One Level Optimisation Problem Formulation for Binary Mixtures

One Level Optimisation Problem Formulation for Binary Mixtures 

It is quite obvious that a two level optimisation formulation can be very expensive in terms of computation time. This is due to the fact that for any particular choice of R1 and xRi a complete solution (sub-optimal) of the two distillation tasks are required. The same is true for each gradient evaluation with respect to the decision variables (B7and xRj). Mujtaba (1989) proposed a faster one level dynamic optimisation formulation for the recycle problem which eliminates the requirement to calculate any sub-optimal or intermediate solution. In this formulation the total distillation time is minimised directly satisfying the separation requirements for the first distillation task as interior point constraints and for the second distillation task as final time constraints. It was found that the proposed formulation was much more robust and at least 5 times faster than the classical two level formulation. 

In addition, all DAE model equations (Type IV-CMH) act as equality constraints in problem P4 with suitable boundary conditions as mentioned in the two-level formulation. 

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