Hybrid methods using genetic algorithms for global optimization

Area of Science:

• Computational Mathematics
• Optimization Theory
• Bio-inspired Computing

Background:

• Traditional optimization methods like Quasi-Newton and Nelder-Mead's simplex present trade-offs between accuracy, reliability, and computational cost.
• Genetic algorithms offer reliability but can be computationally intensive and less accurate than gradient-based methods.

Purpose of the Study:

• To investigate the inherent trade-offs in global optimization concerning accuracy, reliability, and computation time.
• To develop novel hybrid optimization techniques that improve upon existing methods.
• To apply these methods to the challenge of nonlinear system identification.

Main Methods:

• Exploration of traditional optimization algorithms (Quasi-Newton, Nelder-Mead's simplex) and genetic algorithms.
• Design of hybrid methods integrating genetic algorithms (evolution) with Quasi-Newton (individual learning).
• Evaluation of hybrid methods using nonlinear system identification as a benchmark application.

Main Results:

• A novel hybrid method demonstrates a superior balance of accuracy, reliability, and computational efficiency.
• This hybrid approach combines the robustness of genetic algorithms with the precision of the Quasi-Newton method.
• The developed method achieves state-of-the-art performance with only a marginal increase in computation time compared to Quasi-Newton.

Conclusions:

• Hybrid optimization strategies offer a promising solution to the accuracy-reliability-computation time dilemma.
• Bio-inspired hybrid methods, merging evolutionary and local search techniques, represent a significant advancement in global optimization.
• The proposed hybrid method is highly effective for complex problems like nonlinear system identification.