The Editor-in-Chief and the publisher have retracted this article. The article was submitted to be part of a guest-edited issue. An investigation by the publisher found a number of articles, including this one, with a number of concerns, including but not limited to compromised editorial handling and peer review process, inappropriate or irrelevant references or not being in scope of the journal or guest-edited issue. Based on the investigation's findings, the Editor-in-Chief therefore no longer has confidence in the results and conclusions of this article.Jiangze Qu has not responded to correspondence regarding this retraction. Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

With the continuous development of computer technology and the popularization and application of various types of intelligent algorithms, there are also applications in the current administrative judicial system in China. In order to be able to reasonably realize the fairness of criminal justice activities, the relevant deficiencies in the implementation of the supervision of criminal penalty enforcement are made up. In order to reasonably improve the execution plan, the legal authority of judicial administration is established. The implementation of the judicial enforcement program in the administrative law system is researched based on the annealing algorithm. The optimization of the annealing algorithm is used to optimize the execution of the program flow. The results show that the annealing algorithm can optimize this solution.