Varied granularity encoding based evolutionary algorithm for multi-objective intensity-modulated radiation therapy optimization

Intensity-modulated radiation therapy is an interesting multi-objective optimization problem, which holds a large number of aperture shape-related variables, posing a stiff challenge to existing algorithms. To efficiently solve this problem, we propose a varied granularity encoding method in this paper, where the granularity of encoding of the shape in the multi-leaf collimator is progressively refined during the optimization. Specifically, at the beginning of the search, a coarse encoding is adopted by dividing the aperture shape-related variables into several groups and representing each group by one bit, which achieves effective search space reduction for the aperture shape. During the evolution, the granularity of encoding aperture shape-related variables is gradually varied from coarse to fine by reducing the size of each group until only one variable is contained in the group. With the proposed varied granularity encoding method, an evolutionary algorithm is suggested based on a popular evolutionary multi-objective framework (NSGA-II), where an adaptive switching method is developed to determine whether the granularity level needs to be reduced according to the convergence status of the population. The experiment empirically investigates the performance of the proposed varied granularity encoding method based evolutionary algorithm on eight clinical instances with the number of aperture shape-related variables ranging from 1932 to 3180. Compared with seven representative evolutionary algorithms and one traditional direct aperture optimization algorithm, the proposed algorithm demonstrates statistically significant improvements in hypervolume, inverted generational distance, and dose-volume histogram. The experimental results reveal that the proposed algorithm not only exhibits competitiveness but reduces computational time in radiotherapy optimization.