Abstract: Addressing the synthesis problem of sparse rectangular planar arrays under multiple constraints such as array aperture, number of array elements, and minimum element spacing, traditional methods generally suffer from core bottlenecks such as insufficient freedom in element arrangement, poor initial solution quality, imbalance between global optimization and local exploitation, and susceptibility to local optima. This paper proposes a hybrid optimization method based on an improved Hippo Optimization Algorithm (IHOA) and Bayesian Compressive Sensing (BCS) guided asymmetric mapping. Firstly, a high-quality initial weight matrix is generated through a Bayesian compressive sensing model with Gaussian Scale Mixture (GSM) mixed priors, addressing the inherent defects of traditional randomly selected matrices. Secondly, an improved asymmetric mapping method is proposed to decouple the minimum spacing constraint and transform it into an unconstrained optimization problem, maximizing the freedom in element arrangement. Finally, a multi-strategy enhanced Hippo Optimization Algorithm and sequential quadratic programming are utilized to achieve global and local collaborative optimization, effectively suppressing the peak sidelobe level of the array. This provides a new technical path for the synthesis of sparse arrays under multiple constraints. Theoretical analysis and simulation experiments verify the progressiveness and engineering practicality of this method.