Large-Scale Evolution Strategy Based on Search Direction Adaptation.

Area of Science:

• Optimization Algorithms
• Computational Intelligence
• Machine Learning

Background:

• Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is effective for real-valued optimization.
• High-dimensional problems pose challenges for CMA-ES due to complexity.
• Sparse or low-rank constraints on covariance matrices can enhance CMA-ES efficiency.

Purpose of the Study:

• Propose a novel Search Direction Adaptation Evolution Strategy (SDA-ES).
• Achieve linear time and space complexity for large-scale optimization.
• Improve efficiency and scalability of evolutionary algorithms.

Main Methods:

• Model the covariance matrix using an identity matrix and multiple search directions.
• Employ a heuristic update for search directions, inspired by Principal Component Analysis.
• Generalize the 1/5th success rule for mutation strength adaptation (derandomization).

Main Results:

• SDA-ES achieves linear time and space complexity.
• The algorithm is invariant under search-space rotational transformations.
• Demonstrates scalability with increasing numbers of variables.
• Exhibits competitive performance on generic black-box problems.

Conclusions:

• SDA-ES offers a scalable and computationally efficient alternative to traditional CMA-ES for high-dimensional problems.
• The proposed method effectively balances solution quality and computational resources.
• SDA-ES shows promise for large-scale real-valued optimization tasks.