In the assembly of the engine rotor, the unbalance quantity of the rotor has a profound impact on equipment quality. Specifically, the selection and position of blades are crucial factors that determine the level of rotor unbalance. Aiming at the multiple installations and repeated adjustments in the assembly process, we study a variant of the single-stage blade selection and position problem (SSBSP) by considering the tolerance criteria. In this paper, we formulate a novel mixed-integer programming model that extends to multiple-rotor assembly for the first time. The objective is to minimize the maximum residual unbalance. Due to the NP-hard in the strong sense of engine rotor blade selection and position, we devise an improved partheno-genetic algorithm to access a near-optimal solution. Furthermore, local search is introduced for deep search and aims to improve the efficiency of the algorithm. A computational analysis is carried out with the aim of analyzing the performance of our methodology in terms of effectiveness and efficiency. Our experimental results demonstrate the superior performance of the proposed algorithm when compared against state-of-the-art heuristics in the literature in terms of solution quality and efficiency.