Center Evolving Optimization Algorithm for Fine Focused Muon Beamlines

The design and optimization of muon beamlines for small beam spot applications present significant computational challenges, particularly when using solenoid-based focusing systems with complex edge field interactions. This paper presents the Center-Evolving (CE) algorithm, a novel hybrid optimization strategy specifically developed for muon beamline design. The CE algorithm combines parallel local search techniques with an evolving center approach to efficiently navigate high-dimensional parameter spaces while avoiding local optima stagnation. Key innovations include automated particle selection, sector-based optimization, and modular parallel computing architecture. The algorithm has been successfully applied to design the surface muon beamline for China’s first muon station (Muon station for sciEnce, technoLOgy and inDustrY - melody), achieving direct optimization for 20 mm diameter beam spots without requiring intermediate large beam spot optimization. Results demonstrate enhanced beam intensity and optimization efficiency, with the algorithm capable of handling over 30 adjustable parameters while maintaining computational efficiency on standard desktop computers.