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Solvent design can be modeled as a mixed integer nonlinear programming problem (MINLP) in which discrete variables denote the presence or absence of molecular structural entities and to what extent they occur in the pure component compound or mixture. On the other hand, continuous variables denote process variables such as temperature and flow rates. In the MINLP model the number of discrete variables can range from several tens to several hundreds. Therefore the use of the standard branch-and-bound method for solving the problem can be computationally intensive since all the variables (discrete and or continuous) must be used as branching variables. To overcome this problem, we have proposed a new strategy in which branching is done using branching functions instead of all the search variables. This approach results in a decrease in the number of branching variables. During branch and bound, the bounding operation is performed in the search variables space, while the branching operation is performed in a reduced dimension space defined by the branching (or splitting) functions. The branching functions are determined from the special tree function representation of both the objective function and constraints. The suggested MINLP solution approach is demonstrated on a solvent design application.

The problem of determining optimal equipment sizes and regimes of chemical processes that guarantee flexibility of the processes under uncertainty is considered in this paper. The effect of multiextremality of the solution is investigated. A comparative analysis of deterministic methods available in the open literature has been carried out as a result. All the methods require some convexity (or concavity) assumptions, which are difficult to verify for practical problems. To address the latter, we have developed algorithms with minimal convexity (or concavity) requirements for this problem.