Fly ash-based geopolymer (FABG), as a promising alternative binder to ordinary Portland cement concrete, must meet construction requirements of strength, cost and environmental protection. To solve this multi-objective design problem of FABG, the study aims at presenting an intelligent mix design method using advanced soft computing techniques. The proposed multi-objective design optimization (MODO) method is based on Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ). While cost and CO2 emission indexes of FABG are calculated using empirical formulas, the reliable and valid calculation model of uniaxial compressive strength (UCS) is established using Back-Propagation Neural Network (BPNN) with a constructed experimental dataset. During the modeling, critical variables are identified using an integrated sequential feature selection strategy, while insignificant variables are removed from the dataset. The proposed MODO method is applied to design FABG with a specific fly ash material, and the design results are verified by experiment. The test and calculation results are nearly identical, with a maximum difference of 15%. It indicates that the proposed MODO method can quickly and accurately obtain FABG Pareto design solutions that trade off strength, cost, and CO2 emissions, which is beneficial for the promotion of FABG in engineering applications.