This study explores the use of global sensitivity analysis (GSA) and harmony search algorithm (HSA) for design optimization of shell and tube heat exchangers (STHXs) from the economic viewpoint. To reduce the size of the optimization problem, non-influential geometrical parameters which have the least effect on total cost of STHXs are identified using GSA. The HSA which is a meta-heuristic based algorithm is then applied to optimize the influential geometrical parameters. To demonstrate the effectiveness and accuracy of the proposed algorithm, an illustrative example is studied. Comparing the HSA results with those obtained using genetic algorithm (GA) reveals that the HSA can converge to optimum solution with higher accuracy.