An outer-approximation algorithm for the solution of multiparametric MINLP problems

Abstract Process synthesis problems involving uncertainty can be mathematically represented as multiparametric mixed integer nonlinear programming (mp-MINLP) models. In this paper, we present an outer-approximation algorithm for the solution of such mp-MINLPs, described by convex process models, linear in the vectors of binary variables and uncertain parameters. The algorithm follows decomposition principles, i.e., constructing a converging sequence of valid upper and lower bounds through the solution of parametric primal and master subproblems. The solution is characterized in different sub-domains of the uncertain parameter space by (i) linear parametric profiles, and (ii) the corresponding integer solutions.

[1]  I. Grossmann,et al.  Relaxation strategy for the structural optimization of process flow sheets , 1987 .

[2]  Arthur M. Geoffrion,et al.  Exceptional Paper—Parametric and Postoptimality Analysis in Integer Linear Programming , 1977 .

[3]  Efstratios N. Pistikopoulos,et al.  A parametric MINLP algorithm for process synthesis problems under uncertainty , 1996 .

[4]  L. Biegler,et al.  A reduced hessian strategy for sensitivity analysis of optimal flowsheets , 1987 .

[5]  Ignacio E. Grossmann,et al.  Mixed-integer programming approach for the synthesis of integrated process flowsheets , 1985 .

[6]  Naonori Nishida,et al.  A branch-and-bound algorithm for 0-1 parametric mixed integer programming , 1985 .

[7]  Ignacio E. Grossmann,et al.  Mixed-integer nonlinear programming techniques for the synthesis of engineering systems , 1990 .

[8]  Andrew N. Hrymak,et al.  Sensitivity analysis for chemical process optimization , 1996 .

[9]  Lorenz T. Biegler,et al.  Flowsheet optimization and optimal sensitivity analysis using analytical derivatives , 1994 .

[10]  T. Gál,et al.  Multiparametric Linear Programming , 1972 .

[11]  E. Pistikopoulos,et al.  A multiparametric programming approach for linear process engineering problems under uncertainty , 1997 .

[12]  I. Grossmann,et al.  A mixed-integer nonlinear programming algorithm for process systems synthesis , 1986 .

[13]  Larry Jenkins.  Parametric Mixed Integer Programming: An Application to Solid Waste Management , 1982 .

[14]  Arthur M. Geoffrion,et al.  Parametric and Postoptimality Analysis in Integer Linear Programming , 1976 .