Multiobjective optimization of an industrial grinding operation under uncertainty

Chemical Engineering Science

Volumn 64, Issue 23, 2009, Pages 5043-5056

  Mitra, Kishalay ^a  

^a TATA CONSULTANCY SERVICES   (India)

Author keywords

Chance constrained programming; Fuzzy simulation; Grinding; Multiobjective optimization; NSGA II; Pareto; Uncertainty

Indexed keywords

CHANCE-CONSTRAINED; CHANCE-CONSTRAINED PROGRAMMING; COMBINATORIAL EXPLOSION; ELITIST NON-DOMINATED SORTING GENETIC ALGORITHMS; EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION; FUZZY SIMULATION; GRINDABILITY INDEX; GRINDING CIRCUITS; GRINDING OPERATIONS; MULTI OBJECTIVE; NON-DOMINATED SORTING GENETIC ALGORITHMS; NONLINEAR MODEL EQUATIONS; NSGA-II; OPTIMIZATION MODELS; PARAMETER UNCERTAINTY; PERFORMANCE METRICS; REGRESSION ERRORS; ROD MILLS; SECONDARY CYCLONE; SIZE CLASS; SIZE FRACTION; SYSTEM CONSTRAINTS; TWO SOURCES; TWO-STAGE STOCHASTIC PROGRAMMING; UNCERTAIN PARAMETERS; UNCERTAINTY PROPAGATION; UPPER BOUND; UPPER BOUND CONSTRAINTS;

BALL MILLING; BALL MILLS; CONSTRAINED OPTIMIZATION; GENETIC ALGORITHMS; GRINDING (COMMINUTION); GRINDING (MACHINING); MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PARETO PRINCIPLE; SIMULATORS; UNCERTAINTY ANALYSIS;

MULTIOBJECTIVE OPTIMIZATION;

EID: 72049100118     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2009.08.012     Document Type: Article

References (90)

1. Agarwal A., and Gupta S.K. Jumping gene adaptations of NSGA-II and their use in the multi-objective optimal design of shell and tube heat exchangers. Chem. Eng. Res. Des. 86 (2008) 123-139
2. Ahmed S., and Sahinidis N.V. Robust process planning under uncertainty. Ind. Eng. Chem. Res. 37 (1998) 1883-1892
3. Austin L.G., Klimpel R.R., and Luckie P.T. Process Engineering of Size Reduction: Ball Milling (1984), SME of AIME, New York
4. Ayoub N., Martins R., Wang K., Seki H., and Naka Y. Two levels decision system for efficient planning and implementation of bioenergy production. Energy Convers. Manage. 48 (2007) 709
5. Balasubramanian J., and Grossmann I.E. Scheduling optimization under uncertainty-an alternative approach. Comput. Chem. Eng. 27 (2003) 469
6. Beale E.M.L. On minimizing a convex function subject to linear inequalities. J. R. Stat. Soc. 17B (1955) 173-184
7. Bellman R.E. Dynamic Programming (1957), Princeton University Press, Princeton, USA
8. Bellman R., and Zadeh L.A. Decision-making in a fuzzy environment. Manage. Sci. 17 (1970) 141-161
9. Birge J.R., and Louveaux F. Introduction to Stochastic Programming (1997), Springer, New York
10. Bond F.C. The third theory of comminution. Trans. SME/AIME 193 (1952) 484-494
11. Bond F.C. Crushing and grinding calculations parts I and II. Br. Chem. Eng. 6 (1961) 378-385
12. Chakraborti N. Genetic Algorithms in Materials Design and Processing. International Materials Review 49 (2004) 246-260
13. Chakraborti N., Shekhar A., Singhal A., Chakraborty S., Chowdhury S., and Sripriya R. Fluid flow in hydrocyclones optimized through multiobjective genetic algorithms. Inv. Probl. Sci. Eng. 16 (2008) 1023-1046
14. Chakraborti N., Siva Kumar B., Satish Babu V., Moitra S., and Mukhopadhyay A. A new multi-objective genetic algorithm applied to hot-rolling process. Appl. Math. Model. 32 (2008) 1781-1789
15. Charnes A., and Cooper W.W. Chance-constrained programming. Manage. Sci. 6 (1959) 73-79
16. Clay R.L., and Grossmann I.E. Optimization of stochastic production planning models. Chem. Eng. Des. Res. 72 (1994) 415
17. Coello C.A., and Becerra R.L. Evolutionary multiobjective optimization in material science and engineering. Mater. Manuf. Processes 24 (2009) 119-129
18. Coello C.A., Veldhuizen D., and Lamont G. Evolutionary Algorithms for Solving Multiobjective Problems (2002), Kluwer Academic Publishers, Dordrecht
19. Cundall P.A., and Strack O.D.L. A discrete numerical model for granular assemblies. Geotechnique 29 (1979) 47-65
20. Dantzig G.B. Linear programming under uncertainty. Manage. Sci. 1 (1955) 197-206
21. Datta A., and Rajamani R.K. A direct approach of modelling batch grinding in ball mills using population balance principles and impact energy distribution. Int. J. Miner. Process. 64 (2002) 181-200
22. Deb K. Multi-objective optimization using evolutionary algorithms (2001), Wiley, Chichester, UK
23. Deb K. Unveiling innovative design principles by means of multiple conflicting objectives. Engineering Optimization 35 (2003) 445-470
24. Deb K., Pratap A., Agarwal S., and Meyarivan T. A fast and elitist multi-objective genetic algorithms. IEEE Trans. Evol. Comput. 6 (2002) 182
25. Deb K., Mitra K., Dewri R., and Majumdar S. Towards a better understanding of the epoxy polymerization process using multi-objective evolutionary computation. Chem. Eng. Sci. 59 (2004) 4261-4277
26. Dey S., Dey P., Datta S., and Sil J. Rough set approach to predict the strength and ductility of TRIP steel. Mater. Manuf. Processes 24 (2009) 150-154
27. Diwekar U.M. Introduction to applied optimization (2003), Kluwer Academic Publishers, Norwell, MA
28. Diwekar U., and Kalagnanam E. Efficient sampling technique for optimization under uncertainty. A.I.Ch.E. J. 43 (1997) 440-447
29. Dubois D., and Prade H. Fundamentals of Fuzzy Sets (2000), Kluwer Academic Publishers, Dordrecht
30. Floudas C.A. Research challenges, opportunities and synergism in systems engineering and computational biology. Ann. Oper. Res. 51 (2005) 1872-1884
31. Floudas C.A., and Lin X. Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review. Comput. Chem. Eng. 28 (2004) 2109-2129
32. Floudas C.A., and Lin X. Mixed integer linear programming in process scheduling: modeling, algorithms, and applications. Ann. Oper. Res. 139 (2005) 131-162
33. Fonseca, C.M., Fleming, P.J., 1993. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, California, pp. 416-423.
34. Gill P.E., Murray W., and Wright M.H. Practical Optimization (1981), Addison-Wesley, USA
35. Goldberg D.E. Genetic Algorithms in Search, Optimization and Machine Learning (1989), Addison-Wesley, USA
36. Gupta A., and Maranas C.D. A Two-Stage Modeling and Solution Framework for Multisite Midterm Planning under Demand Uncertainty. Ind. Eng. Chem. Res. 39 (2000) 3799-3813
37. Gupta A., Maranas C.D., and McDonald C. A two-stage modeling and solution framework for multisite midterm planning under demand uncertainty. Comput. Chem. Eng. 24 (2000) 2613-2621
38. Gupta A., and Maranas C.D. Managing demand uncertainty in supply chain planning. Comput. Chem. Eng. 27 (2003) 1219-1227
39. Herbst J.A., and Fuerstenau D.W. Scale-up procedure for continuous grinding mill design using population balance models. Int. J. Miner. Process. 7 (1980) 1-31
40. Herbst J.A., and Fuerstenau D.W. Mathematical simulation of dry ball milling using specific power information. Trans. AIME 254 (1973) 343
41. Herbst J.A., Siddique M., Rajamani K., and Sanchez E. Population based approach to ball mill scale-up: bench and pilot scale investigations. Trans. AIME 272 (1983) 1945-1954
42. Ierapetritou M.G., Pistikopoulos E.N., and Floudas C.A. Operational planning under uncertainty. Comput. Chem. Eng. S18 (1994) S553-S557
43. Ierapetritou M.G., and Pistikopoulos E.N. Novel optimization approach of stochastic planning models. Ind. Eng. Chem. Res. 33 (1994) 1930-1942
44. Ierapetritou M.G., and Pistikopoulos E.N. Simultaneous incorporation of flexibility and economic risk in operational planning under uncertainty. Comput. Chem. Eng. 18 (1994) 163-189
45. Kall P., and Wallace S.W. Stochastic Programming (1994), Wiley, New York
46. Kim K.J., and Diwekar U.M. Efficient combinatorial optimization under uncertainty. 2. Application to stochastic solvent selection. Ind. Eng. Chem. Res. 41 (2002) 1285-1296
47. Kinneberg D.J., and Herbst J.A. A comparison of linear and nonlinear models for open-circuit ball mill grinding. International Journal of Mineral Processing 13 (1984) 143-165
48. Knowles J.D., and Corne D.W. Approximating the nondominated front using the Pareto archived evolutionary strategy. Evolutionary Computation Journal 8 (2000) 149-172
49. Li X.D. A real coded predator-prey genetic algorithm for multiobjective optimization, evolutionary multi-criteria optimization. Lect. Notes Comput. Sci. 2632 (2003) 207-221
50. Li P., Arellano-Garcia H., and Wozny G. Chance constrained programming approach to process optimization under uncertainty. Comput. Chem. Eng. 32 (2008) 25
51. Liu B., and Iwamura K. Chance constrained programming with fuzzy parameters. Fuzzy Sets Syst. 94 (1998) 227-237
52. Liu B., and Iwamura K. A note on chance constrained programming with fuzzy coefficients. Fuzzy Sets Syst. 100 (1998) 229-233
53. Liu M.L., and Sahinidis N.V. Optimization in process planning under uncertainty. Ind. Eng. Chem. Res. 35 (1996) 4154-4165
54. Liu M.L., and Sahinidis N.V. Process planning in a fuzzy environment. Eur. J. Oper. Res. 100 (1997) 142
55. Loeve M. Probability Theory (1963), Van Nostrand-Reinhold, Princeton, NJ
56. Lynch, A.J., Rao, T.C., 1975. Modeling and scale up of hydrocyclone classifiers. In: Proceedings of the 11th International Mineral Processing Congress, Cagliari, pp. 245-269.
57. Majumdar S., Mitra K., and Raha S. Optimized species growth in epoxy polymerization with real coded NSGA II. Polymer 46 (2005) 11858-11869
58. Maranas C.D. Optimal molecular design under property prediction uncertainty. A.I.Ch.E. J. 43 (1997) 1250
59. Miettinen K. Nonlinear Multiobjective Optimization (1999), Kluwer, Boston
60. Mishra, B.K., 1991. Study of media mechanics in tumbling mills by the discrete element method. Ph.D. Thesis, Department of Metallurgical Engineering, University of Utah.
61. Mishra B.K., and Rajamani R.K. Simulation of charge motion in ball mills: numerical simulation. Int. J. Miner. Process. 40 (1994) 171-197
62. Mitra K., and Majumdar S. Selection of catalyst for the esterification step of the PPT polymerization process. Macromol. Theory Simulations 15 (2006) 497-506
63. Mitra K., and Ghosh S. Unveiling salient operating principles for reducing meniscus level fluctuations in an industrial thin slab caster using evolutionary multi-criteria Pareto optimization. Mater. Manuf. Processes 24 (2009) 88-99
64. Mitra K., Majumder S., and Runkana V. Multiobjective Pareto optimization of straight grate iron ore sintering process using evolutionary algorithms. Mater. Manuf. Processes 24 (2009) 343-350
65. Mitra K., and Gopinath R. Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm. Chem. Eng. Sci. 59 (2004) 385-396
66. Mitra K. Genetic algorithms in polymeric material production, design, processing and other applications: a review. Int. Mater. Rev. 53 (2008) 275-297
67. Mitra K., Gudi R.D., Patwardhan S.C., and Sardar G. Mid term supply chain planning under uncertainty: a multi-objective chance constrained programming framework. Ind. Eng. Chem. Res. 47 (2008) 5501-5511
68. Mitra K., Gudi R.D., Patwardhan S.C., and Sardar G. Towards resilient supply chains: uncertainty analysis using fuzzy mathematical programming. Chem. Eng. Res. Des. 24 (2009) 343-350
69. Morrell, S., Sterns, U.J., Weller, K.R., 1993. The application of population balance models to very fine grinding in tower mills. In: Proceedings of the XIX International Mineral Processing Congress, Sydney, vol. 1, pp. 61-66.
70. Napier-Munn T.J., Morrell S., Morrison R.D., and Kojovic T. Mineral Comminution Circuits (1996), JKMRC, Queensland, Australia
71. Nath N.K., and Mitra K. Mathematical modeling and optimization of two-layer sintering process for sinter quality and fuel efficiency by genetic algorithm two-layer sintering of iron ore. Mater. Manuf. Processes 20 (2005) 335-349
72. Petkov S.B., and Maranas C.D. Design of single-product campaign batch plants under demand uncertainty. A.I.Ch.E. J. 44 (1998) 896-911
73. Pettersson F., Chakraborti N., and Saxen H. A genetic algorithm based multi-objective neural net applied to noisy blast furnace data. Appl. Soft Comput. 7 (2007) 387-397
74. Pettersson F., Saxen H., and Deb K. Genetic algorithm based multicriteria optimization of iron making in the blast furnace. Mater. Manuf. Processes 24 (2009) 343-349
75. Petzold L.R. A description of DASSL: a differential/algebraic system solver. In: Stepleman R.S., et al. (Ed). Scientific Computing (1983), North-Holland, Amsterdam 65-68
76. Pistikopoulos E.N. Uncertainty in process design and operations. Comput. Chem. Eng. 19S (1995) S553-S563
77. Pistikopoulos E.N., and Ierapetritou M.G. Novel approach for optimal process design under uncertainty. Comput. Chem. Eng. 19 (1995) 1089-1110
78. Powell M.S., and Morrison R.D. The future of comminution modeling. Int. J Miner. Process. 84 (2007) 228-239
79. Prekopa A. Stochastic Programming (1995), Kluwer Academic Publishers, Dordrecht
80. Rajamani R.K., and Herbst J.A. Optimal control of a ball mill grinding circuit-I. Grinding circuit modeling and dynamic simulation. Chem. Eng. Sci. 46 (1991) 861-870
81. Rajamani R.K., and Herbst J.A. Optimal control of a ball mill grinding circuit-II. Feedback and optimal control. Chem. Eng. Sci. 46 3 (1991) 871-879
82. Sahinidis N.V. Optimization under uncertainty: state-of-the-art and opportunities. Comput. Chem. Eng. 28 (2004) 971
83. Shah N., and Pantelides C.C. Design of multipurpose batch plants with uncertain production requirements. Ind. Eng. Chem. Res. 31 (1992) 1325
84. Subrahmanyam S., Pekny J.F., and Reklaitis G.V. Design of batch chemical plants under market uncertainty. Ind. Eng. Chem. Res. 33 (1994) 2688
85. Tintner, G., 1955. Stochastic linear programming with applications to agricultural economics. In: Antosiewicz, H.A. (Ed.), Proceedings of the Second Symposium in Linear Programming, National Bureau of Standards, Washington, DC, pp. 197-228.
86. Wei D., and Craig I.K. Grinding mill circuits-a survey of control and economic concerns. Int. J. Min. Process. 90 (2009) 56-66
87. Whiten W.J. A model for simulating crushing plants. J. S. Afr. Inst. Min. Metall. 72 (1972) 257-264
88. Zimmermann H.J. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1 (1978) 45-55
89. Zimmermann H.J. Fuzzy set theory and its application (1991), Kluwer Academic Publishers, Boston
90. Zitzler E., and Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3 (1999) 257-271