1. A dispersion compensation design system, comprising: a memory; and at least one processor connected with the memory, configured to: set a changed value for an amount of dispersion compensation for at least one of spans connecting nodes constituting an optical network; determine whether respective paths in the optical network are capable of transmission on an assumption that the amount of dispersion compensation is updated with the changed value, and classify one or more of the paths as second category paths based on the determination results, wherein a path is classified as the second category path when the path itself is incapable of transmission but a longer path that includes the path and is capable of transmission exists, and capability of transmission is determined based on whether amounts of cumulative dispersion of the respective paths are within a range; compare a retained previous classification result with a latest classification result, and update the amount of dispersion compensation for the at least one of the spans with the changed value and retain the latest classification result when a number of the second category paths in the latest classification result is less than a number of the second category paths in the retained previous classification result; and prevent use of combinations of amounts of dispersion compensation applied to the spans in the second category paths in the latest classification result, and repeat setting of the changed value, the classification of the paths, and updating of the amount of dispersion compensation when not all of the paths in the optical network are capable of transmission, wherein one or more of the paths are classified as first category paths and one or more of the paths are classified as the second category paths, wherein a path is classified as the first category path when the path itself is capable of transmission and all shorter paths included in the path are capable of transmission, the amount of dispersion compensation is updated for the at least one of the spans with the changed value and retain the latest classification result when all the first category paths in a retained initial classification result are still capable of transmission in the latest classification result, and the number of the second category paths in the latest classification result is less than the number of the second category paths in the retained previous classification result.