Dynamic Exploration-Exploitation Pareto Approach for High-Dimensional Expensive Black-Box Optimization

Abstract

Surrogate-based optimization is commonly used in engineering design problems to determine optimal performance parameters for computationally expensive simulations. The sampling phase of surrogate optimization plays a critical role in identifying the most promising input data points for evaluation. This paper proposes a Pareto sampling approach coupled with a dynamic discretization schema for efficiently optimizing high-dimensional black-box functions. Our proposed Dynamic Exploration-Exploitation Pareto Approach (DEEPA) incorporates dynamic coordinate importance for effective sample generation in solving high-dimensional and complex functions. We employ model-based and model-agnostic feature selection strategies to assign importance probabilities to perturb each coordinate and investigate the impact of importance-based perturbation on the convergence to a near-optimal region. Additionally, we demonstrate the flexibility of DEEPA for fixed-batch evaluation environments. Using complex global optimization test problems with different topological properties, we compare the performance of DEEPA with practical state-of-the-art black-box optimization algorithms. Our experimental results indicate DEEPA's superior performance for complex problems with several local minima.

Keywords: Surrogate optimization, Black-box functions, Pareto Sampling, Exploration-Exploitation, Feature Importance