The synthesis of a heat exchanger network (HEN) is an active field of interest in process engineering in order to develop a systematic procedure for finding an optimal network and individual heat transfer areas to meet the target temperatures at minimum total cost, which consists of energy and capital costs. Previous methods have given priority to identifying the minimum energy cost at a given minimum approach temperature (Delta T-min) common to all heat matches between the heat sources and sinks beforehand. However, Delta T-min for each match depends on the physical properties, the temperature levels and the locations of the process stream sources, which are strongly related to the total cost effect.The purpose of this study is to develop a HEN synthesis method considering the energy and capital costs simultaneously, and an evolutionary approach is found to be suitable for the nature of this problem. In adopting this approach, generating an initial network and searching for the neighboring ones becomes important, In this study, an algorithm of selection criterion is developed to generate an initial network based on the thermodynamic and economic consideration. Moreover, three evolutionary rules : changing the neighboring heat match; adding heat match; and varying heat transfer area have been proposed. These rules enable evolutionary searching without missing a better network. Finally, the effect of the developed evolutionary method is demonstrated through an illustrative example problem.