Developing an efficient radiation-shielding concrete composition holds paramount importance for nuclear, medical, and defence facilities. The intricate interactions between various radiation particles and materials across different energy ranges present challenges in designing effective and resilient overall shielding structures. This study presents a novel approach that integrates machine learning and genetic algorithms (GA) to optimize concrete compositions for enhanced radiation shielding against gamma and neutron rays across a wide energy spectrum. By leveraging these advanced techniques, six compositions (concrete_1-concrete_6) spanning different density ranges were derived from an extensive database developed from the previous experimental researches. Subsequently, the shielding effectiveness of these compositions against all radiation particles was evaluated and compared using the OpenMC Code. The findings revealed that the proposed concrete_5 and concrete_6 compositions, comprising iron, boron, nickel, and tungsten at specified weight fractions, outperform other state-of-the-art compositions in overall radiation shielding. Furthermore, the analysis indicated a 65.89% reduction in Global Warming Potential (GWP) with the adoption of concrete_6 composition compared to conventional concrete composition.