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On Supportedness in Multi-Objective Integer Linear Programming
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DOI：10.1002/mcda.70024.png)
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Abstract
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This paper addresses an inconsistency in various definitions of supported non-dominated points within multi-objective integer linear optimization problems (MOILPs). MOILP problems are known to contain supported and unsupported non-dominated points, with the latter typically outnumbering the former. Supported points are, in general, easier to determine, can serve as representations and are used in two-phase methods to generate the entire non-dominated point set. Despite their importance, several different characterizations for supported efficient solutions (and supported non-dominated points) are used in the literature. While these definitions are equivalent for multi-objective linear optimization problems, they can yield different sets of supported non-dominated points for MOILP problems. We show by an example that these definitions are not equivalent for MOILP or general multi-objective optimization problems. Moreover, we analyse the structural and computational properties of the resulting sets of supported non-dominated points. These considerations motivate us to summarise equivalent definitions and characterizations for supported efficient solutions and to introduce a distinction between supported and weakly supported efficient solutions.
Keywords:
multi-objective combinatorial optimization
multi-objective integer linear programming
supported efficient solutions
weakly supported efficient
weighted sum scalarization
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2.4
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