Abstract
With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given ``elite'' status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitness of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. The machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.
Highlights
Dynamic aperture and energy acceptance can be evaluated through direct single-particle tracking simulations
Recent studies have found that the spread from a constant of the action obtained with the square matrix method [24,25,26,27] represents a kind of nonlinearity measure of a lattice, which can be treated as an optimization objective as well
It is possible to reuse the data with machine learning techniques to intervene on the evolution process
Summary
Population-based optimization techniques, such as evolutionary (genetic) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and particle swarm [17,18,19] algorithms, have become popular in modern accelerator design. The application of MOGA on dynamic aperture optimization can be driven by either direct particle tracking, or analytical calculation of nonlinear characterization It is time-consuming to evaluate the fitness quantitatively, as seen with the calculation of a large-scale storage ring’s dynamic aperture using the symplectic integrator [31]. It classifies the candidates in the search space, and second, it increases the ratio of potential elites among the population without loss of diversity. This method was demonstrated by optimizing the NSLS-II storage ring’s dynamic aperture.
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