A machine learning approach for fighting the curse of dimensionality in global optimization

TL;DR

This paper introduces a machine learning method that uses autoencoders to reduce the search space in high-dimensional global optimization problems, enabling more efficient and effective finding of global optima.

Contribution

The paper presents a novel approach that leverages autoencoders to identify lower intrinsic dimensionality in cost functions, improving global optimization in high-dimensional spaces.

Findings

Successfully estimated intrinsic lower dimensionality of functions

Achieved better or comparable results to existing methods on benchmarks

Reduced computational effort in high-dimensional optimization

Abstract

Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality. Furthermore, multimodal cost functions render local gradient-based search techniques ineffective. To overcome these difficulties, we propose to trim uninteresting regions of the search space where global optima are unlikely to be found by means of autoencoders, exploiting the lower intrinsic dimensionality of certain cost functions; optima are then searched over lower-dimensional latent spaces. The methodology is tested on benchmark functions and on multiple variations of a structural topology optimization problem, where we show that we can estimate this intrinsic lower dimensionality and based thereon obtain the global optimum at best or superior results compared to established optimization procedures at worst.