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

Yong Wang¹, Zixing Cai

¹School of Information Science and Engineering, Central South University, Changsha 410083, People's Republic of China. ywang@csu.edu.cn

Evolutionary Computation

|September 3, 2010

Summary

This study introduces a novel (μ + λ)-constrained differential evolution ((μ + λ)-CDE) algorithm for complex optimization problems. The new method demonstrates superior performance, solving 21 out of 24 benchmark functions and achieving top results on 23.

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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.