Modeling/decomposition strategy

Kocis, G. R., and Grossmann, I. E., A Modeling/Decomposition Strategy for MINLP Optimization of Process Flowsheets, paper no. 76a, AIChE Meeting, Washingtonj D.C., 1988. 

Fi(i. 12. Initial flowsheet and subsystems in modelling/decomposition strategy. 

Grossmann IE. A modelling decomposition strategy for MINLP optimisation of process flowsheets. Comput Chem Eng 1989 13 797. 

Kocis GR and Grossmann IE (1988) A Modelling and Decomposition Strategy for the MINLP Optimization of Process Flowsheets, Comput Chem Eng, 13 797. 

A sound decomposition strategy should be applicable to any type of mathematical model of a physical process. Therefore, the set of system equations might include linear or nonlinear equations algebraic, differential, difference, or integral equations continuous or discrete variables with the following restrictions ... 

Kocis, G. R., and Gro.ssmann, E. E., A modeling and decomposition strategy for the MINLP optimization of process flowsheets, Comp, and Chem. Engr. 13, 797 (1988). 

Zhang, N. and Zhu, X.X. (2006) Novel modeling and decomposition strategy for total site optimization. Computers el Chemical Engineering, 30, 765. 

The main achievement of the proposed model is to provide a detailed tank farm inventory management, looking into the sets of tanks of each product (rotation scheme). As future work it is proposed to improve the tanks cycle formulation and develop a set of examples to test the behavior of the Disaggregated Tanks Formulation. Additionally, it is proposed to develop a decomposition strategy to link subsequent time horizons. 

There are many MILP models based on the ones presented in this chapter. A general review of mathematical models and decomposition strategies for SCM problems can be found in the work by Mula et al. [5], A more specific review devoted to process and chemical industries can be found in the work by Grossmann [6,7]. 

Different approaches may be used, but it turns out that the models become very large with growing number of orders. The specific problem considered may be modeled by using a continuous time formulation and the effectively solved by using decomposition methods. Care must be taken when choosing decomposition strategy. Two different decomposition approaches are used, one product based and one time based. Real world problems can be solved using both decomposition schemes. The solution time also depend on the choice of objective function. 

Very large model systems, which are often necessary to track the morphological characteristics responsible for the peculiar properties of polymers, also present a great challenge in polymer simulations. Detailed atomistic multichain polymer models used today seldom contain more than a few thousands of atoms, although domain decomposition strategies on parallel machines offer the possibihty of going up to millions of atoms. 

The integrated formulation leads to an ME.P model with 59,173 equations, 52,603 continuous variables, and 2,520 discrete variables. The problem was solved in 148 CPU s. In order to tackle medium size problems, a decomposition strategy is devised in the next section. 

Despite advances in MILP solution methods, problem size is still a major issue since scheduling problems are known to be NP-hard (i.e., exponential increase of computation time with size in worst case). While effective modeling can help to overcome to some extent the issue of computational efficiency, special solution strategies such as decomposition and aggregation are needed in order to address the ever increasing sizes of real-world problems. 

Certain special problems related to decomposition are also considered. One is whether the process model is determinate, that is, does the model have a solution. Section III indicates how decomposition can help in validating determinacy. Another problem is that of convergence of the iterative strategy. If certain of the equations are too sensitive to the values of the variables being iterated, convergence may not be obtained. Therefore, the decomposition procedure must be constrained so as to choose as iterates only those variables for which the system of equations has suitable sensitivity, as discussed in Section VI. 

---