Adaptive Ranking-Based Constraint Handling for Explicitly Constrained Black-Box Optimization.

Area of Science:

• Optimization
• Evolutionary Computation
• Numerical Analysis

Background:

• Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is robust for black-box optimization.
• Handling explicitly constrained problems requires specialized techniques.
• Existing methods may not fully leverage constraint function properties.

Purpose of the Study:

• To propose a novel constraint-handling technique (CHT) for CMA-ES.
• To address explicitly constrained black-box continuous optimization problems.
• To introduce invariance properties for enhanced robustness.

Main Methods:

• Developed ARCH, a CHT modifying CMA-ES ranking.
• Employed a repair operator and adaptive ranking aggregation.
• Designed test problems to verify invariance properties.

Main Results:

• ARCH demonstrated invariance to affine and increasing transformations.
• Empirical studies verified the algorithm's invariance.
• ARCH outperformed other CHTs on the CEC 2006 benchmark suite.

Conclusions:

• ARCH effectively exploits explicit constraint functions.
• The technique shows superior performance compared to existing CHTs.
• ARCH offers an efficient approach for constrained optimization problems.