1 / 16

Using Preference Constraints to Solve Multi-criteria Decision Making Problems

Using Preference Constraints to Solve Multi-criteria Decision Making Problems. Tanja Magoč, Martine Ceberio, and François Modave Computer Science Department, The University of Texas at El Paso. Outline. Multi-criteria decision making (MCDM) Traditional techniques to solve MCDM problem

christmas
Download Presentation

Using Preference Constraints to Solve Multi-criteria Decision Making Problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Using Preference Constraints to Solve Multi-criteria Decision Making Problems Tanja Magoč, Martine Ceberio, and François Modave Computer Science Department, The University of Texas at El Paso

  2. Outline • Multi-criteria decision making (MCDM) • Traditional techniques to solve MCDM problem • A novel approach • Representing preferences over criteria in terms of constraints • Narrowing down the search space

  3. Multi-criteria decision making • Comparison of multidimensional alternatives to select the optimal one • Pick the “best” car to buy • Elements of a MCDM setting: • a set of alternatives • cars (finitely many) • a set of criteria • color, safety rating, price • a set of values of the criterion • color={red, black, grey}, safety rating={1,2,3,4,5}, price=[11000, 53000] • a preference relation for each criterion: • red>black>grey, lower price is more preferred than higher price, higher safety rating is more preferred than lower safety rating • Challenge: Combine partial preferences into a global preference

  4. Traditional techniques to solve MCDM problems • Utility based approaches: • Maximax strategy • Maximin strategy • Weighted sum approach • Non-additive approaches • The Choquet integral w.r.t. a non-additive measure

  5. Narrow down the search space • Narrow down the search space from all possible values that criteria can take to a smaller space that contains the best alternative based on the preferences of an individual. • Assumption: the decision maker is able to express his/her preference of a criterion over another criterion by means of how much of a criterion he/she would sacrifice in order to obtain higher value of the other criterion. • E.g. the individual knows how much more he/she is willing to pay for an increase in one star of safety rating. • Different tradeoff at different value.

  6. Process of narrowing down the search space • Map the domain of each criterion into an interval • Convert each of the intervals into the interval [0,1] • higher preference is given to values closer to 1 • Original search space=cross product of these intervals • Constraints on the search space: preferences provided by decision maker • Input how much the individual is willing to “pay” using one criterion to increase the value of other criterion by 0.2 • Use standard techniques for solving problems with constraints to narrow the search space

  7. Example: Map domains into intervals • Map domains of criteria into intervals: • Color={red, black, gray}[1,3] with gray<black<red • Safety rating={1,2,3,4,5}[1,5] • Price=[11000,53000] • Convert all interval domains onto a common scale [0,1], where higher number means a higher preference: • Color: u(c)=(c-1)/2 • Safety rating: u(s)=(s-1)/5 • Price: u(p)=(53000-p)/42000

  8. Example: Importance of an increase • The decision maker gives an importance value from 0-10 for each increase in 0.2 value in a criterion relative to another criterion • 0 means the individual is not willing to sacrifice other particular criterion at all for increase in the value of the criteria • 10 means the individual is willing to sacrifice lot for increase in the value of the criteria

  9. Example: Importance of an increase • Safety rating relative to price: • 0.00.2: 10 • 0.20.4: 9 • 0.40.6: 7 • 0.60.8: 5 • 0.81.0: 2 • Sum of values = 33 • Increase in safety rating from 0.0 to 0.2 is worth decreasing value of price by (10/33)*100% • Increase in safety rating from 0.8 to 1.0 is worth decreasing value of price by (2/33)*100%

  10. Example: Constraint based on safety rating and price Price 1.0 0.8 0.6 0.4 0.2 Safety rating 0.2 0.4 0.6 0.8 1.0

  11. Example: Constraint between safety rating and price Price 1.0 0.8 0.6 0.4 0.2 Safety rating 0.2 0.4 0.6 0.8 1.0

  12. Example: Constraint between safety rating and price Price 1.0 0.8 0.6 0.4 0.2 Safety rating 0.2 0.4 0.6 0.8 1.0

  13. Example: All constraints together • Constraints: • safety rating – price • price – color • safety rating – color • Each constraint itself narrows down the search space • Use standard techniques used to narrow down the search space even more

  14. Example: Constraint between safety rating and price Price 1.0 0.8 0.6 0.4 0.2 Safety rating 0.2 0.4 0.6 0.8 1.0

  15. Conclusion • What have we done? • Represent multi-criteria decision making problem in terms of preference constraints defined by the decision maker • Reduce the initial search space by using standard continuous constraint solving techniques • Why is this approach better? • Speeds up the process of finding the best solution by fast elimination of domains that certainly do not contain the best solution • What is the next step? • Define more complex/general preferences • Combine importance and interactions (Choquet) with preferences

  16. Thank you QUESTIONS???

More Related