A Reference Direction Algorithm for Solving Multiple Objective Integer Linear Programming Problems

In this paper, we propose a reference direction approach and an interactive algorithm to solve the general multiple objective integer linear programming problem. At each iteration, only one mixed integer linear programming problem is solved to find an (weak) efficient solution. Each intermediate sol...

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Published in:The Journal of the Operational Research Society Vol. 44; no. 12; pp. 1201 - 1209
Main Authors: Vassilev, Vassil, Narula, Subhash C.
Format: Journal Article
Language:English
Published: London Taylor & Francis 01.12.1993
Macmillan Press
Palgrave Macmillan UK
Palgrave
Pergamon Press
Taylor & Francis Ltd
Subjects:
Algorithms
Applied sciences
Business and Management
Exact sciences and technology
Integer programming
Integers
Iterative solutions
Linear programming
Management
Mathematical models
Mathematical programming
Mathematical vectors
Mathematics
Multiple Criteria
Multiple Objective Integer Programming
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Operations Research/Decision Theory
Optimal solutions
Reference Points
Theoretical Paper
Theoretical Papers
Multiple Criteria
Reference Points
Multiple Objective Integer Programming
Integer programming
Linear programming
Multicriteria analysis
Algorithm
Interaction
Multiobjective programming
ISSN:0160-5682, 1476-9360
Online Access:Get full text
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Abstract In this paper, we propose a reference direction approach and an interactive algorithm to solve the general multiple objective integer linear programming problem. At each iteration, only one mixed integer linear programming problem is solved to find an (weak) efficient solution. Each intermediate solution is integer. The decision maker has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.
AbstractList Since integer programming problems are NP-hard, it is imperative to minimize the number of single objective mixed integer programming problems that have to be solved to find an acceptable compromise solution. The extent to which an algorithm achieves this objective may determine its applicability/acceptability. Furthermore, it is desirable that the demands placed on the decision maker be kept to a minimum. A reference direction approach and an interactive algorithm are proposed to solve the general multiple objective integer linear programming problem. At each iteration, only one mixed integer linear programming problem is solved to find a weak efficient solution. The decision maker has to provide only the reference point at each iteration.
In this paper, we propose a reference direction approach and an interactive algorithm to solve the general multiple objective integer linear programming problem. At each iteration, only one mixed integer linear programming problem is solved to find an (weak) efficient solution. Each intermediate solution is integer. The decision maker has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.
Author Narula, Subhash C.
Vassilev, Vassil
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  organization: Bulgarian Academy of Sciences
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  givenname: Subhash C.
  surname: Narula
  fullname: Narula, Subhash C.
  organization: Virginia Commonwealth University
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ContentType Journal Article
Copyright Copyright © 1993, Operational Research Society 1993
Copyright 1993 The Operational Research Society Limited
Operational Research Society 1993
1994 INIST-CNRS
Copyright Palgrave Macmillan Limited Dec 1993
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Issue 12
Keywords Multiple Criteria
Reference Points
Multiple Objective Integer Programming
Integer programming
Linear programming
Multicriteria analysis
Algorithm
Interaction
Multiobjective programming
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Snippet In this paper, we propose a reference direction approach and an interactive algorithm to solve the general multiple objective integer linear programming...
Since integer programming problems are NP-hard, it is imperative to minimize the number of single objective mixed integer programming problems that have to be...
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SubjectTerms Algorithms
Applied sciences
Business and Management
Exact sciences and technology
Integer programming
Integers
Iterative solutions
Linear programming
Management
Mathematical models
Mathematical programming
Mathematical vectors
Mathematics
Multiple Criteria
Multiple Objective Integer Programming
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Operations Research/Decision Theory
Optimal solutions
Reference Points
Theoretical Paper
Theoretical Papers
Title A Reference Direction Algorithm for Solving Multiple Objective Integer Linear Programming Problems
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