Process modelling and optimization aid

1. Process modelling and optimization aid FONTEIX Christian Professor of Chemical Engineering Polytechnical National Institute of Lorraine Chemical Engineering Sciences Laboratory

2. Process modelling and optimization aidMultiCriteria Decision Aid FONTEIX Christian Professor of Chemical Engineering Polytechnical National Institute of Lorraine Chemical Engineering Sciences Laboratory

3. Multicriteria decision aidGeneralities • Modelling of human preferences • Opposite objectives • Subjectivity • Context influence (social, economic…) • Lobbying • Expert system structure of the model • Mathematical functions • Difficulty to determine the best structure of the model and its characteristics (rules) or parameters • Robustness of a decision

4. Multicriteria decision aidGeneralities • Different methods • Sequential search by single point • The decision maker indicate at each step the search direction. Disadvantages : no entire view of the problem, a priori expression of the preferences • Using a preferences modelling on an alternatives list • To list all the alternatives at first and choose a model • To determine the prefered alternatives with the model • Advantages : entire view and a posteriori expression of the preferences

5. Multicriteria decision aidPreferences modelling types • MCDA is just an aid • It is an information for the decision maker • The decision maker choose the final decision • Parameters determination of preference modelling • Preferences extraction by cognitive determination • Preferences extraction by alternatives comparizon • Preferences extraction by parametric identification from « preferences measurement » • Group consensus

6. Multicriteria decision aid Preferences modelling types • Parametric identification from « preferences measurement » • Choice of a representative set of alternatives • The decision maker score each alternative of the set • The decision maker rank the alternatives of the set • 3 classifications for preferences modelling • Classification by the result (ranking of classification of the totality of the alternatives, or classification) • Compensative or non compensative models • Partial or total aggregation

7. A E C B F H I G Multicriteria decision aid Preferences modelling types • Classification by the result • Alternatives comparizon 2 by 2 • Determination of a Preferences Relationship System • Detection and delating of Cycles • Determination of several classification • Choice of one classification

8. Multicriteria decision aid Preferences modelling types • Classification by the compensation type • Compensative type : for each alternative a bad criterion value can be compensate by a good criterion value (2  criteria) • Non compensative type : for each alternative a bad criterion value cannot be compensate by a good criterion value (2  criteria) • Classification byaggregation type • Total aggregation : the score depends on one alternative • Partial aggregation : the score of one alternative depends also on the others

9. Multicriteria decision aid Preferences modelling types

10. Multicriteria decision aid Preferences modelling types • MAUT : Multi Attribute Utility Theory • AHP : Analytical hierarchical Process (method for MAUT parameters determination) • OWA :Ordered Weighted Average • Choquet integral : complex model (criteria interactions) • ELECTRE : ELimination Et Choix Traduisant la REalité • PROMETHEE : Preference Ranking Organisation METHod for Enrichment Evaluations • GAIA :Graphical Analysis for Interactive Assistance (for PROMETHEE)

11. Multicriteria decision aid Preferences modelling types • Rough Sets : mathematical theory which extend the set theory (as fuzzy sets) • Authors have used the rough sets theory to develop a simple fast multicriteria decision aid • In rough sets theory a set is defined by a maximum set and a minimum set

12. Multicriteria decision aid MAUT • x : alternative of which we calculate the score • fi(x) : value of the criterion i for the alternative x • ui(fi(x)) : utility value corresponding to criterion i • wi : weight associated to criterion i • s(x) : score of the alternative x • u(s(x)) : total utility of the alternative x • n : number of criteria • u(), ui() : utility functions

13. Utility Non exacting 1 Neutral Exacting decison maker Criterion value 0 Minimum Maximum Multicriteria decision aid MAUT • The weights define the relative importance of criteria • The utility functions define the intrinsic exigency of the decision maker on each criterion • The utility ([0, 1]) must be maximized • For a criterion to be minimized :

14. Multicriteria decision aid MAUT • Problem on neutral case • Example (2 criteria to be maximized) : • Parabole with one minimum • Prefered alternatives are f1 or f2 maximum  w1 • No compromise

15. Multicriteria decision aid MAUT • A limit case is given by : • If w1<0.5 the prefered alternative is f2 maximum • If w1>0.5 the prefered alternative is f1 maximum • If w1=0.5 all the alternatives are equivalent

16. Multicriteria decision aid MAUT • In practice :

17. Multicriteria decision aid OWA • x : alternative of which we calculate the score • fi(x) : value of the criterion i for the alternative x • ui(fi(x)) : performance value corresponding to criterion i • wj : weight non associated to criterion i, associated to a performance level j • Example : 0.3, 0.1, 0.8, 0.5 are ranked as 0.8, 0.5, 0.3, 0.1 and (1)=3, (2)=4, (3)=1, (4)=2 • s(x) : score of the alternative x • u(s(x)) : total performance of the alternative x • n : number of criteria • u(), ui() : performance (utility) functions

18. Multicriteria decision aid OWA • The weights define the relative importance of performance level • The performance functions define the intrinsic exigency of the decision maker on each performance level • The performance ([0, 1]) must be maximized

19. Multicriteria decision aid OWA • Example • Weight associated to performance level 1, w1=0.5 • Weight associated to performance level 2, w2=0.2 • Weight associated to performance level 3, w3=0.2 • Weight associated to performance level 4, w4=0.1 • u1=0.3, u2=0.1, u3=0.8, u4=0.5 • u1 is the performance 3, the associated weight is w3=0.2 • u2 is the performance 4, the associated weight is w4=0.1 • u3 is the performance 1, the associated weight is w1=0.5 • u4 is the performance 2, the associated weight is w2=0.2 • u=0.2*0.3+0.1*0.1+0.5*0.8+0.2*0.5=0.57

20. Multicriteria decision aid PROMETHEE • The score of one alternative depends also on the others • Analogy with football : • PROMETHEE is a championship • The alternatives are the team • The score of one alternative is the goal average • The number of goals obtained by team i on team j is ij • The number of teams is N • The score of i is :

21. Multicriteria decision aid PROMETHEE • There is one match between teams i and j • The goals obtained by team i depends of its player quality (and the player quality of team j) • Each player of team i play against the corresponding player of team j • The participation of a player to the score depends on the quality difference of the 2 corresponding players : • fk is the value of criterion k

22. Multicriteria decision aid PROMETHEE • The number of goals obtained by team i on team j is : • n is the number of criteria • Cijk depends of 2 thresholds : The indiference threshold qk The preference threshold pk

23. Multicriteria decision aid PROMETHEE Cijk 1 qk pk ijk 0

24. Multicriteria decision aid Example Emulsion polymerization : latex production Pareto domain Pareto frontier

25. Multicriteria decision aid Example Emulsion polymerization : latex production Pareto domain Pareto frontier

26. Multicriteria decision aid Example Emulsion polymerization : latex production Pareto domain Pareto frontier

27. Multicriteria decision aid Example Production of cow food by extrusion Barrel temperature Prefered zone Die

28. Multicriteria decision aid Example Production of cow food by extrusion Best decisionnal robustness Best technical robustness

29. Optimisation multicritèred’un procédé de mise en pâteà haut rendement J. Thibault (Université d’Ottawa) R. Lanouette (Université du Québec à TR) C. Fonteix (LSGC, Nancy) L.N. Kiss (Université Laval)

30. Outline • Introduction • Modelling of the fermentation process • Multicriteria Optimisation • Pareto domain • Ranking algorithm : Net Flow Method • Results • Conclusion

31. Introduction • In complex processes with a large number of input and output variables, the determination of a suitable set of input variables that would provide an optimal set of outputs is a major chalenge. • Usually dealing with numerous conflicting objectives. • There is a need to develop new optimisation methods to capture the preferences of the decision-maker to lead to an acceptable compromise solution.

32. Introduction • New techniques in multicriteria optimisation are now emerging in the field of engineering to resolve problems of conflicting criteria. • Two of these techniques have been used by the authors: • Net Flow Method • Rough Sets • They are very useful because they allow one to rank the full domain of non-dominated solutions (Pareto domain).

33. WASHED CHIPS PRESTEAMING PLUG SCREW FEEDER CYCLONE WASHING PRIMARY REFINER BLEACHING TOWER WASHING PRESS SECONDARY REFINER TO CLEANING TRANSFER CHEST LATENCY CHEST Schematic of the Process

34. Pulp and Paper Process First stage: Temperature Plate gap Interstage Treatment: H2O2 charge Temperature Retention time NaOH (Y or N) Second stage: Consistency Model Inputs For each output, the model is a stacked neural network (10 levels) having 7 inputs

35. Pulp and Paper Process Model Outputs Brightness Index maximize Specific Refining Energy minimize Extractive Content minimize Breaking Length maximize

36. It is not a one-pass process Experimental Data Modelling We are concerned only with the optimisation in this presentation Optimisation Optimisation Process Experimental Design

37. Input 1 Input 3 Input 4 Input 5 Input 6 Input 2 Optimisation • Approximation of the Pareto domain (with or without NaOH leading to two separate models) Simulation One solution Output 1 Output 2 Output 3 Output 4

38. Dominance and Pareto Domain • Procedure to approximate the Pareto domain: • Randomly select the six input variables and calculate the four criteria for a total of 6000 points. • Compare each point and discard those points that are dominated for all three criteria by at least one other point. Point 1 66.71 7.599 0.1251 4.229 Point 2 65.76 8.603 0.1745 3.837

39. Dominance and Pareto Domain Point 1 66.71 7.599 0.1251 4.229 Point 3 65.76 8.603 0.1745 4.784 A large number of points are generated and compared until 6000 non dominated points are identified.

40. Optimisation • Procedure to approximate the Pareto domain: • Randomly select the four input variables and calculate the three criteria for a total of 6000 points. • Compare each point and discard those points that are dominated for all three criteria by at least one other point. • Keep all non-dominated solutions and 30% of dominated points that are dominated fewest number of times. • Generate new points (up to 6000 points) by random interpolation between two points. • Redo the procedure until 6000 non-dominated points are obtained.

41. Optimisation • The Net Flow Method requires a human expert to give some appreciation as to the nature of each criterion. Four pieces of information must be provided: • The relative importance of each criterion (a relative weighting WK); • The indifference threshold (QK); • The preference threshold (PK); • The veto threshold (VK). 0 ≤ Qk ≤ Pk ≤ Vk

42. ck[i, j] 1 Pk 0 Qk Optimisation • Concordance index: Fk being minimized Individual Global

43. Dk[i, j] 1 Vk 0 Qk Pk Optimisation • Discordance index: Fk being minimized

44. Results Y1 - ISO Brightness Y2 - Specific refining energy Best points are in red color

45. Results Y3 - Extractives Y4 - Rupture length Best points are in red color

46. Results X1 - Temperature of first stage X2 - Plate spacing 200 best points are in dark

47. Results X3 - Consistency X4 - H2O2 Charge 200 best points are in dark

48. Results X5 - Temperature of second stage X6 - Residence time 200 best points are in dark

49. Conclusion • A multicriteria optimisation routine has been applied to optimise a pulping process. • The ranked points of the Pareto domain allow to visualize the zone of optimal operation and help in designing a control strategy.