The aim of this paper was to improve the performance of the adaptive neuro-fuzzy inference system (ANFIS) and to predict the flexural strength of the sandwich panels made with thin medium density fiberboard as surface layers, and polyurethane foam as a core layer, by applying metaheuristic optimization methods. For this purpose, various models, namely ant colony optimization for the continuous domain (ACOR), differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO) were applied and compared, as different efficient bio-inspired paradigms, to assess their suitability for training the adaptive neuro-fuzzy inference system model. The predicted values of the flexural strength resulting from applying adaptive neuro-fuzzy inference system trained by ACOR, DE, GA, and PSO, were compared with the values derived from adaptive neuro-fuzzy inference system classical model. The molar ratio of formaldehyde to melamine and urea, sandwich panel thickness, and the weight ratio of the modified starch to MUF resin (OS/MUF weight ratio) were used as an input variables and the modulus of rupture was used as an output one. The developed hybrid models were used to predict the values of the modulus of rupture obtained from experimental tests. In order to evaluate and compare the performance of the models, three performance criteria were employed namely, determination coefficient (R2), root mean square error, and mean absolute percentage error. It was found that ANFIS–ACOR, ANFIS–DE, ANFIS–GA, and ANFIS–PSO showed different performance ratios compared to the predicting model. In addition, the ANFIS–GA model is found to be by far more accurate than the other hybrid models.