A υ-Constrained Matrix Adaptation Evolution Strategy With Broyden-Based Mutation for Constrained Optimization.

Area of Science:

• Optimization algorithms
• Computational mathematics
• Evolutionary computation

Background:

• Balancing feasible and infeasible solutions is critical for population-based algorithms solving constrained optimization problems (COPs).
• Existing methods struggle with complex, nonlinear inequality and equality constraints.

Purpose of the Study:

• To develop a novel constraint handling technique for nonconvex COPs.
• To enhance the performance of population-based optimization algorithms in handling complex constraints.

Main Methods:

• Propose a υ-level penalty function to transform COPs into unconstrained problems.
• Introduce Broyden-based mutation to find feasible solutions for infeasible ones.
• Integrate these techniques with the Matrix Adaptation Evolution Strategy (MA-ES).

Main Results:

• The proposed algorithm effectively balances feasible and infeasible solutions.
• Demonstrated superior performance in handling nonlinear inequality and equality constraints.
• Outperformed several state-of-the-art constrained evolutionary optimizers on benchmark problems.

Conclusions:

• The novel constraint handling technique and Broyden-based mutation significantly improve optimization performance.
• The integrated MA-ES-based algorithm offers a robust solution for nonconvex COPs.
• This approach advances the field of constrained evolutionary optimization.