Process flowsheet superstructures: Structural multiplicity and redundancy: Part II: Ideal and binarily minimal MINLP representations

The essential problems, namely representativeness and uniqueness, in defining mixed integer non-linear programming (MINLP) representation (MR) is solved in Part I by first defining a basic MR (BMR) that: (1) can be automatically constructed from an easier formable standard GDP representation and (2) serves as a reference representation. Binary and continuous multiplicity of MR are also defined in Part I, and relation is given there between structural redundancy and binary multiplicity.Based on this results, ideal and binarily minimal MR-s are defined, and the different MR-s are compared from numerical point of view in the present (and final) part. Ideal MR represents all the considered structures and not any other structure. Supposing the process graphs are distincted using binary variables, binarily minimal MR uses the minimal number of them.Solvability of the different MR-s, including some combined versions, are tested on a middle scale and an industrial scale process synthesis problems. Total solution time, solution time for subproblems, number of iterations, non-ideality and scale of the solvable problems are compared. Idealization of the representation and decreasing the number of binary variables, as suggested in the article, both enhance the solvability and decrease the solution time in a great extent.