Flexibility analysis and design using a parametric programming framework

This article presents a new framework, based on parametric programming, that unifies the solution of the various flexibility analysis and design optimization problems that arise for linear, convex, and nonconvex, nonlinear systems with deterministic or stochastic uncertainties. This approach generalizes earlier work by Bansal et al. It allows (1) explicit information to be obtained on the dependence of the flexibility characteristics of a nonlinear system on the values of the uncertain parameters and design variables; (2) the critical uncertain parameter points to be identified a priori so that design optimization problems that do not require iteration between a design step and a flexibility analysis step can be solved; and (3) the nonlinearity to be removed from the optimization subproblems that need to be solved when evaluating the flexibility of systems with stochastic uncertainties.

[1]  Efstratios N. Pistikopoulos,et al.  Optimal retrofit design for improving process flexibility in linear systems , 1988 .

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

[3]  Ignacio E. Grossmann,et al.  Optimum design of chemical plants with uncertain parameters , 1978 .

[4]  Ignacio E. Grossmann,et al.  Systematic Methods of Chemical Process Design , 1997 .

[5]  David M. Himmelblau,et al.  Integration of Flexibility and Control in Process Design , 1994 .

[6]  David Bremner,et al.  Primal—Dual Methods for Vertex and Facet Enumeration , 1998, Discret. Comput. Geom..

[7]  C. Floudas,et al.  Active constraint strategy for flexibility analysis in chemical processes , 1987 .

[8]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[9]  H. A. Luther,et al.  Applied numerical methods , 1969 .

[10]  Efstratios N. Pistikopoulos,et al.  A hybrid parametric/stochastic programming approach for mixed-integer nonlinear problems under uncertainty , 1997 .

[11]  David M. Himmelblau,et al.  A new definition of flexibility for chemical process design , 1988 .

[12]  Ignacio E. Grossmann,et al.  A sensitivity based approach for flexibility analysis and design of linear process systems , 1995 .

[13]  E. Pistikopoulos,et al.  A multiparametric programming approach for mixed-integer quadratic engineering problems , 2002 .

[14]  Vikrant Bansal,et al.  Analysis, design and control optimization of process systems under uncertainty , 2000 .

[15]  E. Pistikopoulos,et al.  Algorithms for the Solution of Multiparametric Mixed-Integer Nonlinear Optimization Problems , 1999 .

[16]  E. Pistikopoulos,et al.  Novel approach for optimal process design under uncertainty , 1995 .

[17]  Lorenz T. Biegler,et al.  New strategies for flexibility analysis and design under uncertainty , 2000 .

[18]  Efstratios N. Pistikopoulos,et al.  Flexibility analysis and design of linear systems by parametric programming , 2000 .

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

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

[21]  Ignacio E. Grossmann,et al.  Operability, Resiliency, and Flexibility: process design objectives for a changing world , 1983 .

[22]  Ignacio E. Grossmann,et al.  Optimal process design under uncertainty , 1983 .

[23]  Efstratios N. Pistikopoulos,et al.  Optimal retrofit design for improving process flexibility in nonlinear systems—II. Optimal level of flexibility , 1989 .

[24]  Efstratios N. Pistikopoulos,et al.  An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems , 2000, Ann. Oper. Res..

[25]  Efstratios N. Pistikopoulos,et al.  A novel flexibility analysis approach for processes with stochastic parameters , 1990 .

[26]  A. Fiacco,et al.  Convexity and concavity properties of the optimal value function in parametric nonlinear programming , 1983 .

[27]  Efstratios N. Pistikopoulos,et al.  A unified framework for the flexibility analysis and design of non-linear systems via parametric programming , 2001 .

[28]  Efstratios N. Pistikopoulos,et al.  Evaluation and redesign for improving flexibility in linear systems with infeasible nominal conditions , 1988 .

[29]  Ignacio E. Grossmann,et al.  Integrated stochastic metric of flexibility for systems with discrete state and continuous parameter uncertainties , 1990 .

[30]  G. M. Ostrovsky,et al.  An approach to solving a two-stage optimization problem under uncertainty , 1997 .

[31]  Marianthi G. Ierapetritou,et al.  New Approach for Quantifying Process Feasibility: Convex and 1-D Quasi-Convex Regions , 2001 .

[32]  Fernando P. Bernardo,et al.  Integration and Computational Issues in Stochastic Design and Planning Optimization Problems , 1999 .

[33]  G. M. Ostrovsky,et al.  Flexibility analysis and optimization of chemical plants with uncertain parameters , 1994 .

[34]  Ignacio E. Grossmann,et al.  Design optimization of stochastic flexibility , 1993 .

[35]  K. Papalexandri,et al.  A Parametric Mixed-Integer Optimization Algorithm for Multiobjective Engineering Problems Involving Discrete Decisions , 1998 .

[36]  T. Terlaky,et al.  The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming , 1996 .

[37]  Yiping Wang,et al.  A New Algorithm for Computing Process Flexibility , 2000 .

[38]  Ignacio E. Grossmann,et al.  An index for operational flexibility in chemical process design. Part I , 1983 .

[39]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[40]  Ross E. Swaney,et al.  Worst-case identification in structured process systems , 1992 .

[41]  Efstratios N. Pistikopoulos,et al.  An algorithm for multiparametric mixed-integer linear programming problems , 1999, Oper. Res. Lett..

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