Optimum compression ratio (OCR) of neutron and x-ray radiography images with minimum decomposition distortion is the main target of this paper. Artificial bee colony (ABC) and firefly optimal algorithms are applied for achieving this goal. These algorithms are applied in conjunction with proposed image encoding/decoding and decomposition/decompression algorithms. The encoding/decoding algorithms depend on binary image, Huffman, and hierarchical trees. In addition, the decompression algorithms use real dual-tree transform, Hilbert transform, real a trou transform, and Gaussian pyramidal transform. A fitness function (FF) that correlates to compression ratio and image quality is conducted. The OCR with the best radiography image quality is the purpose of the suggested FF. A comparison between the optimized compressed ratio of x-ray and neutron radiography images for both optimization techniques is demonstrated. The proposed algorithms are validated. For the ABC algorithm, optimum values of 80.3610% and 80.3610% are fulfilled for x-ray and neutron images via hierarchical trees with Hilbert transforms. An optimum value of 85.333333% is attained by the Huffman algorithm with discrete cosine transform for both images. For the firefly optimization algorithm (FOA), the hierarchical trees with Hilbert transform achieve an optimum value of 97.0499% for both images. The binary image encoding with pyramidal transform gives optimum values of 68.8055% and 77.4566% for x-ray and neutron images, respectively. The FOA is noted to accomplish more advanced results over the ABC algorithm for compressed radiography images. Additionally, the binary image algorithm with a trou decompression provides an optimum value of 76.77% for neutron radiography images. The achieved optimum values of neutron images are better than of x-ray images due to the absorption of more energy by neutron radiation. Robustness and the significant task of the supposed FF are clarified. This confirms the applicability of image compression optimization algorithms with neutron and x-ray radiography images.