Mirrored Orthogonal Sampling for Covariance Matrix Adaptation Evolution Strategies.

Area of Science:

• Evolutionary Computation
• Optimization Algorithms
• Machine Learning

Background:

• High-dimensional search spaces pose challenges for optimization algorithms.
• Mirrored sampling enhances sample distribution and convergence in evolution strategies.
• Derandomized sampling techniques aim to improve the efficiency of evolutionary algorithms.

Purpose of the Study:

• Introduce a novel derandomized sampling technique: mirrored orthogonal sampling.
• Analyze and empirically evaluate the performance of mirrored orthogonal sampling.
• Apply and assess mirrored orthogonal sampling within the Covariance Matrix Adaptation Evolution Strategy (CMA-ES).

Main Methods:

• Theoretical analysis of mirrored orthogonal sampling.
• Empirical evaluation on the sphere function.
• Integration with CMA-ES and testing on the Black-Box Optimization Benchmark (BBOB).

Main Results:

• Mirrored orthogonal sampling demonstrably improves sample distribution.
• The technique shows enhanced convergence rates compared to standard mirrored sampling.
• The modified CMA-ES with mirrored orthogonal sampling outperforms standard CMA-ES and its mirrored sampling variant on the BBOB.

Conclusions:

• Mirrored orthogonal sampling is an effective derandomized technique for evolution strategies.
• The proposed method offers significant performance improvements in high-dimensional optimization.
• This work advances the field of evolutionary computation by providing a more efficient sampling strategy.