The optimization of the total annual cost in heat exchanger networks has been one of the overarching goals when synthesizing these networks. Several methodologies and techniques have been developed to achieve optimal costs in mixed material heat exchanger networks. This paper demonstrates the application of two decomposition methodologies (total decomposition and partial decomposition) for typical cost rules. The objective function was defined as the optimization and minimization of the total annual cost in mixed materials heat exchanger network. Three optimization algorithms, hybrid genetic-particle swarm optimization (GA-PSO), shuffled frog leaping algorithm (SFLA) techniques, and ant colony optimization (ACO), were used to further optimize the total cost in mixed materials heat exchanger network. The results indicate that the total annual cost in partial decomposition method was smaller than that in full integration method and total decomposition method. The reduction of the total annual cost was about 27% for GA-PSO algorithm, 24% for SFLA and 10% for ACO relative to the results reported in this work. In partial decomposition method, at least one mixed material of heat exchanger was used to reduce the hot and cold utility for decreasing the total annual cost. Partial decomposition method resulted in the highest reduction of the total annual cost compared with other methods. Percentage of difference of the total annual cost were 0.36%, 1.92%, and 5.05% for full integration, total decomposition, and partial decomposition methods, respectively, in comparison with the previous studies. Results have been compared with the results of other studies to demonstrate the accuracy of the applied algorithms.