Industrial processes require efficient operation unit that provide minimum mass and heat waste. Heat waste minimization can be obtained through heat integration by utilizing heat exchanger network. Heat exchanger network consist of heat exchanger that connected in series parallel connection. Heat exchanger as one of thermal operation unit transfer heat between two or more fluids through convection and conduction phenomenon. There are some types of heat exchanger available in the market such as shell and tube heat exchanger. Shell and tube heat exchangers are commonly used throughout the process industry to transfer heat. Some of design variables in Shell and tube side of heat exchanger should be optimized in order to achieve the best performances and lowest cost heat exchanger. In the optimization require three components i.e. heat exchanger model, problem formulation and optimization technique. In this research, the objective function is minimizing cost by constraint the heat transfer area and heat duty. The models use some of first principle and empirical models. Generalized Reduced Gradient (GRG) is utilized to solve this optimization problem. The Optimization result shows the design of heat exchanger by using coil wire insert technology provides the lowest cost compare to modern technologies of heat exchanger and conventional of heat exchanger by reducing 50% cost and then afterwards helical baffle 30.75% and then internal fins 30.51% and the least is twisted tape inserts 8.09%.