In this study, an optimization method using various multi-output regression models as model proxies within the NSGA-II framework was applied to determine the geometric parameters (P, W, D) of L-shaped twisted tape inserts for achieving the optimal overall heat transfer performance in a circular heat exchange tube. Herein, 4 multi-output regression models, namely, MOLR, MOSVR, MOGPR, and BPNN, were selected as proxy models and trained on a dataset containing 74 groups of data. The training results indicated that the MOGPR model, balancing high accuracy and low error conditions, exhibited moderate training times among the four algorithms. BPNN showed a comparatively lower comprehensive training effect, obtaining training accuracy close to that of the MOGPR algorithm but with approximately twice the training time. The worst fitting performance was gained with the MOSVR algorithm. Due to its fitting performance, the MOSVR algorithm was excluded from the subsequent NSGA-II model proxy. Through multi-objective optimization with NSGA-II, the optimal structural dimensions for three sets of L-shaped twisted tape inserts were obtained to achieve the best overall heat transfer efficiency within the tube.