Constraint handling in constrained optimization of a storage ring multi-bend-achromat lattice

Abstract

In the design of multi-bend achromat (MBA) lattices for diffraction-limited storage rings (DLSRs), usually, many magnet parameters need to be adjusted, and the constraints to be satisfied can be stringent. When using an evolutionary algorithm to optimize such a complicated lattice, there can be only few or even none of lattice solutions satisfying the constraints in the early evolution stage of the algorithm, which may significantly affect the optimization result. Therefore, the techniques for constraint handling in an evolutionary algorithm will be important for better optimizing MBA lattices. In this paper, three typical constraint handling methods that are incorporated into a multi-objective particle swarm optimization algorithm are used to optimize a hybrid 7BA lattice for a 2.2 GeV DLSR. In this lattice optimization, the impacts of the population size of the algorithm and the constraint condition on the optimization result are studied for these methods, and comparisons are also made among these methods. It is shown that, in general, the penalty function method is a better constraint handling method for optimizing MBA lattices. From the optimization result obtained by the penalty function method, a lattice with a natural emittance of about 84 pm⋅rad is selected, which has large dynamic aperture and momentum aperture.