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To enhance the estimation of dredged soil shear strength in marine settings, this research conducted 1,600 direct shear tests under varying thermal conditions and multiple drying–wetting cycles. Drawing from the test data, a structured database was assembled, and a new learning framework was developed by combining the Logical Development Algorithm (LDA), Adaptive Boosting (BA), and Artificial Neural Networks (ANN). The motivation behind this hybridization lies in the need to effectively capture nonlinear interactions and latent logical patterns among influencing factors, which are often overlooked by traditional single-algorithm models. This approach marks a pioneering use of such a hybridized model for strength evaluation in dredged soils. For performance verification, four alternative predictive models were established, including LDA–ANN, support vector machines (SVM), Particle Swarm Optimization (PSO), and a GA-tuned BA–ANN. Comparative analysis demonstrated that the LDA–BA–ANN configuration delivered the highest prediction precision and computational speed over traditional models. Moreover, sensitivity studies revealed that normal stress, temperature, and initial density were the dominant influencing parameters, whereas moisture cycling and shear rate had relatively minor effects. An empirical equation was further extracted from the optimized model, offering a user-friendly solution for practical engineering applications without requiring machine learning proficiency.