Global and Local Surrogate-Assisted Differential Evolution for Expensive Constrained Optimization Problems With...

Area of Science:

• Computational Mathematics
• Optimization Theory
• Artificial Intelligence

Background:

• Expensive Constrained Optimization Problems (ECOPs) involve computationally intensive objective functions and constraints.
• Existing methods often struggle with efficiency due to the high cost of function evaluations.

Purpose of the Study:

• To propose a novel global and local surrogate-assisted differential evolution (DE) method for solving ECOPs with inequality constraints.
• To significantly reduce the number of required fitness evaluations for ECOPs.

Main Methods:

• A two-phase approach: a global surrogate-assisted phase using DE and generalized regression neural networks, followed by a local surrogate-assisted phase employing interior point methods and radial basis functions.
• Integration of a feasibility rule and an uncertainty-based rule to guide the search and mitigate surrogate inaccuracies.
• Utilizing DE as a search engine and neural networks for efficient trial vector evaluation.

Main Results:

• The proposed method effectively reduces the number of fitness evaluations required for ECOPs.
• Experimental results on benchmark functions and real-world cases demonstrate superior performance compared to state-of-the-art methods.
• The global phase efficiently identifies promising regions, while the local phase accelerates convergence.

Conclusions:

• The combined global and local surrogate-assisted DE approach offers a significant improvement in solving computationally expensive optimization problems.
• This method provides a more efficient and effective solution for ECOPs, reducing computational burden.
• The strategy successfully balances exploration and exploitation for enhanced optimization performance.