Selective Multistart Optimization Based on Adaptive Latin Hypercube Sampling and Interval Enclosures

Solving global optimization problems is a significant challenge, particularly in high-dimensional spaces. This paper proposes a selective multistart optimization framework that employs a modified Latin Hypercube Sampling (LHS) technique to maintain a constant search space coverage rate, alongside Interval Arithmetic (IA) to prioritize sampling points. The proposed methodology addresses key limitations of conventional multistart methods, such as the exponential decline in space coverage with increasing dimensionality. It prioritizes sampling points by leveraging the hypercubes generated through LHS and their corresponding interval enclosures, guiding the optimization process toward regions more likely to contain the global minimum. Unlike conventional multistart methods, which assume uniform sampling without quantifying spatial coverage, the proposed approach constructs interval enclosures around each sample point, enabling explicit estimation and control of the explored search space. Numerical experiments on well-known benchmark functions demonstrate improvements in space coverage efficiency and enhanced local/global minimum identification. The proposed framework offers a promising approach for large-scale optimization problems frequently encountered in machine learning, artificial intelligence, and data-intensive domains.