In this research, optimization of shell-and-tube heat exchangers with dual objectives of achieving upper heat transfer rate and lower total cost has been done by the Genetic algorithm. All geometrical constraints and standards, minimum and maximum velocity limits as well as maximum allowable pressure drops are considered in optimization process. Relations between the objective functions and optimization variables have many complexities so that the gradient approach employed by many optimization algorithms may not be adequate. Special care has been taken in employing Genetic algorithm to assure that the optimized values of variables are not trapped in local optimum domains. To evaluate the precision of computer code of current study, a comprehensive case study has been considered. The optimization has been accomplished by considering 11 variables. In a next attempt the mass flow of cooling fluid, which is the sea water in the case under study, has been added as the 12th variable. The obtained Pareto plots show that the optimized parameters suggested by this study provide upper heat transfer rate and simultaneous lower total cost relative to available results.