Scaling Up Estimation of Distribution Algorithms For Continuous Optimization

TL;DR

This paper introduces EDA-MCC, a novel framework that significantly improves the scalability and efficiency of Estimation of Distribution Algorithms for high-dimensional continuous optimization, enabling solutions up to 500 dimensions.

Contribution

The paper presents EDA-MCC, a new scalable EDA framework with model complexity control, capable of handling high-dimensional problems up to 500D and providing problem structure insights.

Findings

EDA-MCC outperforms traditional EDAs on high-dimensional problems.

EDA-MCC reduces computational cost and population size requirements.

It effectively characterizes problem structure in large-scale optimization.

Abstract

Since Estimation of Distribution Algorithms (EDA) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model based continuous EDAs are still restricted to rather low dimensional problems (smaller than 100D). Traditional EDAs have difficulties in solving higher dimensional problems because of the curse of dimensionality and their rapidly increasing computational cost. However, scaling up continuous EDAs for higher dimensional optimization is still necessary, which is supported by the distinctive feature of EDAs: Because a probabilistic model is explicitly estimated, from the learnt model one can discover useful properties or features of the problem. Besides obtaining a good solution, understanding of the problem structure can be of great benefit, especially for black box optimization. We propose a novel EDA framework with Model Complexity Control (EDA-MCC) to scale up EDAs. By using Weakly dependent variable Identification (WI) and Subspace Modeling (SM), EDA-MCC shows significantly better performance than traditional EDAs on high dimensional problems. Moreover, the computational cost and the requirement of large population sizes can be reduced in EDA-MCC. In addition to being able to find a good solution, EDA-MCC can also produce a useful problem structure characterization. EDA-MCC is the first successful instance of multivariate model based EDAs that can be effectively applied a general class of up to 500D problems. It also outperforms some newly developed algorithms designed specifically for large scale optimization. In order to understand the strength and weakness of EDA-MCC, we have carried out extensive computational studies of EDA-MCC. Our results have revealed when EDA-MCC is likely to outperform others on what kind of benchmark functions.