Constrained evolutionary optimization by means of (μ + λ)-differential evolution and improved adaptive trade-off...

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Constrained optimization problems present significant challenges in various scientific and engineering fields.
• Existing evolutionary algorithms often struggle with effectively handling complex constraints, limiting their applicability.
• The need for robust and efficient algorithms to solve real-world constrained optimization tasks is critical.

Purpose of the Study:

• To develop a novel and effective algorithm for solving constrained optimization problems.
• To enhance the global exploration capabilities of differential evolution through improved mutation strategies.
• To introduce an adaptive trade-off mechanism for superior constraint handling.

Main Methods:

• A (μ + λ)-differential evolution framework incorporating three mutation strategies (rand/1, current-to-best/1, rand/2) and binomial crossover.
• An improved current-to-best/1 mutation strategy that leverages the feasibility proportion of the population.
• An adaptive trade-off model with distinct mechanisms for infeasible, semi-feasible, and feasible population situations.

Main Results:

• The proposed (μ + λ)-constrained differential evolution ((μ + λ)-CDE) algorithm was tested on 24 benchmark functions from CEC2006.
• The (μ + λ)-CDE achieved the best known solutions for 23 out of 24 test functions.
• The algorithm successfully solved 21 test functions in all runs, demonstrating high robustness and effectiveness.

Conclusions:

• The developed (μ + λ)-CDE algorithm is a highly promising method for tackling constrained optimization problems.
• A self-adaptive version of the (μ + λ)-CDE emerged as the most competitive algorithm among CEC2006 entries.
• The proposed approach offers significant advancements in handling complex constraints within evolutionary optimization.