The agile Earth observation satellite scheduling problem (AEOSSP) with time-dependent transition time is a combinatorial optimization challenge. Due to its NP-hardness, problem-tailored methods are sensitive to instances and require massive computational overhead. Recently, deep reinforcement learning (DRL) models have shown promise in efficiently addressing the AEOSSP. However, these models may make decision mistakes in specific scenarios due to prioritizing maximizing average reward expectation over individual decision accuracy during DRL training, directly leading to resource wastage. To address these issues, we propose a reconstruction model (RCM), which is a DRL-based two-stage construction model (CM), including a CM and a reconstruction mechanism (RM). RCM constructs solutions initially using a DRL-trained CM, which are subsequently refined by RM. CM utilizes a more efficient network for policy representation to make decisions. RM applies two operators, "repair" and "removal," with a "repair-removal-repair" solution reconstruction process to identify and rectify decision mistakes from CM, offering a modular component to enhance the stability and solution quality. Experimental results demonstrate that the proposed RCM outperforms the state-of-the-art AEOSSP iterative search method, achieving such performance within a computational time of 0.1 s. Additionally, CM surpasses the state-of-the-art DRL policy model and RM can effectively rectify decision errors or suboptimalities, underscoring its effectiveness in enhancing DRL outcomes.

The quadratic unconstrained binary optimization (QUBO) is a well-known NP-hard problem that takes an $n\times n$ matrix $Q$ as input and decides an $n$-dimensional 0-1 vector $x$, to optimize a quadratic function. Existing learning-based models that always formulate the solution process as sequential decisions suffer from high computational overload. To overcome this issue, we propose a neural solver called the Value Classification Model (VCM) that formulates the solution process from a classification perspective. It applies a Depth Value Network (DVN) based on graph convolution that exploits the symmetry property in $Q$ to auto-grasp value features. These features are then fed into a Value Classification Network (VCN) which directly generates classification solutions. Trained by a highly efficient model-tailored Greedy-guided Self Trainer (GST) which does not require any priori optimal labels, VCM significantly outperforms competitors in both computational efficiency and solution quality with a remarkable generalization ability. It can achieve near-optimal solutions in milliseconds with an average optimality gap of just 0.362\% on benchmarks with up to 2500 variables. Notably, a VCM trained at a specific DVN depth can steadily find better solutions by simply extending the testing depth, which narrows the gap to 0.034\% on benchmarks. To our knowledge, this is the first learning-based model to reach such a performance.