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Generating interior search directions for multiobjective linear programming
Author(s) -
Arbel Ami,
Oren Shmuel S.
Publication year - 1993
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.4020020204
Subject(s) - interior point method , linear programming , mathematical optimization , polytope , scaling , affine transformation , mathematics , point (geometry) , function (biology) , algorithm , preference , computer science , combinatorics , statistics , geometry , evolutionary biology , pure mathematics , biology
A new multiobjective linear programming (MOLP) algorithm is presented. The algorithm uses a variant of Karmarkar's interior‐point algorithm known as the affine‐scaling primal algorithm. Using this single‐objective algorithm, interior search directions are generated and used to provide an approximation to the gradient of the (implicitly known) utility function. The approximation is guided by assessing locally relevant preference information for the various interior directions through interaction with a decision maker (DM). The resulting algorithm is an interactive approach that makes its progress towards the solution through the interior of the constraints polytope.