This paper proposes a novel Independent Success History Adaptation Competitive Differential Evolution (ISHACDE) algorithm to address the functional optimization problems and the Space Mission Trajectory Optimization (SMTO). ISHACDE is developed based on the efficient optimizer Competitive Differential Evolution (CDE) and integrates an independent success history adaptation scheme. This scheme inherits the hypothesis from Success History Adaptive Differential Evolution (SHADE) that the scaling factor F and crossover rate Cr from success evolution may contribute to accelerating the evolution of the whole population, and we further hypothesize that the independent evolution of F in CDE may perform better. We conduct comprehensive numerical experiments on median-scale CEC2017, large-scale CEC2020, small-scale CEC2022, and the single-objective GTOPX benchmark to evaluate the performance of ISHACDE. Ten state-of-the-art optimizers and ten recently proposed optimizers are employed as competitor algorithms. The experimental results and statistical analysis confirm the competitiveness of the proposed ISHACDE against twenty optimizers, and the ablation experiments practically prove the effectiveness of the independent success history adaptation scheme. The source code of this research can be found in https://github.com/RuiZhong961230/ISHACDE.