A Class of Algorithms for Mixed-Integer Bilevel Min-Max Optimization Problems with Applications

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Material Information

Title:
A Class of Algorithms for Mixed-Integer Bilevel Min-Max Optimization Problems with Applications
Physical Description:
1 online resource (114 p.)
Language:
english
Creator:
Tang, Yen Thi
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Industrial and Systems Engineering
Committee Chair:
RICHARD,JEAN-PHILIPPE P
Committee Co-Chair:
SMITH,JONATHAN COLE
Committee Members:
GEUNES,JOSEPH PATRICK
YIN,YAFENG

Subjects

Subjects / Keywords:
bilevel -- evacuation -- interdiction -- mixed-integer -- network -- optimization
Industrial and Systems Engineering -- Dissertations, Academic -- UF
Genre:
Industrial and Systems Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In this dissertation, we construct algorithms to solve  a class of mixed-integer bilevel min-max optimization problems, with applications to knapsack, clique, and  evacuation problems. These optimization problems involve two players, a leader and a follower, who play  a Stackelberg game. We investigate first a problem in which the leader seeks to minimize, over a set of discrete variables, the maximum objective that  the follower can achieve. We study bilevel min-max programs that can be used to obtain lower and upper bounds on the optimal objective  value of the problem. We then develop a class of  algorithms  that finitely terminate with an optimal solution when the leader variables take binary values. We report the results of a computational study aimed at evaluating the quality of our algorithms on bilevel knapsack and bilevel clique instances. We study an application of the bilevel min-max optimization problem, which we call  multilevel evacuation problem. This problem seeks to construct arcs in a network to minimize the cost needed to evacuate a population in the face of disaster, assuming that "nature'' is an intelligent agent. We consider four variants of this problem, corresponding to assumptions where the disaster either is or is not restricted to a set of fixed locations, and where the number of people to be evacuated from an area affected by the disaster either does or does not depend on the distance from that area to the epicenter of the disaster. We formulate this problem as a three-level optimization problem. We then reformulate it into a  bilevel model of a form similar to that studied in the first part of this dissertation. We extend  the methodology introduced in the first part of this dissertation to construct a finitely convergent algorithm to solve the multilevel evacuation problem. We present numerical results last.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Yen Thi Tang.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: RICHARD,JEAN-PHILIPPE P.
Local:
Co-adviser: SMITH,JONATHAN COLE.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2016-05-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2014
System ID:
UFE0046155:00001