A Fuzzy Rule-Based Penalty Function Approach for Constrained Evolutionary Optimization.

Area of Science:

• Optimization Theory
• Computational Intelligence
• Mathematical Programming

Background:

• Conventional penalty functions for constrained optimization are simple but lack robustness.
• Adaptive penalties aim to improve robustness but can be complex.
• Parameter dependency is a key challenge in existing constraint handling techniques.

Purpose of the Study:

• To propose a novel fuzzy rule-based penalty function approach for single-objective nonlinearly constrained optimization problems.
• To overcome the limitations of conventional and adaptive penalty methods, particularly parameter dependency.
• To develop a robust and effective constraint handling strategy using fuzzy logic.

Main Methods:

• A Mamdani type IF-THEN rule-based fuzzy inference system was developed.
• The fuzzy system incorporates criteria for self-adaptive penalty without explicit mathematical mapping.
• The approach was validated using standard optimality theorems in mathematical programming.

Main Results:

• The proposed fuzzy penalty function approach demonstrated superior performance compared to self-adaptive penalty methods.
• Simulation results indicate competitive performance against other complex constraint handling strategies.
• Empirical validation confirmed the effectiveness of the fuzzy approach in handling nonlinear constraints.

Conclusions:

• The fuzzy rule-based penalty function offers a robust and effective alternative for constrained optimization.
• This novel approach mitigates parameter dependency issues inherent in traditional methods.
• The fuzzy logic system provides a competitive and potentially superior method for handling complex constraints in optimization.