Multi-objective Decision Making Techniques

Transcription

1 Multi-objective Decision Making Techniques Dept. of Water-Atmosphere-Environment Univ. of Natural Resources and Life Sciences Water Resources Plannning and Decision Making: Module 5

2 Structure of Presentation Objectives and introduction Classification of techniques Three examples Discussion and conclusions

3 Multi-Objective Decision Making Objective: Overview of the concepts applied in MCDM One decision maker quantitative (Compromise Programming) and qualitative criteria (ELECTRE I-IV) analysis of pro s and con s applicability

4 Multi-Objective Decision Making already in the 1970 s is was recognised that single objective decision making is not successful a multi-objective framework including - economic - social - ecological goals was developed (Principles and standards in water resources planning USA 1973, 1975; EU-Framework directive on water, 2001) In the last 10 years the decision making process gained public interest

5 Example of Objectives and Subobjectives Improve national economy increase net benefits (NPV( ); multiplier effects,..) create job opportunity (permanent jobs (#), temporary jobs (#).) reduce imports (energy, high tech products,.

6 Example of Objectives and Subobjectives Improve environmental conditions preserve/extend aquatic wetlands (area (ha), natural diversity (index) ) preserve/improve groundwater quality (nitrate conc. (mg/l), dissolved iron (mg/l), heavy metals (mg/l), recharge (m3/a) preserve/stabilise endangered species (number (#), reproduction rate (%) )

7 Example of Objectives and Subobjectives Improve the social situation (job opportunities (#/a), recreational opportunities (# people/day) development should be based on regional resources (investment in the region ( ), improve equity within society benefits and adverse project impacts should be balanced within the region avoid adverse external impacts

8 Techniques Methods without preferences Methods with given preferences distance-based techniques outranking techniques (for discrete alternatives only) value- or utility-based techniques Methods with iteratively formulated preferences

9 General Concept of MO or MCDM Environmental Quality A3>A5>A7 A2>A5>A7 Nondominated alternatives A6>A7 Pareto optimal alternatives A2 A8 A3 A1 A5 A10 A7 Dominated alternatives A6 A4 A9 Economic benefit

10 Methods Without Preferences Identification of the Nondominated Set 1.st step

11 Methods Without Preferences Identification of the Nondominated Set 1.st step 2nd. step

12 Methods Without Preferences Identification of the Nondominated Set NISE-Approximation (Non Inferior Set Estimation) Within a few steps a good approximation has been achieved 3rd step

13 Methods Without Preferences -Constraint Method Stepwise optimisation with a new constraint

14 Distance Based Techniques Require quantitatively expressed criteria Require preferences (weigths and scales) Number of alternatives may be infinite (optimisation) Yield a full ranking of alternatives Might be iteratively applied

15 Procedure Impact table: expresses the consequences of each alternative with respect to each criterion in measureable units Efficiency or payoff table transformation of impacts into efficiency measures (scaling) Estimation of the overall efficiency ( best solutions )

16 Impact Table Criteria C1 ( ) C2 C3 (mg/l) Cj CJ (ha) A1 c11 c21 c31 cj1 cj1 full set of alternatives A A2 A3 Ai c12 c13 c1i c22 c23 c2i c32 c33 c3i cj2 cj3 cji cj2 cj3 cji AN c1n c2n c3n cjn cjn

17 Payoff Table The physical outcomes have to be transformed into appreciation values (often the efficiency in reaching an objective is used) ai, j ci, j c jmin c jmax c jmin

18 Sometimes Utility and Membership Functions are Used Increase in water temperature Dissolved Oxygen Water depth in river available water volume Variablity in width

19 Efficiency or Payoff Table Criteria C1 (%) C2 C3 (%) Cj CJ (%) full set of alternatives A A2 A3 Ai A1 a11 a12 a13 a1i a21 a22 a23 a2i a31 a32 a33 a3i aj1 aj2 aj3 aji aj1 aj2 aj3 aji AN a1n a2n a3n ajn ajn

20 Selection of Favourable Solutions Unfeasible Domain Ak Favourable Domain Ai Non dominated Domain Feasible Domain Ecological Objective

21 Selection of Favourable Solutions Compromise Programming D1i Ai Di Di unscaled distance di scaled distance D2i Ecological Objective

22 Identification of Favourable Solutions d i, j 1 ai, j Li ( p ) ( w j d ip, j )1 / p Distance with respect to one criterion Overall distance wj p weights trade-off factor What is the role of weights? What is the role of p?

23 Ranking of Alternatives For a set of given weights and a p value the distance of each alternative from the ideal point can be computed The alternatives are ranked in increasing distances The alternatives with small distances are preferred

24 Outranking Techniques Often, a pairwise comparison of alternatives is performed e.g. A3>A4, A5>A4, A4>A2, A3>A2 In ELECTRE (I) only an incomplete ranking can be achieved In ELECTRE (IV) a complete ranking is achieved Both approaches require weigths and scales for describing the preferences.

25 ELECTRE I Simple example: 2 alternatives, 3 criteria C1 C2 C3 A1 c11 c21 c31 A2 c12 c22 c32 W w1 w2 w3 S s1 s2 s3

26 ELECTRE I C1 NPV in (Mio ) C2 (mg/l) water pollution C3 (# of created jobs)

27 ELECTRE I Impact table W weight S scale A1 C1 1.5 C2 10 C3 100 A W Scale Best Worst

28 ELECTRE: Concordance and Discordance Concordance expresses the dominance of Ai>Aj Discordance expresses the weakness of Ai<Aj CO (i, j ) ( wk ( for _ c(i, k ) c( j, k )) 1 / 2 wk ( for _ c(i, k ) c( j, k ))) / wk k k k scale _( c(i, k ) c( j, k )) DI (i, j ) Max Scale( k )

29 ELECTRE I CO(1,2)=0.2, CO(2,1)= 0.8 DI(1,2)= Max (0.3, 0,2)=0.3 DI(2,1)=Max(10/50)=0.2 Finally two matrices CO(,) and DI(,) are obtained A threshold level CO* and DI* is introduced (e.g. CO* = 0.75,DI*=0.2 then A2>A1

30 Example for a Distance Based Technique: 2 Countries share the same river They have different development plans They have different preferences (one has strong environmental interests, the other is weak with respect to environmental plans, it wants to develop economy The project impacts are different in each country

31 Example Impact table Country A Impact table Country B Different ranking of alternatives in each country Look for an alternative which is close to the preferred alternative in each country

32 Other Distance Based Techniques Goal Programming Compromise Programming Cooperative Game Theory

33 Utility Based Techniques Often single attribute utility theory is applied If possible, MAUT (Multi-Attribute-Utility Theory) should be applied Utility Value 5 Cj (m3) 10 available amount of water

34 Utility Theory (1) (2) (3) (4) Impact matrix Transformation of impacts into utilities Definition of weigths for each criterion Overall utility value UVi of alternative Ai is UVi w j uvij j

35 1-D and 2-D Utility Functions 1-D Utility 2-D Utility

36 Conclusions Numerous methods exist for evaluation of water resources projects Multi-objective decision making is a daily problem The concepts of multiple objectives is found in many international/national case studies The major steps are in the problem definition in the impact assessment in knowing about the preferences The numerical methods are helpful in improving the understanding of the problem and for exploring the feasible domain