Differential evolution for population diversity mechanism based on covariance matrix.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Heuristic Search

Background:

• Differential Evolution (DE) is a population-based heuristic global search algorithm effective for continuous-domain problems.
• Standard DE can struggle with insufficient local search ability and premature convergence to local optima in complex optimization tasks.
• Existing DE variants often face challenges in maintaining population diversity and achieving robust convergence.

Purpose of the Study:

• To propose an improved Differential Evolution algorithm, termed Covariance Matrix DE (CM-DE), addressing limitations in local search and premature convergence.
• To enhance population diversity and convergence speed through novel parameter adaptation and perturbation strategies.
• To prevent local optima by utilizing population covariance matrix information to monitor individual similarity.

Main Methods:

• Introduced a new parameter adaptation strategy: scale factor F updated using wavelet basis functions (early stage) and Cauchy distribution (later stage); crossover rate CR generated via normal distribution.
• Incorporated a perturbation strategy into the crossover operator to bolster the search capabilities of the DE algorithm.
• Constructed a population covariance matrix, using its variance as an indicator of individual similarity to mitigate low population diversity issues.

Main Results:

• CM-DE demonstrated superior performance against state-of-the-art DE variants (LSHADE, jSO, LPalmDE, PaDE, LSHADE-cnEpSin) on 88 benchmark functions from CEC2013, CEC2014, and CEC2017 test suites.
• On CEC2017 50D optimization, CM-DE outperformed other algorithms on 22-28 out of 30 benchmark functions.
• For CEC2017 30D optimization, CM-DE showed faster convergence on 19 out of 30 benchmark functions, and validated its feasibility on a real-world application.

Conclusions:

• The proposed CM-DE algorithm effectively enhances population diversity and local search ability, overcoming limitations of traditional DE.
• CM-DE exhibits highly competitive performance in terms of solution accuracy and convergence speed compared to leading DE variants.
• The algorithm's feasibility and effectiveness are confirmed through rigorous testing on benchmark functions and a real-world application.