QUasi-affine TRansformation Evolutionary (QUATRE) algorithm: A parameter-reduced differential evolution algorithm for optimization problems

Differential Evolution (DE) is arguably a very powerful stochastic real-parameter optimization algorithm, and the performance of DE is highly dependent on parameter control and mutation strategy. Many investigations though have been conducted with regards to parameter control, it is still a tedious but important task for users to make parameter selection regarding to specific problems. This paper presents a new parameter-reduced differential evolution approach, which gets rid of the crossover rate parameter Cr by using an automatically generated crossover matrix and gives a self-adaptive tuning scheme of F value. The only one left parameter in the new proposed algorithm is population size, and it is also can be reduced by a restart with population increase approach. The particles' evolution in the new algorithm can be written in an affine-transformation-like form, so it is named after QUsi-Affine TRansformation Evolutionary (QUATRE) algorithm. The users who use this algorithm do not bother parameter tuning problems and conducted experiments under CEC2013 test suites on real-parameter optimization and COmparing Continuous Optimizers (COCO) framework under Black-Box Optimization Benchmarking (BBOB) show that QUA-TRE algorithm outperforms other state-of-the-art swarm based algorithms including PSO variants, DE variants even some CMA-ES variants.