In recent years, Deep Reinforcement Learning (DRL) models have demonstrated potential in effectively addressing the Agile Earth Observation Satellite Scheduling Problem (AEOSSP). However, these policy models prioritize optimizing overall policy expectations over individual decision accuracy, resulting in decision errors in certain scenes. To mitigate this issue, we propose a DRL-based Self-Repair Construction Method (SRCM), which is a two-stage method that includes an Improved Construction Model (ICM) and a Self-Repair Process (SRP). The ICM, an encoder-decoder based neural policy model, is specifically designed to construct initial solutions for the AEOSSP. The SRP incorporates two mechanisms relaxation-insertion and relaxation-masking to investigate and repair decision-making errors in DRL model solutions. Comparative experiments demonstrate that the proposed SRCM surpasses the state-of-the-art problem-specific meta-heuristics in both solution quality and timeliness. The results from our model study indicate that the ICM within SRCM outperforms other neural policy models in extensive validations. Moreover, the mechanism study of the SRP shows that decision-making errors are prevalent across all test neural policy models and confirms the effectiveness of the SRP in rectifications.

Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto sub-sets (PSs) corresponding to a single Pareto front (PF), resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these PSs. Widely used to solve MMOPs, evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the solutions. To enhance performance in solving MMOPs, this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity improving. Specifically, a hybrid operator mechanism is devised to ensure the exploration of the decision space in the early stage and approximation to the optima in the latter stage. Moreover, an elitist-assisted differential evolution mechanism is designed for the early exploration stage. In addition, a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and PSs. Experimental studies on 11 widely used benchmark instances from a test suite verify the superiority or at least competitiveness of the proposed methods compared to five state-of-the-art algorithms tailored for MMOPs.