To address the challenge of multimodal anomaly data governance in ship maintenance-cost prediction, this study proposes a three-stage hybrid data-cleansing framework integrating physical constraints and intelligent optimization. First, we construct a multi-dimensional engineering physical constraints rule base to identify contradiction-type anomalies through ship hydrodynamics validation and business logic verification. Second, we develop a Feature-Weighted Isolation Forest Algorithm (W-iForest) algorithm that dynamically optimizes feature selection strategies by incorporating rule triggering frequency and expert knowledge, thereby enhancing detection efficiency for discrete-type anomalies. Finally, we create a Genetic Algorithm-Ant Colony Optimization Collaborative Random Forest (GA-ACO-RF) to resolve local optima issues in high-dimensional missing data imputation. Experimental results demonstrate that the proposed method achieves a physical compliance rate of 88.2% on ship-maintenance datasets, with a 25% reduction in RMSE compared to conventional prediction methods, validating its superior data governance capability and prediction accuracy under complex operating conditions. This research establishes a reliable data preprocessing paradigm for maritime operational assurance, exhibiting substantial engineering applicability in real-world maintenance scenarios.

Software effort estimation (SEE) serves as a cornerstone of effective software project management, and case-based reasoning (CBR) stands out as one of the most extensively adopted approaches within this domain. Nevertheless, CBR-based SEE models are still plagued by two critical challenges: conventional case retrieval mechanisms lack the ability to differentiate the relative importance of various features, and data scarcity remains a persistent bottleneck. Both issues significantly compromise the estimation accuracy and interpretability of the models. To address these limitations, we propose a SHAP–Mixup synergistic framework that enhances both feature-aware similarity learning and data distribution modeling. Specifically, we introduce (1) a stability-aware SHAP-weighted similarity metric that integrates both the magnitude and variance of feature contributions to improve retrieval robustness, and (2) a density-aware Mixup augmentation strategy that generates synthetic samples guided by local data manifold structure rather than random interpolation. Experimental results on seven benchmark datasets demonstrate that the proposed method reduces MAE and MSE by up to 20.2% on average compared to baseline CBR models, while consistently improving Pred(0.25). Furthermore, by enhancing model interpretability, the proposed method equips project managers with actionable insights into the key drivers of software effort, thereby facilitating more informed and efficient resource allocation. Building on these findings, this study provides a novel and effective pathway for developing SEE models that are more accurate, robust, and transparent.

This paper proposes a novel instance selection (IS) method for multi-target regression (MTR). The proposed method introduces Sparse Modeling Representative Selection (SMRS) to characterize the self-representativeness of instances, where a block-sparse coefficient matrix is learned to identify representative training samples. Considering that MTR data contain both input-space structures and multi-target output-space dependencies, we assume that the self-representative relationships in the input and output spaces should be consistent. Based on this assumption, a Frobenius-norm-based discrepancy minimization term and a Hilbert-Schmidt Independence Criterion (HSIC)-based relevance maximization term are incorporated to encourage the model to learn consistent and statistically dependent self-representation structures across the two spaces. To capture nonlinear instance relationships, the proposed model is further extended to a kernelized formulation. In addition, an ensemble framework is developed to exploit target correlations from multiple target-aware subspaces, thereby improving the robustness of instance selection. A parameter-free adaptive thresholding strategy is also designed to automatically determine the selected subset from the learned instance-score distribution. Extensive experiments on multiple benchmark MTR datasets demonstrate that the proposed methods can effectively reduce the training data size while preserving or improving downstream predictive performance compared with representative instance selection and data reduction baselines.

To address the problem in predicting target prices for ship equipment orders where small sample sizes, high feature dimensions, and strong business constraints lead traditional models to overfit and have insufficient generalization ability, a method combining GAN and NVP-D for small-sample data augmentation and price prediction is proposed. This method integrates the advantages of adversarial training in Generative Adversarial Networks (GAN) with the explicit density estimation and stable training characteristics of Normalizing Flow NVP-D. By using dual-weight collaborative optimization of the objective function, it alleviates gradient vanishing and mode collapse, generating high-quality virtual samples that closely follow the real data distribution. Redundant features are removed using Boruta-Lasso joint feature selection to reduce model complexity. CatBoost is employed as the prediction model to complete price estimation. Experiments were conducted on a ship equipment dataset with 33 original samples and 24 features, strictly following the standard procedure of augmentation only within the training set and 5-fold cross-validation. Compared with NVP, NVP-G, MAF, traditional GAN, and Mixup methods, the results show that the proposed integrated model achieves optimal performance when augmenting 400 samples, with an RMSE of 0.0675, MAE of 0.0510, and R² of 0.9228. After feature selection, prediction accuracy further improves, with RMSE decreasing to 0.0615 and R² increasing to 0.9341. Limited by the scale of the original samples, the statistical robustness and cross-dataset generalization capability of this method still need validation with larger datasets. However, under the current small-sample constraints, it can effectively alleviate modeling bottlenecks and provide high-precision support for equipment procurement argumentation, budget preparation, and cost control in stages.

To address three major industry pain points—the lack of quantified profit-sharing standards in the two-stage pricing under the separation model of military research and production, the absence of stable Nash equilibrium in single-layer synchronous optimization, and insufficient incentives for full-cycle process optimization in design units—this paper constructs a two-level Stackelberg leader–follower game model with the general contracting unit as the leader and design and general contracting units as followers. This aligns with current prototype incentives and phased pricing policies for production rewards and penalties. At the theoretical level, it improves the complete proof system for the two-stage concave profit two-level Stackelberg Nash equilibrium, distinguishes the mathematical differences in equilibrium existence between sequential decision-making and synchronous optimization, and extracts general rules for phased differentiated profit sharing: high-innovation segments should be allocated more profit weight; simply maximizing total alliance profit may cause imbalanced interests, while introducing a minimum net profit-weighted objective can achieve Pareto improvements without profit loss. This conclusion can be applied to multi-stage general contracting scenarios across industries, such as EPC and military–civil collaborative innovation, enriching the basic theory of profit sharing and hierarchical games. Theoretically, the existence of the lower-level Nash equilibrium is proven using Brouwer’s fixed-point theorem, and combining it with the strictly monotonically decreasing feature of the best response function, uniqueness of the equilibrium is derived. Multiple sets of differentiated initial values are simulated to rule out multi-equilibrium bifurcation risk. The model incorporates the military’s reward and penalty policies as rigid exogenous constraints, sets dual individual rationality constraints of ‘cooperative profit greater than baseline profit with no allocation, and both parties’ net profit non-negative,’ and introduces differentiated cost-reduction efficiency and quadratic increasing effort costs to characterize the heterogeneous input of the two types of development entities. For models with piecewise nonlinearity and multi-constraint nonconvex structures, this paper modifies the standard PSO into a Bi-PSO solving framework through hierarchical temporal adaptation. It does not innovate the underlying particle update mechanism and is only used to match the sequential decision order of the leader–follower game. By comparing five algorithms—IPM, GA, SA, DE, and adaptive PSO—through 20 repeated simulations: gradient-based interior point methods easily get stuck in locally invalid solutions that violate cooperation thresholds; differential evolution has the best numerical global search performance, but all general evolutionary algorithms optimize allocation and effort variables simultaneously, disrupting the Stackelberg hierarchical timing. Only Bi-PSO maintains consistent game logic. Using a pricing case for a certain type of equipment and jointly calibrating all parameters with policy documents, three simulation scenarios were set up: no allocation, equal 50/50 split, and single-layer profit maximization. Under the no-allocation mode, R&D investment from the design unit drops to zero and alliance benefits plummet; a blanket equal split ignores differences in technical contributions across two stages, leading to clear efficiency losses; single-layer optimization only pursues total profit maximization, causing a severe imbalance in profit distribution. The two-layer basic framework can achieve the upper limit of alliance benefits, and by adding a weighted optimization goal that considers both total profit and cooperation fairness, it can achieve equal net profits for both parties without reducing overall profit. Through single-parameter sweeps and two-factor heatmap simulations, the study further revealed the coupled effects of main party efficiency and mass production rewards and penalties on equilibrium input and optimal sharing ranges. A robust check was performed by replacing the logarithmic concave output function, producing a standardized allocation range resilient to parameter perturbations: optimal split for the prototype stage is 0.4–0.6 for the design unit, and for mass production stage 0.7–0.9. The findings suggest that high-contribution stages in multi-phase collaboration contracts should receive more benefits, and a weighted fairness objective can achieve Pareto improvements. These conclusions can extend to multi-stage collaboration scenarios such as EPC and military–civilian cooperation. Theoretically, this research further completes the equilibrium proof system for two-party concave payoff two-layer games, providing a new reference for the theory of phased differentiated benefit-sharing contracts in the military sector. Methodologically, it proposes a two-layer intelligent solving tool adapted to leader–follower sequential decisions, effectively mitigating issues where single-layer model equilibria fail or analytical algorithms struggle with multi-constraint nonconvex games. The results can provide quantitative support for the military, general contracting unit, and design unit in drafting equipment incentive pricing contracts and managing full-cycle cost collaboration.

Predicting maintenance costs for industrial equipment faces the dual challenges of small sample sizes and long-tailed data distributions. Existing methods struggle to ensure both point prediction accuracy and reliable intervals for the tail. This paper proposes the Swarm-driven Adaptive Data Augmentation and Heterogeneous Ensemble with Distribution-Aware Quantile Fusion (SADA-HEDQF) framework. In the SADA stage, Differential Evolution automatically derives high-order features within a domain-specific operator space, and Particle Swarm Optimization optimizes the parameters of the Synthetic Minority Oversampling Technique, enhancing data from both feature and sample dimensions. In the HEDQF stage, a multi-objective Whale Optimization Algorithm constructs a decorrelated heterogeneous base learner pool, and a Quantile Long Short-Term Memory network is designed as the gated fusion meta-learner. Driven by the quantile loss, the meta-learner simultaneously outputs point estimates and multiple confidence intervals. Experiments on 673 real ship maintenance records demonstrate that SADA-HEDQF reduces the point prediction RMSE by 25.8% compared to the best single model, and the error in high-cost regions drops by 46.4%. The normalized average width of the 90% confidence interval is 0.379, and the Coverage Width-based Criterion with penalty on the tail subset reaches 294.5, both significantly outperforming benchmarks such as Quantile Regression Forest. Ablation studies and SHAP analysis quantify the layered contributions of each component and verify the physical interpretability of the derived features, respectively. The framework provides effective prediction and uncertainty quantification support for small-sample long-tailed regression tasks, such as ship maintenance cost prediction, and shows potential for transfer to similar structured prediction scenarios.