Dynamic Exploration–Exploitation Pareto Approach for high-dimensional expensive black-box optimization

Abstract

Surrogate Optimization (SO) plays a vital role in optimizing performance parameters for computationally expensive simulations. However, SO encounters significant challenges in high-dimensional spaces due to the curse of dimensionality, hampering effective point sampling around global optima. In this paper, we introduce “Dynamic Exploration–Exploitation Pareto Approach (DEEPA),” a novel SO method that combines Pareto sampling with a dynamic discretization schema to optimize high-dimensional black-box functions. Unlike traditional SO methods that heavily rely on specific surrogate models, Pareto sampling offers a more adaptable approach. Improvement-based acquisition functions, frequently employed in black-box optimization, are sensitive to model accuracy and tend to prioritize exploitation, potentially missing valuable regions of interest in complex landscapes. Furthermore, they can encounter challenges when dealing with high-dimensional problems due to the curse of dimensionality. DEEPA leverages dynamic coordinate importance to generate samples effectively, providing a solution for addressing high-dimensionality and complex functions. We employ feature selection strategies to assign importance probabilities to perturb each coordinate, demonstrating the impact of importance-based perturbation on convergence to a near-optimal region. We showcase DEEPA’s versatility in fixed-batch evaluation environments using complex global optimization test problems with various topological properties. We compare DEEPA’s performance with state-of-the-art black-box optimization algorithms, and our experimental results demonstrate DEEPA’s superior performance, particularly in complex problems with multiple local minima.