Skip to main content
Research Highlight | Mathematics and Computer Science

Penalties and goals – not just in football but also in optimization algorithms for particle accelerators

Particle accelerators are vital tools for studying the structure and behavior of the particles that make up matter.

Such accelerators can comprise thousands of components with diverse input ranges. Scientists have therefore formulated optimization algorithms to determine better design configurations, but these can require thousands of simulations on large computational resources to find optimal solutions for even one section of a machine – a time-consuming and costly process. As a result, many possible design configurations go unexplored.

To address this situation, a team of researchers from SLAC, Stanford University and Argonne National Laboratory investigated three popular optimization algorithms for the photoinjector of the Linac Coherent Light Source (LCLS) at SLAC.

The researchers chose the LCLS-II photoinjector (see Fig. 1) because it involves an established optimization problem and is broadly applicable to other accelerator labs. The three optimization methods they compared were a genetic algorithm, a scalarization technique (essentially a multistart framework combined with local optimization) and a surrogate-based method combined with parameters such as trust-region techniques and adaptive weighting.

Each optimization method was allowed 1,000 simulation evaluations. Simulations on Bebop, a high-performance computer in Argonne’s Laboratory Computing Resource Center, showed that all three methods achieved the expected results. More interesting, however, was the number of evaluations required for a method to reach a solution. Because the cost of evaluating the objective is high, users want optimization methods that can reach a solution in as few simulation evaluations as possible. In this case, the local method with multistart was the most efficient of the three optimization methods.

Two key results were of particular importance. One was that the use of objective penalties has a strong effect on the efficiency of the methods.

Penalties are needed because the search space is so large that many combinations of parameters lead to infeasible solutions,” said Tyler Chang, a postdoctoral appointee in Argonne’s Mathematics and Computer Science (MCS) Division. He noted that in the initial testing of the search space without penalties, as few as 250 out of 1,000 simulations were viable.

We found that the use of an emittance penalty is important to keep the optimization algorithm focused,” Chang said. Emittance refers to the momentum and physical space occupied by a charged particle beam. With strong objective penalties on poor emittance scores the multistart local algorithm reduced evaluations from 10,000 to 1,000 or 2,000 – a potential savings of 2000 CPU-hours.  

A second key finding was the importance of the optimization goal.

If the goal is to find optimal parameters in specific regions of the objective space, using a multistart algorithm with a model-based approach provides an efficient use of CPU-hours,” said Stephen Hudson, a principal specialist, software engineering at Argonne’s MCS Division. But if the goal is a fast initial exploration (exploiting highly parallel resources), the genetic algorithm using a heuristic approach is a good choice.”

The researchers also stressed the importance of generating random samples of the input variables before optimization. Doing so can reduce the sampling error and improve the design of the simulation experiments. In the tests reported here, optimizations started from Latin hypercube samples were found to outperform optimizations started from uniform random samples.

For the full paper reporting the research, see N. Neveu, T. H. Chang, P. Franz, S. Hudson, and J. Larson, Comparison of multiobjective optimization methods for the LCLS-II photoinjector,” Computer Physics Communications 283, 2023, 108566.