional procedures. As such this study examines if this overhead is justified from an overall search effectiveness perspective, namely, if changes in the hyperparameter yield significant performance differences. Analysis based on extensive numerical experiments shows that changes are significant in functions with low to moderate multimodality but are less significant in functions with highly multimodality.

A multi-model assisted differential evolution algorithm for computationally expensive optimization problems

Surrogate models are commonly used to reduce the number of required expensive fitness evaluations in optimizing computationally expensive problems. Although many competitive surrogate-assisted evolutionary algorithms have been proposed, it remains a challenging issue to develop an effective model management strategy to address problems with different landscape features under a limited computational budget. This paper adopts a coarse-to-fine evaluation scheme basing on two surrogate models, i.e., a coarse Gaussian process and a fine radial basis function, for assisting a differential evolution algorithm to solve computationally expensive optimization problems. The coarse Gaussian process model is meant to capture the general contour of the fitness landscape to estimate the fitness and its degree of uncertainty. A surrogate-assisted environmental selection strategy is then developed according to the non-dominance relationship between approximated fitness and estimated uncertainty. Meanwhile, the fine radial basis function model aims to learn the details of the local fitness landscape to refine the approximation quality of the new parent population and find the local optima for real-evaluations. The performance and scalability of the proposed method are extensively evaluated on two sets of widely used benchmark problems. Experimental results show that the proposed method can outperform several state-of-the-art algorithms within a limited computational budget.

A bi-stage surrogate-assisted hybrid algorithm for expensive optimization problems

Surrogate-assisted meta-heuristic algorithms have shown good performance to solve the computationally expensive problems within a limited computational resource. Compared to the method that only one surrogate model is utilized, the surrogate ensembles have shown more efficiency to get a good optimal solution. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm to solve the expensive optimization problems. The framework of the proposed method is composed of two stages. In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space. In the second stage, the local search is added to exploit the sub-space, where the best position found so far locates, to find a better solution for real expensive evaluation. Furthermore, the local and global searches in the second stage take turns to be conducted to balance the trade-off of the exploration and exploitation. Two different meta-heuristic algorithms are, respectively, utilized for the global and local search. To evaluate the performance of our proposed method, we conduct the experiments on seven benchmark problems, the Lennard–Jones potential problem and a constrained test problem, respectively, and compare with five state-of-the-art methods proposed for solving expensive problems. The experimental results show that our proposed method can obtain better results, especially on high-dimensional problems.