Generalized equitable preference in multiobjective programming

The concept of equitability in multiobjective programming is generalized within a framework of convex cones. Two models are presented. First, more general polyhedral cones are assumed to determine the equitable preference. Second, the Pareto cone appearing in the monotonicity axiom of equitability is replaced with a permutation-invariant polyhedral cone. The conditions under which the new models are related and satisfy original and modified axioms of the equitable preference are developed. Relationships between generalized equitability and relative importance of criteria and stochastic dominance are revealed.

[1]  Xavier Gandibleux,et al.  MultiObjective Programming and Goal Programming , 2003 .

[2]  H. Levy.  Stochastic Dominance: Investment Decision Making under Uncertainty , 2010 .

[3]  Vladimir D. Noghin,et al.  Using quantitative information on the relative importance of criteria for decision making , 2000 .

[4]  Michael M. Kostreva,et al.  Linear optimization with multiple equitable criteria , 1999, RAIRO Oper. Res..

[5]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[6]  Adam Wierzbicki,et al.  A multi-criteria approach to fair and efficient bandwidth allocation , 2008 .

[7]  Wlodzimierz Ogryczak,et al.  Dual Stochastic Dominance and Related Mean-Risk Models , 2002, SIAM J. Optim..

[8]  M. O. Lorenz,et al.  Methods of Measuring the Concentration of Wealth , 1905, Publications of the American Statistical Association.

[9]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[10]  Hirotaka Nakayama,et al.  Theory of Multiobjective Optimization , 1985 .

[11]  Wlodzimierz Ogryczak,et al.  Conditional Median: A Parametric Solution Concept for Location Problems , 2002, Ann. Oper. Res..

[12]  Wlodzimierz Ogryczak,et al.  Multiple criteria linear programming model for portfolio selection , 2000, Ann. Oper. Res..

[13]  Adam Wierzbicki,et al.  Equitable aggregations and multiple criteria analysis , 2004, Eur. J. Oper. Res..

[14]  M. Wiecek.  Advances in Cone-Based Preference Modeling for Decision Making with Multiple Criteria , 2007 .

[15]  Włodzimierz Ogryczak,et al.  Multiple criteria optimization and decisions under risk , 2002 .

[16]  Justo Puerto,et al.  Sequential incorporation of imprecise information in multiple criteria decision processes , 2002, Eur. J. Oper. Res..

[17]  Brian J. Hunt.  Multiobjective Programming with Convex Cones: Methodology and Applications , 2004 .

[18]  Margaret M. Wiecek,et al.  Modeling relative importance of design criteria with a modified pareto preference , 2007 .

[19]  Wlodzimierz Ogryczak,et al.  Inequality measures and equitable approaches to location problems , 2000, Eur. J. Oper. Res..

[20]  A. Shorrocks.  Ranking Income Distributions , 1983 .

[21]  G. Pflug,et al.  Quantitative Fund Management , 2008 .

[22]  Margaret M. Wiecek,et al.  Advancing equitability in multiobjective programming , 2006, Comput. Math. Appl..

[23]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[24]  Wlodzimierz Ogryczak,et al.  On solving linear programs with the ordered weighted averaging objective , 2003, Eur. J. Oper. Res..

[25]  Gautam Mitra,et al.  Portfolio construction based on stochastic dominance and target return distributions , 2006, Math. Program..

[26]  V. Noghin.  Relative importance of criteria: a quantitative approach , 1997 .

[27]  Patrice Perny,et al.  A decision-theoretic approach to robust optimization in multivalued graphs , 2006, Ann. Oper. Res..

[28]  Margaret M. Wiecek,et al.  Relative importance of criteria in multiobjective programming: A cone-based approach , 2010, Eur. J. Oper. Res..

[29]  Margaret M. Wiecek,et al.  Cones to Aid Decision Making in Multicriteria Programming , 2003 .

[30]  Vijay P. Singh.  Equitable efficiency in multiple criteria optimization , 2007 .

[31]  Wlodzimierz Ogryczak,et al.  On efficient WOWA optimization for decision support under risk , 2009, Int. J. Approx. Reason..