Adaptive Genetic Algorithm with Implementation Enhancements

An Adaptive Genetic Algorithm is an enhanced version of traditional genetic algorithms that dynamically adjusts crossover and mutation probabilities based on the population's evolutionary state. This adaptation improves convergence speed and optimization performance. Unlike standard genetic algorithms, the self-adjusting mechanism helps prevent premature convergence and local optimum entrapment, making it suitable for complex optimization problems.

In MATLAB implementation, Gram-Schmidt (G-S) orthogonal decomposition is commonly employed to handle constraint conditions or specific problem structures in optimization. While G-S decomposition offers stability, it has relatively low computational efficiency. For optimization, consider replacing it with QR decomposition, which provides better numerical stability and simplifies computational processes—particularly beneficial when dealing with large-scale matrices.

The core algorithmic approach includes: Dynamically adjusting crossover and mutation probabilities to maintain strong exploration capability in early stages and stable convergence in later phases. Integrating orthogonal decomposition methods (such as G-S or QR decomposition) to optimize constraint handling or fitness calculations, thereby improving solution accuracy. Managing population diversity to prevent premature convergence and enhance global search capability.

For further optimization, replacing G-S decomposition with QR decomposition is recommended to reduce computational complexity. Comparative analysis of both methods across different problem scales can reveal performance differences in solution quality and computation time.