Slag blended concrete is widely used as a mineral admixture in the modern concrete industry. This study shows an optimization process that determines the optimal mixture of air-entrained slag blended concrete considering carbonation durability, frost durability, CO2 emission, and materials cost. First, the aim of optimization is set as total cost, which equals material cost plus CO2 emission cost. The constraints of optimization consist of strength, workability, carbonation durability with climate change, frost durability, range of components and component ratio, and absolute volume. A genetic algorithm is used to determine optimal mixtures considering aim function and various constraints. Second, mixture design examples are shown considering four different cases, namely, mixtures without considering carbonation (Case 1), mixtures considering carbonation (Case 2), mixtures considering carbonation coupled with climate change (Case 3), and mixtures of high strength concrete (Case 4). The results show that the carbonization is the controlling factor of the mixture design of the concrete with ordinary strength (the designed strength is 30MPa). To meet the challenge of climate change, stronger concrete must be used. For high-strength slag blended concrete (design strength is 55MPa), strength is the control factor of mixture design.