ESI 6912 Section 6129 Spring 08 Advanced Network Optimization

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ESI 6912 Section 6129 (Spring 08)Advanced
Network Optimization

• Introduction

Ravindra K. Ahuja Professor, Industrial Systems
Engg. University of Florida Gainesville
ahuja_at_ufl.edu [phone] www.ise.ufl.edu/ahuja
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Course Objectives

• To provide an in-depth understanding of the
  underlying theory of network flows.
• To present a range of algorithms available to
  solve such problems.
• To present a range of applications of network
  optimization problems in many setting.
• To demonstrate how to solve these problems using
  advanced network optimization techniques.
• To help each student develop his or her intuition
  about algorithm design, development and analysis.

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Course Topics

• Shortest Paths
• Label-correcting algorithms
• Scaling versions of the label-correcting
  algorithm
• All-pairs shortest path algorithm
• Minimum cost-to-time ratio problem
• Applications of shortest path problem
• Maximum Flows
• Generic preflow-push algorithm
• FIFO preflow-Push Algorithm
• Highest Label Preflow-Push Algorithm
• Excess Scaling Algorithm
• Bipartite Flow Algorithm

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Course Topics (contd.)

• Minimum Cost Flows
• Cycle canceling algorithm
• Successive shortest path algorithm
• Capacity scaling algorithm
• Chinese postman problem
• Dynamic lot-sizing problems
• Weapon-target assignment problem
• Convex Cost Flows
• Applications
• Transformations to a minimum cost flow problem
• Pseudo-polynomial time algorithms
• A polynomial-time algorithm

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Course Topics (contd.)

• Generalized Flows
• Basis structure
• Optimality condition
• Primal simplex algorithm
• Lagrangian Relaxation
• Decomposition
• The technique
• Subgradient relaxation
• Applications
• Multi-commodity Flows
• Applications and different formulations
• Lagrangian relaxation algorithm
• Decomposition algorithm

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Course Topics (contd.)

• Applications
• The railroad blocking problem
• The locomotive planning problem
• The crew scheduling problem
• The weapon-target assignment problem
• The radiation therapy treatment planning problem

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Course Details

• Place FLG 275
• Office Hours
• Monday, Period 3, 930 1030 AM
• Text Books
• R. K. Ahuja, T. L. Magnanti, and J. B. Orlin,
  1993, Network Flows Theory, Algorithms, and
  Applications, Prentice Hall, NJ. ISBN
  0-13-617549-X.
• Recommended website to buy the books
  www.addall.com, www.amazon.com.
• Lecture Hours
• Monday Periods 4, 5, and 6 (1040 AM to 140 PM)
• Makeup Lecture Hours
• To be decided

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Home Work Assignments (contd.)

• One practice problem set will be distributed
  every week.
• Tutorials may be held by TA to answer questions
  related to practice problem sets.
• There will be a 15-minute test in every other
  class. The test will be either from the practice
  problem set or something similar.
• Solutions of the problem set to be submitted will
  be provided after the test.
• Some programming assignments may be given during
  the course.

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Grading

• There will be two midterm examination, each of
  two hour duration.
• First midterm will be taken in the middle of the
  semester. The second midterm will take place near
  the end of the semester. Exact dates will be
  decided later. There wont be any final exam.
• The course grade will be based on two midterm
  exams and weekly tests. The weights for these
  components will be as follows
• First Midterm Exam 35
• Second Midterm Exam 35
• Class Tests 20
• Class Attendance 10

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Additional Links

• Reference
• Ahuja, Magnanti, and Orlin, Network Flows
  Theory, Algorithms, and Applications, Prentice
  Hall, 1993.
• Class Website
• www.ise.ufl.edu/ANO