The Mixed Integer Linear Bilevel Programming Problem

A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are various...

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Bibliographic Details
Published in:Operations research Vol. 38; no. 5; pp. 911 - 921
Main Authors: Moore, James T, Bard, Jonathan F
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.09.1990
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Applied sciences
Bards
Computer programming
Constraints
Exact sciences and technology
Game theory
games: noncooperative
Heuristic
Heuristics
Incumbents
Index sets
Integer programming
integer: branch-and-bound algorithms
Integers
Integrality
Mathematical models
Mathematical programming
Mathematical vectors
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Optimal solutions
programming
Statistical analysis
Studies
Theory
Integer programming
Experimental result
Mixed programming
Non cooperative game
Branch and bound method
Heuristic method
Two person game
Linear programming
Algorithm
Mathematical programming
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are variously partitioned into continuous and discrete sets. The leader goes first, and through his choice may influence but not control the responses available to the follower. For two reasons the resultant problem is extremely difficult to solve, even by complete enumeration. First, it is not possible to obtain tight upper bounds from the natural relaxation; and second, two of the three standard fathoming rules common to branch and bound cannot be applied fully. In light of these limitations, we develop a basic implicit enumeration scheme that finds good feasible solutions within relatively few iterations. A series of heuristics are then proposed in an effort to strike a balance between accuracy and speed. The computational results suggest that some compromise is needed when the problem contains more than a modest number of integer variables.
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.38.5.911