## 1 Introduction
[38] proposed a dynamic scheduling algorithm with a mission merging strategy with the aims of the minimum perturbation, maximum satisfaction ratio, and minimum energy consumption. [PERSON] et al. [39] established a multi-objective scheduling model for the observation-mission-scheduling problem in uncertain environments and proposed a hybrid local replanning strategy. It is worth noting that these two multi-objective dynamic scheduling algorithms [38; 39] search for the optimal solution by simple heuristic operators and can only find one or a few optimal non-dominated solutions. However, in practical observational applications, multiple optimal alternative observation plans are necessary and crucial. The multiple optimal alternative solutions facilitate the decision-maker of the EOS system in selecting the most appropriate observation plan based on the current status of the EOS and the observation environment. Therefore, it is urgent and meaningful to design an effective multi-objective scheduling algorithm, which can optimize the profit and perturbation simultaneously. It is evident that the initial observation plan is the scheduling plan with the minimum perturbation and lowest profits as there are no dynamic tasks scheduled. In addition, it is essential to take both the initial observation plan and dynamic tasks into consideration in order to achieve an observation scheme with higher profit in the mission observation scheduling. Consequently, significant perturbations are unavoidable for the scheduling plans with high profits. Therefore, in the dynamic mission scheduling considering the profit and perturbation (DMP-PP), maximizing profit and minimizing perturbation are strongly opposed to each other. However, the existing multi-objective evolutionary algorithms (MOEAs) perform poorly in addressing the DMP-PP, particularly in terms of solution diversity. The main reasons are that evolutionary operators, such as crossover and mutation, will introduce significant perturbations, and these perturbations will accumulate during the iteration process. Consequently, the non-dominated solutions obtained by existing MOEAs are mostly distributed in solution spaces with high perturbations. To address this issue, we develop a multi-objective dynamic mission-scheduling algorithm (MODMSA) based on the SPEA2. The core idea of the MODMSA is to enhance the exploration of solution space with low perturbations by searching the solution space in ascending order according to the perturbations. Specifically, the MODMSA gradually expands the maximum allowable perturbation with the iterations and retains the non-dominated solutions within the limited perturbation in the archive. In the MODMSA, a novel two-stage individual representation and a minimum perturbation random initialization are designed to reduce perturbation generated during the population initialization and decoding. The multi-point crossover and greedy mutation are improved based on the features and domain knowledge of the DMP-PP. In addition, a profit-oriented local search algorithm is introduced into the SPEA2 to further improve the quality of the solutions. Most importantly, an adaptive perturbation control strategy is presented to gradually increase the maximum allowable perturbation with the iterations. The main contributions and innovations of this paper are as follows:  
* A mathematical model for the multi-objective dynamic scheduling problem is formulated to maximize the observation profit and minimize the perturbation. * A multi-objective dynamic mission-scheduling algorithm (MODMSA) is developed for the DMP-PP. To improve the diversity and quality of non-dominated solutions, a two-stage individual representation, a minimum perturbation random initialization, multi-point crossover, and greedy mutation are designed based on the characteristic of the DMP-PP. A profit-oriented local search algorithm is proposed to improved the profits of the solutions, and an adaptive perturbation control strategy is developed to enhance the exploitation in the solution space.