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Non-linear global optimization via parameterization and inverse function approximation: an artificial neural networks
René V Mayorga1, Mariano Arriaga
1Faculty of Engineering, University of Regina, Canada. Rene.Mayorga@uregina.ca
International Journal of Neural Systems
|December 22, 2007
Summary
This study introduces a new global optimization technique using Artificial Neural Networks (ANNs) to efficiently find optimal solutions for complex non-linear problems, outperforming existing methods.
Area of Science:
- Computational Mathematics
- Artificial Intelligence
Background:
- Non-linear global optimization is crucial for solving complex problems.
- Existing methods often struggle with local minima and computational cost.
Purpose of the Study:
- To present a novel technique for non-linear global optimization.
- To avoid sub-optimal local solutions and inflection points.
- To reduce computational effort using Artificial Neural Networks (ANNs).
Main Methods:
- A two-step approach: decreasing the objective function and approximating its inverse.
- Implementation of a novel Artificial Neural Network (ANN) for inverse function approximation.
- Testing on highly non-linear functions with multiple local minima.
Main Results:
- The ANN-based approach significantly reduces computational requirements.
- The technique successfully avoids local minima and converges towards global solutions.
- Demonstrated favorable comparison against conventional and non-conventional optimization methods.
Conclusions:
- The proposed ANN-enhanced optimization technique is effective for non-linear global optimization.
- It offers a computationally efficient alternative to traditional methods.
- This approach shows promise for complex optimization challenges.
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