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Many studies have been conducted on the proportional design of fly-ash-blended low-CO2 concrete, but those studies did not consider the limitation of its carbonation durability. Especially due to climate change, the carbonation reaction is accelerated and the necessity for carbonation durability is enhanced. This study presents a computational program to design fly ash-blended concrete considering CO2 emission, strength, and carbonation under different climate-change scenarios. First, CO2 emission is calculated from concrete mixtures. Compressive strength and carbonation depth are evaluated using an integrated hydration-strength-durability model. Regarding the carbonation durability issue, two exposure conditions combined with three climate-change scenarios are considered. Second, a genetic algorithm (GA) is used to find the optimal concrete mixture. CO2 emission is set as the fitness function, and compressive strength and carbonation depth are set as the constraint conditions of the GA. The optimal mixture has the minimum CO2 emission and can meet various constraints. Based on case studies of concrete mixtures under different exposure conditions and climate change scenarios, the effect of climate change on the proportional design of fly ash-blended concrete is clarified. To meet the challenges of climate change, a richer mixture of fly ash-blended concrete is necessary. As the compressive strength of fly ash-blended concrete increases, the CO2 emissions also increase.