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This paper describes a new approach towards optimum selection of the different parameters of the mould oscillation system in the continuous casting process of steel manufacturing. The objective of optimization is to enhance lubrication within the mould, especially at higher casting speeds, and reduce the intensity of oscillation marks. The need to improve lubrication conditions is primarily addressed by making the mould oscillate on its longitudinal axis. It is known that non-sinusoidal oscillation, where the time for upward motion of the mould is longer than that of downward motion in an oscillation cycle, reduces depth of oscillation marks while providing better lubrication. In the present work, a Genetic Algorithm is applied to optimize the amplitude, frequency, and waveform of the oscillation of the continuous casting mould based on objective functions that maximize the lubrication, and minimize the depth of oscillation marks and the cycle peak friction. Optimization is performed within constraints imposed by machine limits. The objective function and constraints are extracted from an analysis of the physics of oscillation, lubrication and heat transfer within the continuous casting process. The application of the Genetic Algorithm within a unified framework encompassing all oscillation performance metrics and constraints is seen to generate an optimal parameter set that provides better performance than existing oscillation parameters supplied by Original Equipment Manufacturers.