Concrete compressive strength prediction is an essential process for material design and sustainability. This study investigates several novel hybrid adaptive neuro-fuzzy inference system (ANFIS) evolutionary models, i.e., ANFIS–particle swarm optimization (PSO), ANFIS–ant colony, ANFIS–differential evolution (DE), and ANFIS–genetic algorithm to predict the foamed concrete compressive strength. Several concrete properties, including cement content (C), oven dry density (O), water-to-binder ratio (W), and foamed volume (F) are used as input variables. A relevant data set is obtained from open-access published experimental investigations and used to build predictive models. The performance of the proposed predictive models is evaluated based on the mean performance (MP), which is the mean value of several statistical error indices. To optimize each predictive model and its input variables, univariate (C, O, W, and F), bivariate (C–O, C–W, C–F, O–W, O–F, and W–F), trivariate (C–O–W, C–W–F, O–W–F), and four-variate (C–O–W–F) combinations of input variables are constructed for each model. The results indicate that the best predictions obtained using the univariate, bivariate, trivariate, and four-variate models are ANFIS–DE– (O) (MP= 0.96), ANFIS–PSO– (C-O) (MP= 0.88), ANFIS–DE– (O–W–F) (MP= 0.94), and ANFIS–PSO– (C–O–W–F) (MP= 0.89), respectively. ANFIS–PSO– (C–O) yielded the best accurate prediction of compressive strength with an MP value of 0.96.