Finding all nondominated points of multi-objective integer programs

We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional...

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Bibliographic Details
Published in:Journal of global optimization Vol. 57; no. 2; pp. 347 - 365
Main Authors: Lokman, Banu, Köksalan, Murat
Format: Journal Article
Language:English
Published: Boston Springer US 01.10.2013
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Decision making
Experiments
Graph theory
Industrial engineering
Integer programming
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Objectives
Operations research
Operations Research/Decision Theory
Optimization
Real Functions
Searching
Shortest-path problems
Nondominated point
Combinatorial optimization
Multiple criteria
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Description
Summary:We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9955-7