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Indifference sets of reference points in multi‐objective integer linear programming
Author(s) -
Alves Maria João,
Clímaco João
Publication year - 2001
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.301
Subject(s) - integer programming , integer (computer science) , linear programming , set (abstract data type) , representation (politics) , function (biology) , metric (unit) , point (geometry) , mathematics , reference model , reference data , mathematical optimization , computer science , data mining , geometry , operations management , software engineering , evolutionary biology , politics , political science , law , economics , biology , programming language
Reference point approaches for multi‐objective problems rely on the definition of an achievement scalarizing function that projects reference points onto the non‐dominated solution set. In this paper, we investigate the behaviour of reference points using a Tchebycheff metric‐based scalarizing function in multi‐objective pure integer linear programming (MOILP). Since the non‐dominated solutions are discrete in MOILP, there are multiple reference points that lead to the same solution, i.e. there are indifference sets on the reference point space. We investigate some properties of the reference points in MOILP and also the graphical representation of indifference sets for tri‐objective problems. We further investigate properties of the reference points when additional limitations on the objective function values are introduced. Copyright © 2001 John Wiley & Sons, Ltd.