Robust economic optimization of process design under uncertainty

In this study, ranges of model parameters are analyzed for robustness measures. In particular, the properties of partial mean and worst-case cost in robust optimization are investigated. The robust optimization models are considered as multiobjective problems having two objectives, the expected performance (i.e. expected cost) and a robustness measure (Suh, M. and Lee, T. (2001) Robust optimization method for the economic term in chemical process design and planning. Industrial & Engineering Chemical Research, 40, 5950–5959). The robust partial mean model is defined with objectives of expected value and partial mean. The robust worst-case model is defined with the objective of expected value and worst-case. They are proved to guarantee Pareto optimality, which should be satisfied for multiobjective optimization problems. A graphical representation of the meaningful parameter ranges is clearly defined with mathematical proofs. The robustness of the solutions is discussed, based on the analysis of the ranges of the parameters. Three meaningful ranges of the parameters are investigated to choose a proper target value for the robust partial mean model. The worst-case value obtained from the worst-case analysis is recommended as the most effective target value, in order to obtain the optimal solution in a tradeoff between robustness and optimality. The proposed analysis in this study is validated with examples in chemical process design problems.

[1]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[2]  Roger J.-B. Wets.  Challenges in stochastic programming , 1996, Math. Program..

[3]  Ignacio E. Grossmann,et al.  Optimization strategies for flexible chemical processes , 1983 .

[4]  Lazaros G. Papageorgiou,et al.  Robustness metrics for dynamic optimization models under parameter uncertainty , 1998 .

[5]  Shabbir Ahmed,et al.  Robust Process Planning under Uncertainty , 1998 .

[6]  C. Pantelides,et al.  Design of multipurpose batch plants with uncertain production requirements , 1992 .

[7]  Efstratios N. Pistikopoulos,et al.  An integrated framework for robust and flexible process systems , 1999 .

[8]  Sunwon Park,et al.  Robust investment model for long-range capacity expansion of chemical processing networks under uncertain demand forecast scenarios , 1998 .

[9]  D. Bonvin,et al.  Optimization of batch reactor operation under parametric uncertainty — computational aspects , 1995 .

[10]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[11]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[12]  Tai-yong Lee,et al.  Robust Optimization Method for the Economic Term in Chemical Process Design and Planning , 2001 .

[13]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[14]  P. Fishburn.  Mean-Risk Analysis with Risk Associated with Below-Target Returns , 1977 .

[15]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

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

[17]  G. Reklaitis,et al.  DESIGN OF BATCH CHEMICAL PLANTS UNDER MARKET UNCERTAINTY , 1994 .

[18]  Scott A. Malcolm,et al.  Robust Optimization for Power Systems Capacity Expansion under Uncertainty , 1994 .

[19]  Linus Schrage,et al.  OR Practice - A Scenario Approach to Capacity Planning , 1989, Oper. Res..

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