In this study a new and robust procedure is presented to solve synthesis of isothermal reactor networks (RNs) which considers more than one objective function. This method uses non-dominated sorting genetic algorithm II (NSGAII) to produce structural modification coupled with quasi Linear Programming ((LP)) method for handling continuous variables. The quasi (LP) consists of an (LP) by adding a search loop to find the best reactor conversions as well as split and recycle ratios which are much easier to solve. To prevent complexity and ensure optimum solution, only ideal continuous stirred tank reactors (CSTRs), plug flow reactors (PFRs) and PFR with recycle stream are considered in producing reactor networks. Also, to avoid differential equations which appear in design equations of PFR reactors, CSTRs in series are replaced for each PFR. Results show that the proposed method finds better solutions than those reported in the literature.

In this study, we discussed a fuzzy Programming approach to bi-level Linear Programming problems and their application. Bi-level Linear Programming is characterized as mathematical Programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important for the contemporary decentralized organization where each unit seeks to optimize its own objective. In addition to this, we have considered Bi-Level Linear Programming (B(LP)P) and applied the Fuzzy Mathematical Programming (FMP) approach to get the solution of the system. We have suggested the FMP method for the minimization of the objectives in terms of the Linear membership functions. FMP is a supervised search procedure (supervised by the upper Decision Maker (DM)). The upper-level decision-maker provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction).