Multiobjective Bayesian optimization for the shape design of rf cavity in particle accelerators

The design of radio frequency (rf) cavities in particle accelerators constitutes a multiobjective optimization problem (MOOP) characterized by strict equality constraints and computationally expensive evaluations. Here, a multiobjective Bayesian optimization (MOBO) framework is applied to rf cavity design for the first time to efficiently identify high-quality Pareto-optimal solutions under limited simulation budgets. To maintain high sample efficiency of the MOBO framework in problems with extremely strict equality constraints, two constraint-handling strategies are investigated: a penalty-based scalar acquisition function (sAF) strategy and a novel two-stage acquisition strategy (tAS). The tAS divides the sampling process into two stages. In the first stage, a vectorized acquisition function (vAF) is combined with a multiobjective evolutionary algorithm (MOEA) to efficiently search for candidate points in the full high-dimensional objective space. In the second stage, a sAF is employed to select the most promising point from candidate points for actual evaluation. Results on a test problem and the design of a practical 499.65 MHz rf cavity show that tAS outperforms penalty-based sAF in handling equality constraints within the MOBO framework. Furthermore, by using the MOBO framework with tAS, high-quality Pareto-optimal solutions are obtained within 1000 simulations, demonstrating a significant advantage of efficiency over conventional rf cavity optimization algorithms. Additionally, tAS allows for the flexible adjustment of MOEA, vAF, and sAF configurations, thereby providing flexible adaptation to other MOOPs in particle accelerators.