Study of solution diversity in multi-objective optimization of storage ring lattice

Abstract

Evolutionary algorithms, including multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), have been widely used for storage ring lattice designs, showing good performance in searching the optimal objective function values (i.e. Pareto front). Mathematically, different variable values can have the same objective function value, which is called many-to-one mapping. Different from focusing on the convergence of Pareto front, in this paper we study the diversity of variables in the optimization of storage ring lattice and make a comparison between MOGA and MOPSO. Two different lattices are taken as study examples. The study shows that the lattice solutions with almost the same objectives and different variables can show difference in some storage ring properties, which is beneficial for lattice selection. Besides, compared to MOPSO, MOGA gives a wider distribution of optimal lattice solutions in the variable space, though both algorithms can obtain almost the same Pareto front.