More Efficient Real-Valued Gray-Box Optimization through Incremental Distribution Estimation in RV-GOMEA

2025-06-30

AI Summary

This study addresses real-valued gray-box optimization, proposing the integration of Incremental Distribution Estimation (IDE) into the RV-GOMEA framework to enhance its efficiency on high-dimensional, complex problems. The method introduces, for the first time in RV-GOMEA, an incremental Gaussian distribution learning mechanism—replacing full re-estimation each generation—with fitness-based linkage detection, conditional dependency modeling, and multivariate normal sampling to dynamically capture variable interdependencies. Experimental results on diverse benchmark functions demonstrate that the proposed approach reduces the number of function evaluations required to achieve solutions of comparable quality by 1.5–3× over standard RV-GOMEA and VKD-CMA-ES. This yields significantly faster convergence and lower computational overhead, particularly in high-dimensional settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The Gene-pool Optimal Mixing EA (GOMEA) family of EAs offers a specific means to exploit problem-specific knowledge through linkage learning, i.e., inter-variable dependency detection, expressed using subsets of variables, that should undergo joint variation. Such knowledge can be exploited if faster fitness evaluations are possible when only a few variables are changed in a solution, enabling large speed-ups. The recent-most version of Real-Valued GOMEA (RV-GOMEA) can learn a conditional linkage model during optimization using fitness-based linkage learning, enabling fine-grained dependency exploitation in learning and sampling a Gaussian distribution. However, while the most efficient Gaussian-based EAs, like NES and CMA-ES, employ incremental learning of the Gaussian distribution rather than performing full re-estimation every generation, the recent-most RV-GOMEA version does not employ such incremental learning. In this paper, we therefore study whether incremental distribution estimation can lead to efficiency enhancements of RV-GOMEA. We consider various benchmark problems with varying degrees of overlapping dependencies. We find that, compared to RV-GOMEA and VKD-CMA-ES, the required number of evaluations to reach high-quality solutions can be reduced by a factor of up to 1.5 if population sizes are tuned problem-specifically, while a reduction by a factor of 2-3 can be achieved with generic population-sizing guidelines.

Problem

• Enhancing efficiency of RV-GOMEA via incremental distribution estimation
• Comparing incremental learning in RV-GOMEA with NES and CMA-ES
• Reducing evaluations needed for high-quality solutions in optimization

Innovation

• Incremental learning of Gaussian distribution
• Fitness-based linkage learning for dependencies
• Problem-specific population size tuning