The current effort aims at contributing to the algorithmic synthesis of a heat-integrated separation network system involving separations based on various properties, such as volatility, solubility, and permeability. This is unlike any of the previous works on heat-integrated network synthesis involving separation based only on a single property. such as volatility. The network under consideration consists of mixers, dividers, separators, utilities, and heat exchangers. The network system produces pure or multicomponent product streams from a single or multiple feed streams. Meanwhile, it satisfies the heat requirements not only between reboilers and condensers but also between hot and cold streams throughout the entire network of a production plant with the lowest possible annualized cost. The costs of the mixers and dividers are regarded as negligible: the cost of a separator, a linear function of the flowrate of its input stream without an additive constant parameter, and the cost of a utility, proportional to the heat provided or extracted. The cost of a heat exchanger is calculated based on logarithmic-mean temperature difference (LMTD).