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High precision rotary shafts with precise geometrical tolerances are generally mounted with a micron level clearance between the gears and casing during operation in industrial applications. Dynamics cyclic loads are inevitable in most of these applications which has an adverse effect on the fatigue life of the critical parts. Ensuring close dimensional tolerances and coaxiality during machining is highly desirable, as it affects the rotary characteristics in many applications. Thus, control of coaxiality error plays a vital role in rotating shafts and high precision machine tools. However, use of high precision machining would drastically increase the cost of manufacturing. Thus, a cost-effective machining process that could potentially reduce the coaxiality error is of high industrial importance. The present research efforts made an attempt to achieve minimum coaxiality error on cylindrical machined parts by optimizing parameters (cutting speed, feed rate, depth of cut and cutting tool nose radius). Experiments are planned, viz. central composite design matrix and statistical analysis determine the influence of machine parameters on coaxiality error of high-strength Al 7075 alloy by applying response surface methodology. Feed rate and depth of cut factors showed significant effect on coaxiality error. All machining parameters showed a non-linear effect on coaxiality error, which defines the strong interaction factor effects. The empirical equations derived were used to minimize coaxiality error by determining a set of machining parameters, viz. applying Big-Bang and Big Crunch and Rao (Rao-1, Rao-2 and Rao-3) algorithms. Rao algorithms outperform the Big-Bang and Big Crunch algorithm both in computation effort and solution accuracy. The results of Rao algorithms are experimentally verified, which resulted in reduced coaxiality error equal to 1.013 µm and resulted in 72.6% improvement compared to CCD experiments. [ABSTRACT FROM AUTHOR]