Smoking has emerged as one of the leading global factors that is the source of health issues. It damages almost all of the body's organs. It damages various muscles and causes lung cancer. Additionally, it causes ulcers, pulmonary disease, and vascular deterioration. Except for the financial benefit to tobacco companies, manufacturers, and marketing companies, smoking has no advantages. Due to these factors, the present study exploited a feed forward neural networking based global optimization procedure with a local scheme to solve a mathematical model of smoking. A genetic based algorithm and sequential quadratic programming (GA-SQP) are utilized as hybridized global and local strategies. The model is categorized into five classes: potential smokers, occasional smokers, smokers, temporary quit, and permanent quit smokers. An objective optimization function is constructed to minimize the mean square error using the designed smoking model in form of feed forward neural networking. The comparative evaluation of hybrid GA-SQP and Adam numerical scheme is also assessed to authenticate the precision and correctness of the solution of the smoking model. The robustness, perfection, and convergence stability of GA-SQP are verified by establishing various statistical performance indicators. The quantitative analysis provides the minimum, mean, and semi-inter quartile range values for absolute errors up to 6 to 13 decimal places, demonstrating the worthiness and precision of the proposed GA-SQP. [ABSTRACT FROM AUTHOR]