Design and optimization of diffraction-limited storage ring lattices based on many-objective evolutionary algorithms

Multi-objective evolutionary algorithms (MOEAs) are typically used to optimize two or three objectives in the accelerator field and perform well. However, the performance of these algorithms may severely deteriorate when the optimization objectives for an accelerator [A1] are equal to or greater than four. Recently, many-objective evolutionary algorithms (MaOEAs) that can solve problems with four or more optimization objectives have received extensive attention. In this study, two diffraction-limited storage ring (DLSR) lattices of the ESRF-EBS [A2] type with different energies were designed and optimized using three MaOEAs and a widely used MOEA. The initial population[A3]  was found to have a significant impact on the performance of the algorithms and was carefully studied. The performances of the four algorithms were compared, and the results demonstrated that the grid-based evolutionary algorithm (GrEA) had the best performance. MaOEAs were applied in many-objective optimization of DLSR lattices for the first time, and lattices with natural emittances of 116 pm∙rad and 23 pm∙rad were obtained at energies of 2 GeV and 6 GeV, respectively, both with reasonable dynamic aperture and local momentum aperture (LMA). This work provides a valuable reference for future multi-objective optimization of DLSRs.