Power supply noise has emerged as a critical bottleneck in modern integrated circuit design, where increasing current densities and higher operating frequencies pose significant challenges to system reliability. While decoupling capacitors (decaps) serve as the primary solution for suppressing power delivery network (PDN) noise, determining their optimal values and placement remains computationally prohibitive using traditional methods. This article introduces ConvGA, a novel framework that seamlessly integrates convolutional neural networks (CNNs) with genetic algorithms (GAs) to revolutionize PDN decap optimization. At the heart of ConvGA is a specialized CNN architecture trained on comprehensive boundary element method (BEM) simulations, enabling ultrafast impedance prediction for arbitrary PCB configurations. Our CNN achieves remarkable accuracy while reducing impedance computation time from hours to mere milliseconds-a 500 & times; speedup over conventional BEM calculations. This acceleration enables the GA to efficiently explore vast design spaces through adaptive population control and dynamic constraint mechanisms, systematically minimizing both the number of required capacitors and the deviation from target impedance. Extensive experiments on industrial-scale PDNs demonstrate that ConvGA achieves a 15 & times; reduction in optimization time while requiring 30% fewer capacitors compared to state-of-the-art methods, consistently producing high-quality solutions across diverse PDN configurations.