Comparison of constrained optimization methods for designing a multi-bend achromat lattice

In the design of a multi-bend achromat (MBA) lattice for a diffraction-limited storage ring, there are usually many magnet parameters to be optimized and some stringent constraints to be satisfied. For example, to cancel out nonlinear dynamics effects, the phase advances between some sections are generally required to be set to certain values in the lattice design. For better designing a MBA lattice using an evolutionary algorithm, the handling of constraints will be important, because it is very hard to satisfy the constraints for most or even all of solutions in the early generations of the algorithm. This paper will first describe some methods for handling constraints, which are then applied to designing a hybrid 7BA lattice. The comparison of these methods shows that better lattice solutions can be obtained by including constraints into objective functions. (paper)