A novel hybrid genetic algorithm and Nelder-Mead approach and it's application for parameter estimation

Area of Science:

• Computational Science
• Optimization Algorithms

Background:

• Traditional optimization methods face challenges in balancing global exploration and local refinement for complex problems.
• A novel hybrid strategy, the Genetic and Nelder-Mead Algorithm (GANMA), is introduced to address these limitations.

Purpose of the Study:

• To develop and evaluate a hybrid optimization strategy integrating the Genetic Algorithm (GA) and Nelder-Mead (NM) technique.
• To enhance performance in benchmark functions and parameter estimation tasks.

Main Methods:

• The Genetic and Nelder-Mead Algorithm (GANMA) combines GA's global search with NM's local refinement.
• GANMA was tested on 15 benchmark functions and applied to parameter estimation problems.

Main Results:

• GANMA demonstrated superior robustness, convergence speed, and solution quality compared to traditional methods.
• The algorithm excelled in high-dimensionality and multimodal function landscapes.
• Improved model accuracy and interpretability were observed in parameter estimation tasks.

Conclusions:

• GANMA is a flexible and powerful optimization method for both benchmark and real-world challenges.
• Its ability to efficiently explore and refine solutions makes it valuable for scientific, engineering, and economic applications.
• GANMA offers improved model performance and effective handling of complex optimization problems.