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This paper explores the influence of different turbocharging modes and multi-parameter coordinated control on the performance of compression-ignition (CI) aviation piston engine (APE). Firstly, based on a constructed one-dimensional thermodynamic model of a CI APE, the study investigates the effects of different turbocharging modes and combinations of high and low-pressure stage variable geometry turbines (VGT) on the operational performance of the engine. Subsequently, a novel stepwise approximate multi-objective optimization algorithm is proposed, combining backpropagation neural networks and the non-dominated sorting genetic algorithm II. This algorithm evaluates the influence of multiple control parameters on a two-stage turbocharged engine's performance, achieving a balance between fuel economy and reliability. The research shows that equipping CI APEs with twin VGT for supercharging can notably enhance engine performance, enabling the achievement of favorable power recovery objectives at an altitude of 8000 m. The proposed optimization algorithm exhibits strong predictability and reliability, substantially accelerating the computation speed and reducing the data volume by approximately 95%. At an engine speed of 3887 rpm, compared to the unoptimized conditions, the brake specific fuel consumption of the best scenario at altitudes of 2000 m, 4000 m, 6000 m, and 8000 m is reduced by 7.1%, 7.2%, 8.6%, and 6.9%, respectively. • Influences of different turbocharging modes on the performance of a CI APE are investigated. • A novel stepwise approximate multi-objective optimization method based on a hybrid model is proposed. • Explored the altitude-varying control strategy under coordinated multi-parameter optimization. • Increased the altitude ceiling for the CI APE, reaching 82% power recovery target at 8000 m. [ABSTRACT FROM AUTHOR]