## 2 Materials and Methods
### Autocontouring Algorithm  
A tumor-autocontouring algorithm [36] has been developed in-house using a U-Net architecture [25], whose hyperparameters are optimized with Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [37]. Compared to the previous version of the algorithm based on pulse-coupled neural networks [32], this algorithm, originally developed by [PERSON] et al. [38] and further improved by [PERSON] et al. [36], is more robust, having the capability of autocontouring challenging tumor sites such as the liver and prostate. As shown by [PERSON] et al. [36], the algorithm also outperformed the standardized segmentation algorithms, including non-optimized U-Net [25] and nnU-Net [39]. CMA-ES is a stochastic, population-based optimization technique designed for the real-parameter optimization of non-linear, non-convex functions. The optimization process begins by generating a population of candidate solutions sampled randomly from a normal distribution. After evaluating the objective function of each solution, the best portion of the population is chosen, and the corresponding covariance matrix is computed to modify the shape of the next sampling distribution. This allows the search to move in the directions of the previously successful steps, potentially leading to rapid convergence to the global minimum. As the clinical standard for tumor segmentation is manual contouring by experts, the algorithm design accounts for the contouring tendencies of each expert in each session for a patient. This is achieved through PES-specific hyperparameter optimization (HPO) and training of the algorithm. The set of six hyperparameters--the number of consecutive convolutions before or after each pooling or up-convolution, filter size for convolutions, the number of feature maps, the number of poolings, the initial learning rate of the Adam optimizer, and the number of training images--was independently optimized for each PES within specified search ranges to obtain a PES-specific U-Net model. With 30 patients, 3 experts, and 2 sessions involved in this study, a total of 180 different PES-specific U-Net models were obtained. A potential clinical workflow for implementing the algorithm is shown in Figure 1. The overall aim of HPO and training (step #3 in Figure 1) was to achieve \(\geq\) 0.9 contouring accuracy from the testing images, measured by DC (\(\in\)[0, 1], where 1 represents complete agreement) between manual contours and autocontours. Since the mean (standard deviation (SD)) of intra- and inter-observer variations in experts' manual contouring for lung cancer patients were previously found to be 0.88 (0.04) and 0.87 (0.04), respectively [32], a comparable number of 0.9 was set as a goal to determine reasonable autocontouring accuracy. The HPO and training process starts with the first iteration, in which 10 hyperparameter sets (solutions) are sampled using CMA-ES. The size of the solution population for CMA-ES was maintained at 10 for faster execution time for all PES cases. Each solution is then used to construct a modified U-Net, which is subsequently trained usingthe Dice loss function. The number of epochs for the training process of each solution is determined by an early-stopping method. This method was implemented to prevent the networks from overfitting to the training images, rather than generalizing to all imaging data (training, validation, and testing images). The early-stopping point (optimal number of epochs) below 15,000 is found for each solution by monitoring the validation accuracy. This process was terminated after 10 iterations for the entire solution population, which resulted in a validation accuracy of ~0.9 for all PES cases. The empirically determined training-validation-testing ratio of 160-70-70 was used in this study (with a search range of [10; 160] for the number of training images) for each PES-specific HPO and training, with the last 70 testing images unseen by the algorithm before testing.