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Cost minimization of shell and tube heat exchanger is the key objective. Traditional design approaches besides being time consuming, do not guarantee the reach of an economically optimal solution. So, in this project, a new shell and tube heat exchanger optimization design approach is developed based on four nontraditional optimization algorithms Genetic algorithm, Simulated Annehealing, Pattern search and fmincon algorithm. In this study all the four optimization algorithms are applied to minimize the total cost of equipment including capital investment and the sum of discounted annual energy expenditures related to pumping of shell and tube heat exchanger by varying various design variables such as length, tube outer diameter, pitch size, baffle spacing, etc. Based on proposed methods, a full computer code was developed for optimal design of shell and tube heat exchanger. Finally the results are compared to those obtained by literature.