An adaptive Cauchy differential evolution algorithm for global numerical optimization.

Area of Science:

• Optimization Algorithms
• Computational Intelligence
• Evolutionary Computation

Background:

• Differential Evolution (DE) performance is sensitive to control parameter settings (scaling factor F, crossover rate CR, population size NP).
• Existing adaptive and self-adaptive parameter control methods offer improvements but adapting parameters effectively remains challenging.
• Proper parameter adaptation is crucial for optimizing DE algorithm efficiency and robustness.

Purpose of the Study:

• To develop a novel adaptive parameter control strategy for Differential Evolution.
• To enhance the robustness and performance of DE algorithms across diverse optimization problems.
• To enable each individual within the DE population to possess and adapt its own unique control parameters.

Main Methods:

• Proposed an adaptive parameter control DE algorithm where each individual maintains its own control parameters.
• Implemented a parameter adaptation mechanism based on the average parameter values of successfully evolved individuals.
• Utilized the Cauchy distribution to introduce variability, allowing parameters to be near or far from the average for potential improvement.

Main Results:

• The proposed adaptive DE algorithm demonstrated superior robustness compared to the standard DE algorithm.
• Experimental results indicated improved performance over several state-of-the-art adaptive DE algorithms.
• The algorithm effectively solved a range of unimodal and multimodal optimization problems.

Conclusions:

• The presented adaptive parameter control strategy significantly enhances DE algorithm robustness.
• Individualized parameter adaptation using Cauchy distribution shows promise for improving DE performance.
• This approach offers a more effective method for tackling complex optimization challenges with Differential Evolution.