A multi-constraint gradient coil optimization method based on an improved MOEA/D

Gradient coils are critical subsystems of magnetic resonance imaging (MRI) scanners, requiring tradeoffs among multiple performance metrics. Single-constraint target-field methods (TFMs) often fail to optimize these conflicting objectives simultaneously, and Tikhonov regularization relies on empirically selected coefficients and may lead to ill-conditioned problems as additional constraints are introduced. This study proposes a multi-constraint gradient coil design framework using an improved decomposition-based multi-objective evolutionary algorithm (MOEA/D). Shielding field, power dissipation, magnetic energy, winding smoothness, and Lorentz torque are incorporated as regularization constraints, with the corresponding seven regularization coefficients treated as decision variables. Target field inhomogeneity is enforced as a hard constraint, formulating the problem as a multi-objective minimization. To improve optimization efficiency, a Gaussian Process Regression (GPR) surrogate model is incorporated to reduce repeated electromagnetic evaluations. In addition, two problem specific strategies are developed to address the high-dimensional, strongly coupled nature of this problem: (1) an adaptive directional mutation strategy based on the correlation analysis between regularization coefficients and Lorentz torque performance, which guides a physics informed search toward the Lorentz torque objective; (2) an elite preservation and diversity injection mechanism that prioritizes field inhomogeneity to prevent premature convergence and the loss of feasible solutions. The method is validated by designing a three-axis asymmetric gradient coil for a 1.5T head-only MRI system developed by the Wuhan National High Magnetic Field Center (WHMFC). Compared with designs without multi-constraint optimization, the proposed approach reduces Z coil resistance and inductance by 35.1% and 56.1%, and X coil resistance, inductance, and torque by 53.4%, 41.2%, and 96.1%, respectively, while maintaining gradient inhomogeneity within ±5% over the designated spherical volume (DSV). Convergence analysis indicates that the improved MOEA/D exhibits superior stability relative to conventional MOEA/D and NSGA-II. Subsequent coil fabrication and volunteer brain imaging experiments confirm the engineering feasibility and practical utility of the proposed method.