A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global...

Area of Science:

• Optimization
• Computational Intelligence
• Engineering Mathematics

Background:

• Multiobjective optimization (MOO) is widely used for nonconvex constrained optimization problems (COPs).
• Existing research primarily uses Pareto dominance, overlooking other effective MOO frameworks like reference vector (RV)-based and decomposition-based methods.
• This gap limits the application of advanced MOO techniques to complex constrained problems.

Purpose of the Study:

• To develop a novel ranking strategy for COP solutions using RV-based MOO concepts.
• To integrate this strategy into the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for improved COP solving.
• To enhance the adaptability and robustness of evolutionary algorithms for constrained optimization.

Main Methods:

• Transforming a COP into a biobjective optimization problem (BOP).
• Employing an RV-based ranking strategy within CMA-ES to update the mean and covariance matrix.
• Explicitly tuning RVs during optimization and incorporating a repair mechanism for infeasible solutions.
• Implementing a restart strategy to aid population escape from infeasible regions.

Main Results:

• The proposed RV-based ranking strategy significantly enhances CMA-ES performance on COPs.
• The algorithm demonstrates competitive or superior results compared to state-of-the-art constrained optimizers.
• Extensive testing on IEEE CEC 2010 and 2017 benchmark suites and a power flow problem validates the approach.

Conclusions:

• The RV-based MOO framework offers a powerful alternative for addressing COPs.
• The proposed ranking strategy and integrated mechanisms improve the efficiency and effectiveness of evolutionary algorithms for constrained optimization.
• This research opens new avenues for applying advanced MOO techniques to challenging real-world engineering problems.