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The accuracy of computer numerical control machine tools can be improved by identifying error sources affecting the overall position error and orientation errors. Because of their inevitable nature, the position errors cannot be entirely eliminated from the machinery, but they can be identified, measured and compensated during the manufacturing process of the components by developing and using a mathematical model. In this present work, different mathematical models have been developed for the errors measured by laser interferometer at different nominal positions of X, Y and Z axes both in forward and reverse direction movement as per VDI 3441 Germany standard. Using Akaike information criterion, the best model is selected for each axis and later the best model's coefficients have been optimized by considering both minimizing sum square errors and maximizing R 2 values using teaching–learning-based optimization algorithm. Technique for Order Preference by Similarity to the Ideal Solution method has been adopted to convert the dual objectives into a single objective. An improvement of 1%–71% in R 2 values was reported to prove the effectiveness of the proposed optimization algorithm, Teaching–Learning-Based Optimization algorithm, with the same sum square error values. [ABSTRACT FROM AUTHOR]