A machine learning approach for fighting the curse of dimensionality in global optimization
This addresses the curse of dimensionality for researchers and practitioners in optimization, though it is incremental as it builds on existing autoencoder techniques.
The paper tackles the challenge of global optimization in high-dimensional spaces by using autoencoders to reduce dimensionality and search in latent spaces, achieving superior or comparable results to established methods on benchmark functions and structural topology optimization problems.
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.