Tivadar Farkas

Process flowsheet superstructures: Structural multiplicity and redundancy Part I: Basic GDP and MINLP representations

Abstract Structural multiplicity has a significant effect on the solution of an MINLP model for process synthesis problems. The optimization model may also have built-in redundancy that cannot always be directly derived from the multiplicity of the superstructure. A basic GDP representation (BGR) involving logical relations is defined, and can be constructed by applying a standard natural representation of the process. Basic MINLP representation (BMR) is defined by transforming the logical relations to algebraic ones. MINLP representation (MR) is defined through a fixed form of BMR. Equivalency and representativeness of MR-s in general form can be analyzed by reducing them to their BMRs. BMR can be automatically generated, and can serve as a reference representation. Binary and continuous multiplicity of MR are defined. If the supergraph, i.e. the graph representing the superstructure, is structurally redundant (i.e. there are isomorphic graphs amongst their subgraphs) then BMR has binary multiplicity. Conversely, the structural redundancy of the graph does not follow from the binary multiplicity of its BMR. Different kinds of multiplicity and redundancy measures of the MINLP representation will be defined in Part II of this series in order to help inventing tools for decreasing their detrimental effect. Alternative MINLP representations will there be defined, constructed, and compared from the viewpoint of ideality, minimality, and solution properties.

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

Abstract 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.

NEW HYBRID METHOD FOR MASS EXCHANGE NETWORK OPTIMIZATION

A new hybrid optimization method is presented that is fairly robust and can be accomplished in an automatic way. The main idea is using integer cuts and bounds, based on driving force plot analysis, for the lean streams to decrease the possibility of being trapped in local optima. A new initial solution is constructed if the MINLP solution is infeasible; otherwise the earlier found best solution is used. In consequence, the MINLP model is modified in the iteration steps. The iteration is stopped when the total annual cost (TAC) in the solution reaches 1.1·TACtarget.

New hybrid method for mass exchange network optimisation

Abstract A new hybrid optimisation method is presented, that is fairly robust and can be accomplished in an automatic way. The main idea is using integer cuts and bounds, calculated based on driving force plot analysis, for the lean streams to decrease the possibility of being trapped in local optimum. A new initial solution is constructed only if the MINLP solution is infeasible, otherwise the best solution found earlier is used. In consequence, the MINLP model changes in the iteration steps. The iteration is stopped if the total annual cost (TAC) in the solution is less than 1.1 *TAC target .

Short-cut design of batch extractive distillation using MINLP

Abstract An automatic design method for batch extractive distillation, one of the most important techniques for separating low relative volatility or azeotropic mixtures, is presented. Example calculations are performed to the acetone-methanol mixture using water as entrainer. The NLP and MINLP problems are solved with applying GAMS DICOPT++.

Structural multiplicity and redundancy in chemical process synthesis with MINLP

Abstract How easy the solution of an MINLP model of a superstructure is usually analyzed according to the shape (linearity, convexity, relaxation, etc) of the equations, see e.g. Grossmann (1996) . Here relations between the (super)structures and their MINLP representation are studied. In order to analyze this relation, we have defined ideal MINLP and binarily minimal MINLP representations. The effect of ideality and the number of binary variables on the solution time are compared on test examples. The first example is the synthesis problem of Kocis and Grossmann (1987) . An ideal and, in the same time, binarily minimal MINLP representation has been constructed and solved. The second example is the membrane train of an industrial ethanol dehydration problem ( Lelkes et al., 2000 ). The representations, solved on a Sun Sparc station using GAMS DICOPT++ solver, are compared according to the maximal size of solvable problems.

Selection of MINLP model of distillation column synthesis by case-based reasoning

Abstract A case-based library for distillation column and distillation sequences synthesis using MINLP has been developed. The retrieval algorithm, including inductive retrieval and nearest neighbor techniques, is presented. The retrieval method and the adaptation of the solution is tested by a heptane-toluene example.

Multicommodity transportation and supply problem with stepwise constant cost function

Abstract A new model has been developed for multicommodity transportation and supply chain problems including stepwise constant costs. The model is expressed as an MILP problem. The modelling equations are presented here. The new model has been tested on multicommodity problem of SABMiller Europe, and compared to other methods from the literature. A feasibility checking method has been developed for large scale MILP problems having binary variables in the objetive function only. This feasibility checking is made by solving a special relaxed LP problem; and the most probable physical reason is pointed out by the feasibility check results in case of infeasibility.

R-graph-based distillation column superstructure and MINLP model

Abstract A new model has been developed for distillation column synthesis and optimization based on R-graph represented superstructure. A GDP model is generated first; this is transformed into an MINLP model which represents only the considered structures, and uses minimum number of binary variables to make distinctions between the different structures. The MINLP model is compared to literature models ( Viswanathan and Grossmann, 1993 , and Yeomans and Grossmann, 2000 ). The new model uses less number of binary variables, and is significantly faster.

Supply chain optimization with homogenous product transport constraints

Abstract Provimi Pet Food is the pet food division of Provimi, one of the worlds largest animal feed manufacturing and commercial companies. The dynamic growth of the company in the last years resulted in the necessity to optimize the supply chain. The supply chain problem has special characteristics such as special logical constraints of homogeneous transport, complex cost function, and large size. The developed mathematical model and computational experiences are presented here.