Multi-objective optimization of shoulder muscle forces during forward flexion using NSGA-II

Shoulder forward flexion underlies daily upper-limb activities including reaching, lifting and drinking. This coordinated multi-muscle motion is critical for exploring shoulder biomechanics and muscle control. This study established a 2D rigid-body musculoskeletal model for single-degree-of-freedom shoulder flexion. A multi-objective optimization framework combined with NSGA-II was adopted to solve muscle force redundancy and obtain Pareto-optimal muscle force distributions under kinematic constraints. Results show different objective functions produce distinct muscle coordination patterns. Minimizing peak stress reduces loads on key muscles, while minimizing squared stress improves global energy efficiency. This work reveals neuromuscular coordination during shoulder flexion and provides theoretical support for exoskeleton design and motor control analysis.