This study concerns shell and double concentric tube heat exchangers, which is a new type of heat exchangers. Shell and double concentric tube heat exchangers are used in many specific applications such as cryogenics, chemical processing, waste heat recovery, air conditioning, transport, power generation, distillation, food processing, pharmaceutical industries, etc. This work presents the use of Cuckoo Optimization Algorithm (COA) in the sizing of the shell and double concentric tube heat exchanger, where the objective function is the total cost which is the sum of the capital cost of the heat exchanger and the operating cost. The use of the techno-economic method of optimization technique on heat exchangers, the sizing allows the device that satisfies the technical specification with the lowest possible levels of operating and investment costs. The Logarithmic Mean Temperature Difference (LMTD) method is applied to calculate the heat exchanger surface area. This type of heat exchanger is more profitable and more economic than that of existing shell and tube heat exchanger, the total cost decreased of about 30 to 35 %. Use of COA and design modifications the sizing also allows improving the compactness of the heat exchanger.