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Modeling and optimization for compliant mechanisms are challenging tasks thanks to an unclear kinematic merging among rigid and flexible links. Hence, this paper develops a computational intelligence-based method for modeling and optimization. The proposed method concerns about statistics, numerical simulation, computational intelligence, and metaheuristics. A two degrees of freedom compliant mechanism is investigated to illustrate the effectiveness of the suggested computational intelligence method. First, numerical datasets are collected by simulations. Then, sensitivity of design parameters is analyzed by analysis of variance and Taguchi technique. The results of sensitivity are employed to separate a few populations for lightning attachment procedure optimization (LAPO). Next, the values of two output performances of the mechanism are changed into the values in the range from zero to one through desirability function method. The calculated output values become two inputs of the fuzzy logic model, and the output of this system is a single objective function (SOF). Subsequently, the SOF is modeled by using adaptive neuro-fuzzy inference system (ANFIS). LAPO algorithm is then utilized to maximize the SOF. The results revealed that the numerical example 3 is the best design for the mechanism. In comparison with artificial intelligence techniques and regression, the results show that the performance indexes of the proposed ANFIS model (R2 close 1, MSE about 10–4, and RMSE about 10–2) are superior to those of the multilayer perceptron, deep neural network, and multiple-linear regression. Additionally, the proposed computational intelligence method is more effective than the Taguchi-fuzzy logic, ANFIS-integrated teaching learning-based optimization, and ANFIS-integrated Jaya in searching the optimal design of the compliant mechanism. The results determined that the optimal displacement and parasitic error are about 2.2109 mm and 0.0028 mm, respectively. [ABSTRACT FROM AUTHOR]