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

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Process modelling and optimization aid

Process modelling and optimization aid

FONTEIX Christian

Professor of Chemical Engineering

Polytechnical National Institute of Lorraine

Chemical Engineering Sciences Laboratory


Process modelling and optimization aid multicriteria decision aid

Process modelling and optimization aidMultiCriteria Decision Aid

FONTEIX Christian

Professor of Chemical Engineering

Polytechnical National Institute of Lorraine

Chemical Engineering Sciences Laboratory


Multicriteria decision aid generalities
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


Multicriteria decision aid generalities1
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


Multicriteria decision aid preferences modelling types
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


Multicriteria decision aid preferences modelling types1
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


Multicriteria decision aid preferences modelling types2

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


Multicriteria decision aid preferences modelling types3
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


Multicriteria decision aid preferences modelling types4
Multicriteria decision aid Preferences modelling types


Multicriteria decision aid preferences modelling types5
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)


Multicriteria decision aid preferences modelling types6
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


Multicriteria decision aid maut
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


Multicriteria decision aid maut1

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 :


Multicriteria decision aid maut2
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


Multicriteria decision aid maut3
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


Multicriteria decision aid maut4
Multicriteria decision aid MAUT

  • In practice :


Multicriteria decision aid owa
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


Multicriteria decision aid owa1
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


Multicriteria decision aid owa2
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


Multicriteria decision aid promethee
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 :


Multicriteria decision aid promethee1
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


Multicriteria decision aid promethee2
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


Multicriteria decision aid promethee3
Multicriteria decision aid PROMETHEE

Cijk

1

qk

pk

ijk

0


Multicriteria decision aid example
Multicriteria decision aid Example

Emulsion polymerization : latex production

Pareto domain

Pareto frontier


Multicriteria decision aid example1
Multicriteria decision aid Example

Emulsion polymerization : latex production

Pareto domain

Pareto frontier


Multicriteria decision aid example2
Multicriteria decision aid Example

Emulsion polymerization : latex production

Pareto domain

Pareto frontier


Multicriteria decision aid example3
Multicriteria decision aid Example

Production of cow food by extrusion

Barrel temperature

Prefered zone

Die


Multicriteria decision aid example4
Multicriteria decision aid Example

Production of cow food by extrusion

Best decisionnal

robustness

Best technical

robustness


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)


Outline

  • Introduction

  • Modelling of the fermentation process

  • Multicriteria Optimisation

    • Pareto domain

    • Ranking algorithm : Net Flow Method

  • Results

  • Conclusion


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.


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).


Schematic of the process

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


Pulp and paper process
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


Pulp and paper process1
Pulp and Paper Process

Model Outputs

Brightness Index

maximize

Specific Refining Energy

minimize

Extractive Content

minimize

Breaking Length

maximize


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


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


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


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.


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.


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


ck[i, j]

1

Pk

0

Qk

Optimisation

  • Concordance index:

Fk being minimized

Individual

Global


Dk[i, j]

1

Vk

0

Qk

Pk

Optimisation

  • Discordance index:

Fk being minimized


Results

Y1 - ISO Brightness

Y2 - Specific refining energy

Best points are in red color


Results

Y3 - Extractives

Y4 - Rupture length

Best points are in red color


Results

X1 - Temperature of first stage

X2 - Plate spacing

200 best points are in dark


Results

X3 - Consistency

X4 - H2O2 Charge

200 best points are in dark


Results

X5 - Temperature of second stage

X6 - Residence time

200 best points are in dark


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.


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