A rigorous mathematical formulation is presented for the problem of optimal design under uncertainty. This formulation involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region. To circumvent the problem of infinite dimensionality in the constraints, an equivalence for the feasibility condition is established which leads to a max-min-max constraint. It is shown that if the inequalities are convex, only the vertices in the polyhedron need to be considered to satisfy this constraint. Based on this feature, an algorithm is proposed which uses only a small subset of the vertices in an iterative multiperiod design formulation. Examples are presented to illustrate the application to flexible design problems.
[1]
A. H. Masso,et al.
Branch and Bound Synthesis of Integrated Process Designs
,
1970
.
[2]
B. A. Murtagh,et al.
Projection methods for non-linear programming
,
1973,
Math. Program..
[3]
Ignacio E. Grossmann,et al.
Optimum design of chemical plants with uncertain parameters
,
1978
.
[4]
E. Polak,et al.
Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem
,
1979
.
[5]
HettichR.,et al.
Semi-infinite programming
,
1979
.
[6]
R. K. Malik,et al.
Optimal design of flexible chemical processes
,
1979
.
[7]
Ignacio E. Grossmann,et al.
A remark on the paper 'Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem'
,
1981
.
[8]
Ignacio E. Grossmann,et al.
Decomposition strategy for designing flexible chemical plants
,
1982
.