Multi-Objective Machine Learning Optimization of Cylindrical TPMS Lattices for Bone Implants

This study presents a multi-objective optimization framework for designing cylindrical triply periodic minimal surface (TPMS) lattices tailored for bone implant applications. Using an artificial neural network (ANN) as a surrogate model trained on simulated data, four key properties-ultimate stress (U), energy absorption (EA), surface area-to-volume ratio (SA/VR), and relative density (RD)-were predicted from seven lattice design parameters. To address anatomical variability, a novel implant size-based categorization (small, medium, and large) was introduced, and separate optimization runs were conducted for each group. The optimization was performed via the NSGA-II algorithm to maximize mechanical performance (U and EA) and surface efficiency (SA/VR), while filtering for biologically relevant RD values (20-40%). Separate optimization runs were conducted for small, medium, and large implant size groups. A total of 105 Pareto-optimal designs were identified, with 75 designs retained after RD filtering. SHapley Additive exPlanations (SHAP) analysis revealed the dominant influence of thickness and unit cell size on target properties. Kernel density and boxplot comparisons confirmed distinct performance trends across size groups. The framework effectively balances competing design goals and enables the selection of size-specific lattices. The proposed approach provides a reproducible pathway for optimizing bioarchitectures, with the potential to accelerate the development of lattice-based implants in personalized medicine.