基于竞争算法优化支持向量机的预测模型及其应用

Prediction Model Based on Imperial Competitive Algorithm-Optimized Support Vector Machine and Its Applications

摘要: 提出一种基于帝国竞争算法(ICA)优化的支持向量机模型(ICA-SVM)，该模型利用ICA优化支持向量机(SVM)的惩罚因子和核函数参数，以提升全局搜索能力和收敛速度。考虑元启发式算法存在随机波动性，对ICA-SVM、PSO-SVM开展30次独立重复实验，输出\(R^2\)、MAPE、RMSE的均值与标准差，引入Wilcoxon符号秩检验开展非参数显著性检验；采用留一法交叉验证(LOOCV)开展模型评估并输出定量结果，降低小样本条件下的评估偏差。为验证ICA-SVM的性能，利用标准测试函数将其与粒子群算法优化的支持向量机(PSO-SVM)进行对比分析，结果表明ICA-SVM在收敛精度和收敛速度上均优于PSO-SVM。将该模型应用于天津市城市居民人均可支配收入预测，选取历年天津市与城市居民人均可支配收入高度相关的人均生产总值、产业结构、固定资产投资等六项核心指标构建预测模型。引入SHAP模型解释工具，量化各输入特征对预测结果的贡献程度，挖掘关键驱动因素。结果显示，显著优于传统参数优化方法，这表明该模型具有良好的合理性。将该模型应用于其他城市进行预测且预测结果良好，这证明该模型具有优秀的泛化能力。将ICA-SVM与SVM预测结果进行对比，结果表明ICA-SVM的预测准确度更高。此外，模型拓展应用于行业可支配效能预测，结果显示工程技术行业效能高于管理行业，为政策制定提供有效数据支持。

Abstract: To address the shortcomings of existing hybrid models combining intelligent optimization algorithms with support vector machines (SVMs), such as insufficient global optimization capability and slow convergence speed, this paper proposes an imperial competitive algorithm (ICA)-optimized SVM model (ICA-SVM). Considering the random volatility of meta-heuristic algorithms, 30 independent repeated experiments are carried out for ICA-SVM and PSO-SVM, and the mean values and standard deviations of R2, MAPE and RMSE are reported. The Wilcoxon signed-rank test is introduced for non-parametric significance test. Leave-one-out cross-validation (LOOCV) is adopted for model evaluation with quantitative outputs to reduce evaluation bias under small-sample conditions. The proposed ICA-SVM model utilizes ICA to optimize the penalty factor and kernel function parameters of the SVM, thereby enhancing its global search ability and convergence speed. To validate the performance of ICA-SVM, its optimization capability was compared with that of a Particle Swarm Optimization-optimized SVM (PSO-SVM) using benchmark test functions. The comparative analysis demonstrates that ICA-SVM outperforms PSO-SVM in both convergence precision and convergence speed. The model is applied to predict the per capita disposable income of urban residents in Tianjin City. Six core indicators highly correlated with urban residents’ per capita disposable income—including per capita GDP, industrial structure, and fixed asset investment—are selected to construct the prediction model. SHAP model-agnostic explanation tool is introduced to quantify the contribution degree of each input feature to the prediction results and mine the key driving factors. Results demonstrate that the ICA-SVM significantly outperforms traditional parameter optimization methods, indicating its strong rationality. Furthermore, the model exhibits excellent generalization capability when applied to predict outcomes in other cities. Comparative analysis reveals higher prediction accuracy in ICA-SVM versus conventional SVM. Additionally, the model is extended to predict disposable efficiency across industries, revealing that the efficiency of engineering and technical industries surpasses that of management industries. This finding provides effective data support for policy formulation.