Machine learning-driven multi-objective optimisation of shape-memory programming parameters in 4D-printed PLA

Abstract

4D printing extends additive manufacturing by introducing time-dependent functionality through stimuli-responsive feedstocks such as shape-memory polymers (SMPs). In 4D-printed PLA, performance is governed by programming temperature, holding time, and recovery temperature, whose effects are reflected in recovery time, shape fixity ratio, and shape recovery ratio. This study combines a replicated 49-condition Latin-square design, machine-learning surrogate models, NSGA-II multi-objective optimisation, and experimental validation to identify a Pareto-optimal process window. Eight regression models were evaluated using leave-one-condition-out (LOCO) cross-validation with nested hyperparameter selection. The surrogates achieved LOCO R2 values of 0.973 (RMSE 7.29 s) for recovery time, 0.874 (1.17 percentage points, pp) for the shape fixity ratio, and 0.975 (4.31 pp) for the shape recovery ratio. The shape fixity ratio increased from 90.2% to 98.8% between 50 and 55 °C before plateauing, with no significant additional effect of holding time. NSGA-II identified a knee point at 67.5 °C programming temperature, 2.0 min holding time, and 80.0 °C recovery temperature, predicting a recovery time of 3.14 s, shape fixity ratio of 99.72%, and shape recovery ratio of 91.70%. Across five validation points, maximum absolute deviations were 0.36 s, 0.75 pp, and 3.82 pp for recovery time, shape fixity ratio, and shape recovery ratio.