AUTHOR=Yang Yanhong , Zhang Mian , Wei Kun 
  
TITLE=Multi-objective optimization of beam transport in medical heavy ion accelerators using an improved non-dominated sorting differential evolution algorithm (NSDE)
  
JOURNAL=Frontiers in Mechanical Engineering
  
VOLUME=Volume 11 - 2025
  
YEAR=2026
  
URL=https://www.frontiersin.org/journals/mechanical-engineering/articles/10.3389/fmech.2025.1736300
  
DOI=10.3389/fmech.2025.1736300
  
ISSN=2297-3079
  
ABSTRACT=To address the issues of high-dimensional coupling parameters easily falling into local optima and multi-objective conflicts in the beam transport of medical heavy ion accelerators, this paper proposes an improved non-dominated sorting differential evolution (NSDE) algorithm. The algorithm employs inverse learning for initialization and introduces an adaptive mechanism to adjust the mutation factor and crossover probability online, balancing exploration and exploitation. Additionally, it incorporates local enhancement based on crowding distance in particle swarm optimization (PSO) to refine non-dominated elite solutions. Large-scale experiments based on FLUKA Monte Carlo coupled simulation (nine-dimensional decision variables) have shown that the improved NSDE has increased the beam transport efficiency from the baseline of 92.42% to 99.21% (an improvement of 6.79%), while also achieving continuous improvements in key physical indicators such as the beam spot size at the end point, system power consumption, and energy retention rate. The research indicates that the proposed method exhibits significant advantages in enhancing optimization quality and maintaining robustness, making it suitable for accelerator engineering optimization that demands stringent real-time performance and multi-objective accuracy.