In the recent past, a different set of algorithms for watermarking and securing the color images have been developed by using transformation, decomposition, and optimization techniques for watermark embedding and extraction. In this paper, we propose an optimized and robust watermarking algorithm coupled with a 4D hyperchaotic system, and its performance is analyzed by extending and differentiating the existing work. Our contribution in the presented work is watermarking and securing the color images by an optimized algorithm that uses transformation technique such as Discrete Wavelet Transformation (DWT) and decomposition techniques such as Hessenberg decomposition (HbD) and singular value decomposition (SVD) coupled with the 4D hyperchaotic system, while the optimization is carried out by improved evolution fruit fly optimization algorithm (IEFOA). The experimental results based on different types of attacks (filter attacks, noise attacks, cropping attack, JPEG compression, motion blur, sharpening, and rotation), key sensitivity, normalized correlation, peak signal-to-noise ratio, and structural similarity index measure are done for measuring the algorithm’s performance regarding invisibility and robustness. The experimental results show that the proposed scheme has excellent invisibility and keeps a good trade-off between invisibility and robustness. The experiment results show that the proposed approach outperforms the previous approaches.