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MULTICRITERIA OPTIMIZATION: A GENERAL CHARACTERIZATION OF EFFICIENT SOLUTIONS *
Author(s) -
Soland Richard M.
Publication year - 1979
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1979.tb00004.x
Subject(s) - mathematical optimization , satisficing , convexity , maximization , multi objective optimization , context (archaeology) , set (abstract data type) , computer science , basis (linear algebra) , pareto principle , mathematics , function (biology) , paleontology , geometry , artificial intelligence , evolutionary biology , financial economics , economics , biology , programming language
In the context of deterministic multicriteria maximization, a Pareto optimal, nondominated , or efficient solution is a feasible solution for which an increase in value of any one criterion can only be achieved at the expense of a decrease in value of at least one other criterion. Without restrictions of convexity or continuity, it is shown that a solution is efficient if and only if it solves an optimization problem that bounds the various criteria values from below and maximizes a strictly increasing function of these several criteria values. Also included are discussions of previous work concerned with generating or characterizing the set of efficient solutions, and of the interactive approach for resolving multicriteria optimization problems. The final section argues that the paper's main result should not actually be used to generate the set of efficient solutions, relates this result to Simon's theory of satisficing, and then indicates why and how it can be used as the basis for interactive procedures with desirable characteristics.