A differential covariance matrix adaptation evolutionary algorithm for global optimization

Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use for non-linear non-convex functions with parameter linkages. Differential Evolution (DE) is again a very powerful but simple evolutionary algorithm for real parameter optimization. In this article we propose a simple but very efficient hybrid evolutionary algorithm named Differential Covariance Matrix Adaptation Evolutionary Algorithm (DCMA-EA), where it creates new population members by using controlled share of its target and the population mean, the scaled difference from current population and the step-size generated through the Covariance Matrix Adaptation. It also incorporates the selection and crossover strategies of DE. The proposed hybrid algorithm has more pronounced explorative and exploitative behaviors than its two ancestors (CMA-ES and DE). We compare DCMA-EA with original CMA-ES, some of the most known DE-variants: SaDE and JADE, and a PSO-based state-of-the-art real optimizer: DMS-PSO (Dynamic Multi Swarm Particle Swarm optimization) and DE/Rand/1/Bin over a test-suite of 20 shifted, rotated, and compositional numerical benchmarks.