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Generally, the performance of evolutionary algorithms (EAs) greatly depends on the setting of their control parameters. Many adaptive setting technologies have been developed to solve the time-consuming task of parameter settings. However, the adaptive technologies for the grey prediction evolution algorithm (GPE), which was proposed by Hu et al. in 2020 with two control parameters, have not been investigated. This paper proposes four adaptive GPE algorithms according to three typical adaptive technologies, i.e. probability distributions, statistics and mathematical models in the field of EAs. Four proposed adaptive GPE are separately based on the uniform distribution (aGPEu), normal distribution (aGPEn), average fitness (aGPEa) and chaotic sequences (aGPEc). The performance of the four proposed adaptive GPE algorithms is evaluated on CEC2014, CEC2017 benchmark functions and a suite of eight engineering constrained design problems. The experimental results show the superiority and competitiveness of all the four proposed algorithms.