Digital watermarking plays an important role in protecting digital content, verifying ownership, and supporting the trustworthy distribution of digital information. However, maintaining watermark robustness without compromising visual quality remains a challenge, particularly when embedding strength is selected through empirical adjustment. This study investigates an adaptive wavelet-domain watermarking method that uses genetic algorithm (GA) optimization to determine embedding energy for digital image protection. The watermark was encrypted using the Data Encryption Standard (DES) and embedded into selected wavelet subbands. A GA was employed to adjust the embedding strength according to an image-distortion criterion, while watermark quality and extraction performance were evaluated using relative error (RE) and other image-quality measures. The proposed method was tested against cropping, rotation, scaling, Joint Photographic Experts Group (JPEG) compression, filtering, Gaussian noise, and other distortions, and its performance was compared with manually selected embedding energy and a least significant bit (LSB) method. The results showed that the GA-based method achieved watermark extraction rates of 87.2% after 25% cropping, 93.4% after 15$^{\circ}$ rotation, and 96.3% under JPEG compression at a quality factor of 50. Under these conditions, the corresponding extraction rates for manually selected embedding energy were 83.1%, 89.2%, and 91.8%, respectively. The proposed method also maintained low visual distortion in the reported imperceptibility test. These findings indicate that GA-based parameter selection is a feasible alternative to manual adjustment in wavelet-domain watermarking. The method provides a technical approach to improving the resilience of embedded ownership information against common image-processing operations, with potential applications in digital content protection and copyright verification.