A partition-based optimization model and its performance benchmark for Generative Anatomy Modeling Language

This paper presents a novel iterative approach and rigorous accuracy testing for geometry modeling language - a Partition-based Optimization Model for Generative Anatomy Modeling Language (POM-GAML). POM-GAML is designed to model and create anatomical structures and their variations by satisfying any imposed geometric constraints using a non-linear optimization model. Model partitioning of POM-GAML creates smaller sub-problems of the original model to reduce the exponential execution time required to solve the constraints in linear time with a manageable error.

We analyzed our model concerning the iterative approach and graph parameters for different constraint hierarchies. The iteration was used to reduce the error for partitions and solve smaller sub-problems generated by various clustering/community detection algorithms. We empirically tested our model with eleven graph parameters. Graphs for each parameter with increasing constraint sets were generated to evaluate the accuracy of our method.

The average decrease in normalized error with respect to the original problem using cluster/community detection algorithms for constraint sets was above 63.97%. The highest decrease in normalized error after five iterations for the constraint set of 3900 was 70.31%, while the lowest decrease for the constraint set of 3000 was with 63.97%. Pearson correlation analysis between graph parameters and normalized error was carried out. We identified that graph parameters such as diameter, average eccentricity, global efficiency, and average local efficiency showed strong correlations to the normalized error.

We observed that iteration monotonically decreases the error in all experiments. Our iteration results showed decreased normalized error using the partitioned constrained optimization by linear approximation to the non-linear optimization model.