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Concrete is the second most consumed material after water and the most widely used construction material in the world. The compressive strength of concrete is one of its most important mechanical properties, which highly depends on its mix design. The present study uses the intelligent methods with instance-based learning ability to predict the compressive strength of concrete. To achieve this objective, first, a set of data pertaining to concrete mix designs containing fly ash was collected. Then, mix design parameters were used as the inputs of the artificial neural network (ANN), support vector machine (SVM), and adaptive neuro-fuzzy inference system (ANFIS) developed for predicting the compressive strength. In all these models, prediction accuracy largely depends on the parameters of the learning model. Hence, the particle swarm optimization (PSO) algorithm, as a powerful population-based algorithm for solving continuous and discrete optimization problems, was used to determine the optimal values of algorithm parameters. The hybrid models were trained and tested with 426 experimental data and their results were compared by statistical criteria. Comparing the results of the developed models with the real values showed that the ANFIS-PSO hybrid model has the best performance and accuracy among the assessed methods.