Process optimization with consideration of uncertainties-An overview

doi:10.1016/j.cjche.2017.09.010

Abstract

Abstract: Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering. Since the solution of an optimization problem generally exhibits high sensitivity to the parameter variations, the deterministic model which neglects the parametric uncertainties is not suitable for practical applications. This paper provides an overview of the key contributions and recent advances in the field of process optimization under uncertainty over the past ten years and discusses their advantages and limitations thoroughly. The discussion is focused on three specific research areas, namely robust optimization, stochastic programming and chance constrained programming, based on which a systematic analysis of their applications, developments and future directions are presented. It shows that the more recent trend has been to integrate different optimization methods to leverage their respective superiority and compensate for their drawbacks. Moreover, data-driven optimization, which combines mathematical programming methods and machine learning algorithms, has become an emerging and competitive tool to handle optimization problems in the presence of uncertainty based on massive historical data.

Key words: Optimization under uncertainty, Robust optimization, Stochastic programming, Chance constrained programming, Data-driven optimization

摘要： Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering. Since the solution of an optimization problem generally exhibits high sensitivity to the parameter variations, the deterministic model which neglects the parametric uncertainties is not suitable for practical applications. This paper provides an overview of the key contributions and recent advances in the field of process optimization under uncertainty over the past ten years and discusses their advantages and limitations thoroughly. The discussion is focused on three specific research areas, namely robust optimization, stochastic programming and chance constrained programming, based on which a systematic analysis of their applications, developments and future directions are presented. It shows that the more recent trend has been to integrate different optimization methods to leverage their respective superiority and compensate for their drawbacks. Moreover, data-driven optimization, which combines mathematical programming methods and machine learning algorithms, has become an emerging and competitive tool to handle optimization problems in the presence of uncertainty based on massive historical data.

关键词: Optimization under uncertainty, Robust optimization, Stochastic programming, Chance constrained programming, Data-driven optimization

Ying Chen, Zhihong Yuan, Bingzhen Chen. Process optimization with consideration of uncertainties-An overview[J]. Chin.J.Chem.Eng., 2018, 26(8): 1700-1706.

Ying Chen, Zhihong Yuan, Bingzhen Chen. Process optimization with consideration of uncertainties-An overview[J]. Chinese Journal of Chemical Engineering, 2018, 26(8): 1700-1706.

References

[1] I.E. Grossmann, R.M. Apap, B.A. Calfa, P. Garcia-Herreros, Q. Zhang, Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty, Comput. Chem. Eng. 91(2016) 3-14.

[2] N.V. Sahinidis, Optimization under uncertainty:state-of-the-art and opportunities, Comput. Chem. Eng. 28(2004) 971-983.

[3] G.I. Schueller, H.A. Jensen, Computational methods in optimization considering uncertainties-An overview, Comput. Methods Appl. Mech. Eng. 198(2008) 2-13.

[4] Z. Li, M. Ierapetritou, Process scheduling under uncertainty:Review and challenges, Comput. Chem. Eng. 32(2008) 715-727.

[5] P.M. Verderame, J.A. Elia, J. Li, C.A. Floudas, Planning and scheduling under uncertainty:A review across multiple sectors, Ind. Eng. Chem. Res. 49(2010) 3993-4017.

[6] Q. Zhang, I.E. Grossmann, R.M. Lima, On the relation between flexibility analysis and robust optimization for linear systems, AIChE J. 62(2016) 3109-3123.

[7] Z. Li, R. Ding, C.A. Floudas, A comparative theoretical and computational study on robust counterpart optimization:I. Robust linear optimization and robust mixed integer linear optimization, Ind. Eng. Chem. Res. 50(2011) 10567-10603.

[8] Z. Li, C.A. Floudas, A comparative theoretical and computational study on robust counterpart optimization:Ⅱ. Probabilistic guarantees on constraint satisfaction, Ind. Eng. Chem. Res. 51(2012) 6769-6788.

[9] Z. Li, C.A. Floudas, A comparative theoretical and computational study on robust counterpart optimization:Ⅲ. Improving the quality of robust solutions, Ind. Eng. Chem. Res. 53(2014) 13112-13124.

[10] Y.A. Guzman, L.R. Matthews, C.A. Floudas, New a priori and a posteriori probabilistic bounds for robust counterpart optimization:I. Unknown probability distributions, Comput. Chem. Eng. 84(2016) 568-598.

[11] Y.A. Guzman, L.R. Matthews, C.A. Floudas, New a priori and a posteriori probabilistic bounds for robust counterpart optimization:Ⅱ. A priori bounds for known symmetric and asymmetric probability distributions, Comput. Chem. Eng. 101(2017) 279-311.

[12] Y.A. Guzman, L.R. Matthews, C.A. Floudas, New a priori and a posteriori probabilistic bounds for robust counterpart optimization:Ⅲ. Exact and near-exact a posteriori expressions for known probability distributions, Comput. Chem. Eng. 103(2017) 116-143.

[13] Y. Zhang, Y. Feng, G. Rong, New robust optimization approach induced by flexible uncertainty set:Optimization under continuous uncertainty, Ind. Eng. Chem. Res. 56(2017) 270-287.

[14] Y. Yuan, Z. Li, B. Huang, Robust optimization under correlated uncertainty:Formulations and computational study, Comput. Chem. Eng. 85(2016) 58-71.

[15] D. Bertsimas, M. Sim, The Price of Robustness, Oper. Res. 52(2004) 35-53.

[16] D. Bertsimas, M. Sim, Robust discrete optimization and network flows, Math. Program. 98(2003) 49-71.

[17] B. Zeng, L. Zhao, Solving two-stage robust optimization problems using a columnand-constraint generation method, Oper. Res. Lett. 41(2013) 457-461.

[18] S.L. Janak, X. Lin, C.A. Floudas, A new robust optimization approach for scheduling under uncertainty, Comput. Chem. Eng. 31(2007) 171-195.

[19] Z. Li, M.G. Ierapetritou, Robust optimization for process scheduling under uncertainty, Ind. Eng. Chem. Res. 47(2008) 4148-4157.

[20] M.G. Ierapetritou, Z. Jia, Short-term scheduling of chemical process including uncertainty, Control. Eng. Pract. 15(2007) 1207-1221.

[21] P.M. Verderame, C.A. Floudas, Operational planning of large-scale industrial batch plants under demand due date and amount uncertainty. I. Robust optimization framework, Ind. Eng. Chem. Res. 48(2009) 7214-7231.

[22] P.M. Verderame, C.A. Floudas, Integration of operational planning and medium-term scheduling for large-scale industrial batch plants under demand and processing time uncertainty, Ind. Eng. Chem. Res. 49(2010) 4948-4965.

[23] P.M. Verderame, C.A. Floudas, Multisite planning under demand and transportation time uncertainty:Robust optimization and conditional value-at-risk frameworks, Ind. Eng. Chem. Res. 50(2011) 4959-4982.

[24] J. Li, R. Misener, C.A. Floudas, Scheduling of crude oil operations under demand uncertainty:A robust optimization framework coupled with global optimization, AIChE J. 58(2012) 2373-2396.

[25] M. Wittmann-Hohlbein, E.N. Pistikopoulos, Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach, AIChE J. 59(2013) 4184-4211.

[26] K. Tong, F. You, G. Rong, Robust design and operations of hydrocarbon biofuel supply chain integrating with existing petroleum refineries considering unit cost objective, Comput. Chem. Eng. 68(2014) 128-139.

[27] Q. Zhang, I.E. Grossmann, C.F. Heuberger, A. Sundaramoorthy, J.M. Pinto, Air separation with cryogenic energy storage:Optimal scheduling considering electric energy and reserve markets, AIChE J. 61(2015) 1547-1558.

[28] Q. Zhang, M.F. Morari, I.E. Grossmann, A. Sundaramoorthy, J.M. Pinto, An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load, Comput. Chem. Eng. 86(2016) 106-119.

[29] H. Shi, F. You, A computational framework and solution algorithms for two-stage adaptive robust scheduling of batch manufacturing processes under uncertainty, AIChE J. 62(2016) 687-703.

[30] J. Gong, D.J. Garcia, F. You, Unraveling optimal biomass processing routes from bioconversion product and process networks under uncertainty:An adaptive robust optimization approach, ACS Sustain. Chem. Eng. 4(2016) 3160-3173.

[31] N.H. Lappas, C.E. Gounaris, Multi-stage adjustable robust optimization for process scheduling under uncertainty, AIChE J. 62(2016) 1646-1667.

[32] J. Gong, F. You, Optimal processing network design under uncertainty for producing fuels and value-added bioproducts from microalgae:Two-stage adaptive robust mixed integer fractional programming model and computationally efficient solution algorithm, AIChE J. 63(2017) 582-600.

[33] C. Ning, F. You, Data-driven adaptive nested robust optimization:General modeling framework and efficient computational algorithm for decision making under uncertainty, AIChE J. 63(2017) 3730-3817.

[34] J.R. Birge, F. Louveaux, Introduction to stochastic programming, Springer Science & Business Media, 2011.

[35] R.M. Apap, I.E. Grossmann, Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties, Comput. Chem. Eng. 103(2017) 233-274.

[36] J. Gao, F. You, Deciphering and handling uncertainty in shale gas supply chain design and optimization:Novel modeling framework and computationally efficient solution algorithm, AIChE J. 61(2015) 3739-3755.

[37] B.H. Gebreslassie, Y. Yao, F. You, Design under uncertainty of hydrocarbon biorefinery supply chains:Multiobjective stochastic programming models, decomposition algorithm, and a comparison between CVaR and downside risk, AIChE J. 58(2012) 2155-2179.

[38] K. Tong, Y. Feng, G. Rong, Planning under demand and yield uncertainties in an oil supply chain, Ind. Eng. Chem. Res. 51(2012) 814-834.

[39] F. You, I.E. Grossmann, Multicut Benders decomposition algorithm for process supply chain planning under uncertainty, Ann. Oper. Res. 210(2011) 191-211.

[40] F. You, J.M. Wassick, I.E. Grossmann, Risk management for a global supply chain planning under uncertainty:Models and algorithms, AIChE J. 55(2009) 931-946.

[41] S. Baptista, M. Isabel Gomes, A.P. Barbosa-Povoa, A two-stage stochastic model for the design and planning of a multi-product closed loop supply chain, in:B. Ian David Lockhart, F. Michael (Eds.), Computer Aided Chemical Engineering, Elsevier, Amsterdam 2012, pp. 412-416.

[42] F. Oliveira, V. Gupta, S. Hamacher, I.E. Grossmann, A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations, Comput. Chem. Eng. 50(2013) 184-195.

[43] V. Gupta, I.E. Grossmann, Solution strategies for multistage stochastic programming with endogenous uncertainties, Comput. Chem. Eng. 35(2011) 2235-2247.

[44] B. Tarhan, I.E. Grossmann, A multistage stochastic programming approach with strategies for uncertainty reduction in the synthesis of process networks with uncertain yields, Comput. Chem. Eng. 32(2008) 766-788.

[45] V. Goel, I.E. Grossmann, A class of stochastic programs with decision dependent uncertainty, Math. Program. 108(2006) 355-394.

[46] J. Steimel, S. Engell, Conceptual design and optimization of chemical processes under uncertainty by two-stage programming, Comput. Chem. Eng. 81(2015) 200-217.

[47] J. Steimel, M. Harrmann, G. Schembecker, S. Engell, Model-based conceptual design and optimization tool support for the early stage development of chemical processes under uncertainty, Comput. Chem. Eng. 59(2013) 63-73.

[48] J. Steimel, S. Engell, Optimization-based support for process design under uncertainty:A case study, AIChE J. 62(2016) 3404-3419 Amsterdam.

[49] V. Gupta, I.E. Grossmann, Multistage stochastic programming approach for offshore oilfield infrastructure planning under production sharing agreements and endogenous uncertainties, J. Pet. Sci. Eng. 124(2014) 180-197.

[50] V. Gupta, I.E. Grossmann, A new decomposition algorithm for multistage stochastic programs with endogenous uncertainties, Comput. Chem. Eng. 62(2014) 62-79.

[51] B. Tarhan, I.E. Grossmann, V. Goel, Stochastic programming approach for the planning of offshore oil or gas field infrastructure under decision-dependent uncertainty, Ind. Eng. Chem. Res. 48(2009) 3078-3097.

[52] S. Mitra, J.M. Pinto, I.E. Grossmann, Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part I:Modeling, Comput. Chem. Eng. 65(2014) 89-101.

[53] S. Mitra, J.M. Pinto, I.E. Grossmann, Optimal multi-scale capacity planning for power-intensive continuous processes under time-sensitive electricity prices and demand uncertainty. Part Ⅱ:Enhanced hybrid bi-level decomposition, Comput. Chem. Eng. 65(2014) 102-111.

[54] Z. Li, C.A. Floudas, Optimal scenario reduction framework based on distance of uncertainty distribution and output performance:I. Single reduction via mixed integer linear optimization, Comput. Chem. Eng. 70(2014) 50-66.

[55] Z. Li, C.A. Floudas, Optimal scenario reduction framework based on distance of uncertainty distribution and output performance:Ⅱ. Sequential reduction, Comput. Chem. Eng. 84(2016) 599-610.

[56] B.A. Calfa, A. Agarwal, I.E. Grossmann, J.M. Wassick, Data-driven multi-stage scenario tree generation via statistical property and distribution matching, Comput. Chem. Eng. 68(2014) 7-23.

[57] F. Oliveira, I.E. Grossmann, S. Hamacher, Accelerating Benders stochastic decomposition for the optimization under uncertainty of the petroleum product supply chain, Comput. Oper. Res. 49(2014) 47-58.

[58] A. Charnes, W.W. Cooper, Chance-constrained programming, Manag. Sci. 6(1959) 73-79.

[59] Chance-constrained programming, in:S.I. Gass, M.C. Fu (Eds.), Encyclopedia of Operations Research and Management Science, Springer US, Boston, MA 2013, p. 160.

[60] P. Li, H. Arellano-Garcia, G. Wozny, Chance constrained programming approach to process optimization under uncertainty, Comput. Chem. Eng. 32(2008) 25-45.

[61] K. Mitra, R.D. Gudi, S.C. Patwardhan, G. Sardar, Midterm supply chain planning under uncertainty:A multiobjective chance constrained programming framework+, Ind. Eng. Chem. Res. 47(2008) 5501-5511.

[62] T. Barz, G.N. Wozny, H. Arellano-Garcia, Robust implementation of optimal decisions using a two-layer chance-constrained approach, Ind. Eng. Chem. Res. 50(2011) 5050-5063.

[63] J. Yang, H. Gu, G. Rong, Supply chain optimization for refinery with considerations of operation mode changeover and yield fluctuations, Ind. Eng. Chem. Res. 49(2010) 276-287.

[64] M. Kloppel, A. Geletu, A. Hoffmann, P. Li, Using sparse-grid methods to improve computation efficiency in solving dynamic nonlinear chance-constrained optimization problems, Ind. Eng. Chem. Res. 50(2011) 5693-5704.

[65] Y. Yuan, Z. Li, B. Huang, Robust optimization approximation for joint chance constrained optimization problem, J. Glob. Optim. 67(2016) 805-827.

[66] Z. Li, Z. Li, Optimal robust optimization approximation for chance constrained optimization problem, Comput. Chem. Eng. 74(2015) 89-99.

[67] B.A. Calfa, I.E. Grossmann, A. Agarwal, S.J. Bury, J.M. Wassick, Data-driven individual and joint chance-constrained optimization via kernel smoothing, Comput. Chem. Eng. 78(2015) 51-69.

[68] R. Jiang, Y. Guan, Data-driven chance constrained stochastic program, Math. Program. 158(2015) 291-327.

[69] Y. Zhang, Y. Feng, G. Rong, Data-driven chance constrained and robust optimization under matrix uncertainty, Ind. Eng. Chem. Res. 55(2016) 6145-6160.

[70] C. Zhao, Y. Guan, Unified stochastic and robust unit commitment, IEEE Trans. Power Syst. 28(2013) 3353-3361.

[71] D. Yue, F. You, Optimal supply chain design and operations under multi-scale uncertainties:Nested stochastic robust optimization modeling framework and solution algorithm, AIChE J. 62(2016) 3041-3055.

[72] C. Liu, C. Lee, H. Chen, S. Mehrotra, Stochastic robust mathematical programming model for power system optimization, IEEE Trans. Power Syst. 31(2016) 821-822.

[73] Y. Ye, J. Li, Z. Li, Q. Tang, X. Xiao, C.A. Floudas, Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty, Comput. Chem. Eng. 66(2014) 165-185.

[74] D. Bertsimas, V. Gupta, N. Kallus, Data-driven robust optimization, Math. Program. (2017) 1-58.

[75] T. Campbell, J.P. How, Bayesian nonparametric set construction for robust optimization, P Amer Contr Conf 2015, pp. 4216-4221.

[76] Y. Feng, S.M. Ryan, Scenario construction and reduction applied to stochastic power generation expansion planning, Comput. Oper. Res. 40(2013) 9-23.

[77] D. Xu, Z. Chen, L. Yang, Scenario tree generation approaches using K-means and LP moment matching methods, J. Comput. Appl. Math. 236(2012) 4561-4579.

[78] M.I. Jordan, T.M. Mitchell, Machine learning:Trends, perspectives, and prospects, Science 349(2015) 255-260.