Influence diagrams with multiple objectives and tradeoff analysis Export

@article{citeulike:2925072, abstract = {Influence diagrams have been important models for decision problems because of their ability to both model a problem rigorously at its mathematical level and depict its high-level structure graphically. Once the structure and numerical details of an influence diagram have been specified, it can be evaluated to determine the optimal decision policy. However, when evaluating multiple objectives, in the past this determination was based on the assumption that utility functions that commensurate the objectives are available. This paper extends the structure and solution algorithm for influence diagrams to allow for the inclusion of noncommensurate objectives using multiobjective tradeoff analysis instead of utility theory. This eliminates the need to specify any preference information before the influence diagram is solved. The proposed multiobjective-based methodology is also useful for decision makers who either do not want to accept the assumptions of utility theory for a particular problem, or are confronted with a problem in which it is neither practical nor viable to construct a utility function. Additionally, this paper establishes the relationship between multiobjective influence diagrams and multiobjective decision trees. This relationship is important because it allows a decisionmaker to utilize the advantages of both representations. An example problem is presented to introduce both the extended multiobjective influence diagram methodology and the relationship linking multiobjective decision trees to multiobjective influence diagrams.}, author = {Diehl, M. and Haimes, Y. Y.}, booktitle = {Systems, Man and Cybernetics, Part A, IEEE Transactions on}, citeulike-article-id = {2925072}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TSMCA.2003.822967}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1288341}, comment = {A nice explication of the difference between an influence diagram (ID) and a decision tree (DT), and under what conditions one can directly convert an ID into a DT. Develops a method for multi-objective decision trees and influence diagram, in which one finds a set of values for a set of utility functions instead of having one (or a combined/multi-attribute) utility function. ``Despite its shortcomings, multiattribute utility theory has provided a good starting point for the development of a variety of new techniques to incorporate multiple objectives in decisionmaking [23]. One such approach, which is termed multiobjective tradeoff analysis, allows for the posterior specification of the decisionmaker's preference after the decision problem has been solved. The main idea behind this approach is to separate solutions or alternatives into two sets at each optimization in the solution procedure, those that are inferior and those that are noninferior. A solution is only considered inferior if another solution has values that are equal or better for all objectives being considered. Only the set of noninferior solutions (also termed as efficient, nondominated, or Pareto optimum) is kept for further analysis after each stage of the problem. Once the set of noninferior solutions is determined, the chosen alternative(s) is identified by evaluating the decisionmaker's preferred tradeoff values. There are multiple ways to accomplish this, including the surrogate worth tradeoff (SWT) method [10], which calculates tradeoff functions and relates the decisionmaker's preferences to these tradeoffs. The main advantage of multiobjective tradeoff analysis is that neither a value function nor the usual assumptions of utility theory are necessary [10]. Nevertheless, this approach is not without its problems. Multiobjective tradeoff analysis is susceptible to dimensionality concerns as the number of objectives and the size of the problem increase, often leading to more noninferior solutions than the decisionmaker can efficiently analyze. Multiobjective tradeoff analysis has already been successfully applied to decision trees by Haimes, Li, and Tulsiani [9]. Their methodology establishes the concept of multiobjective decision trees. A multiobjective decision tree is much like a conventional single objective decision tree except that in the multiobjective case, each alternative and outcome is characterized by a vectorvalued performance measure instead of a single measure. A multiobjective decision tree can be solved by first assigning probabilities and vector-valued performance measures to the appropriate alternatives and outcomes, and then folding back the tree from each terminal point. However, in this case, the fold-back procedure needs to be modified to ensure that all valid noninferior solutions are determined at each stage. This paper applies multiobjective tradeoff analysis to extend the single objective influence diagram. This allows an alternative way of dealing with multiple objectives that avoids some of the problems and issues with multiattribute utility theory. The application of multiobjective tradeoff analysis to influence diagrams requires adaptations to both the structure of the conventional influence diagram and the solution procedure employed to determine its optimal decision policy. These adaptations are described in the following section.'' }, doi = {10.1109/TSMCA.2003.822967}, journal = {Systems, Man and Cybernetics, Part A, IEEE Transactions on}, keywords = {causality}, number = {3}, pages = {293--304}, posted-at = {2008-06-25 06:41:49}, priority = {0}, title = {Influence diagrams with multiple objectives and tradeoff analysis}, url = {http://dx.doi.org/10.1109/TSMCA.2003.822967}, volume = {34}, year = {2004} }

TY - JOUR ID - citeulike:2925072 L3 - citeulike-article-id:2925072 N2 - Influence diagrams have been important models for decision problems because of their ability to both model a problem rigorously at its mathematical level and depict its high-level structure graphically. Once the structure and numerical details of an influence diagram have been specified, it can be evaluated to determine the optimal decision policy. However, when evaluating multiple objectives, in the past this determination was based on the assumption that utility functions that commensurate the objectives are available. This paper extends the structure and solution algorithm for influence diagrams to allow for the inclusion of noncommensurate objectives using multiobjective tradeoff analysis instead of utility theory. This eliminates the need to specify any preference information before the influence diagram is solved. The proposed multiobjective-based methodology is also useful for decision makers who either do not want to accept the assumptions of utility theory for a particular problem, or are confronted with a problem in which it is neither practical nor viable to construct a utility function. Additionally, this paper establishes the relationship between multiobjective influence diagrams and multiobjective decision trees. This relationship is important because it allows a decisionmaker to utilize the advantages of both representations. An example problem is presented to introduce both the extended multiobjective influence diagram methodology and the relationship linking multiobjective decision trees to multiobjective influence diagrams. IS - 3 JF - Systems, Man and Cybernetics, Part A, IEEE Transactions on EP - 304 TI - Influence diagrams with multiple objectives and tradeoff analysis VL - 34 T2 - Systems, Man and Cybernetics, Part A, IEEE Transactions on SP - 293 KW - causality N1 - A nice explication of the difference between an influence diagram (ID) and a decision tree (DT), and under what conditions one can directly convert an ID into a DT. Develops a method for multi-objective decision trees and influence diagram, in which one finds a set of values for a set of utility functions instead of having one (or a combined/multi-attribute) utility function. ``Despite its shortcomings, multiattribute utility theory has provided a good starting point for the development of a variety of new techniques to incorporate multiple objectives in decisionmaking [23]. One such approach, which is termed multiobjective tradeoff analysis, allows for the posterior specification of the decisionmaker’s preference after the decision problem has been solved. The main idea behind this approach is to separate solutions or alternatives into two sets at each optimization in the solution procedure, those that are inferior and those that are noninferior. A solution is only considered inferior if another solution has values that are equal or better for all objectives being considered. Only the set of noninferior solutions (also termed as efficient, nondominated, or Pareto optimum) is kept for further analysis after each stage of the problem. Once the set of noninferior solutions is determined, the chosen alternative(s) is identified by evaluating the decisionmaker’s preferred tradeoff values. There are multiple ways to accomplish this, including the surrogate worth tradeoff (SWT) method [10], which calculates tradeoff functions and relates the decisionmaker’s preferences to these tradeoffs. The main advantage of multiobjective tradeoff analysis is that neither a value function nor the usual assumptions of utility theory are necessary [10]. Nevertheless, this approach is not without its problems. Multiobjective tradeoff analysis is susceptible to dimensionality concerns as the number of objectives and the size of the problem increase, often leading to more noninferior solutions than the decisionmaker can efficiently analyze. Multiobjective tradeoff analysis has already been successfully applied to decision trees by Haimes, Li, and Tulsiani [9]. Their methodology establishes the concept of multiobjective decision trees. A multiobjective decision tree is much like a conventional single objective decision tree except that in the multiobjective case, each alternative and outcome is characterized by a vectorvalued performance measure instead of a single measure. A multiobjective decision tree can be solved by first assigning probabilities and vector-valued performance measures to the appropriate alternatives and outcomes, and then folding back the tree from each terminal point. However, in this case, the fold-back procedure needs to be modified to ensure that all valid noninferior solutions are determined at each stage. This paper applies multiobjective tradeoff analysis to extend the single objective influence diagram. This allows an alternative way of dealing with multiple objectives that avoids some of the problems and issues with multiattribute utility theory. The application of multiobjective tradeoff analysis to influence diagrams requires adaptations to both the structure of the conventional influence diagram and the solution procedure employed to determine its optimal decision policy. These adaptations are described in the following section.'' AU - Diehl, M AU - Haimes, YY PY - 2004/// UR - http://dx.doi.org/10.1109/TSMCA.2003.822967 ER -