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MEIE662 Discrete Optimization (이산최적화)
Dr. Byung-In Kim
Science Building 4-217
279-2371
bkim@postech.ac.kr, http://www.postech.ac.kr/~bkim
Tuesdays, Thursdays 9:30-10:45
Science Building 4-405
http://povis.postech.ac.kr
Sangwon Jeong (pheonix)
Course Overview
This course emphasizes the combination of optimization techniques and information technology.
Various deterministic optimization problems and their solution approaches are introduced. The
problems include Knapsack, Traveling Salesman Problem, various Vehicle Routing Problems,
Facility Location, Scheduling, Transportation and Assignment problems. The solution approaches
include heuristics, network simplex algorithm, tabu search, genetic algorithm, simulated annealing,
branch and bound, branch and cut, and dynamic programming. 3 credit hours
Text
R. L. Rardin, Optimization in Operations Research, Prentice Hall, 1998
Grading
Students are encouraged to actively participate in class discussions. A homework assignment will
be given roughly every three weeks. There will be two exams in the semester. Make-up exam will
be given only under extraordinary circumstances. If a student is unable to take the exam on the
scheduled date for extenuating reason(s), if possible, s/he must notify the instructor before the
exam. Term project is required. Grading details are provided below.
Homework
20 %
Mid Term
20 %
Final Exam
30 %
Term Project
30 %
GRAND TOTAL
100 %
Term Project
Term project requires development of software system for Traveling Salesman Problem or
Vehicle Routing Problem with Time Windows. This is an individual project. Template for the
software development will be provided. The source code of a student from the previous year class
also will be given for reference. Each student needs to implement Exact Algorithm(use CPlex),
Greedy search, Genetic Algorithm, Simulated Annealing, and Tabu search. Further discussion will
be provided during the semester. The project is due on the last class.
Attendance
Students are expected to attend class. Students are responsible for all material presented in class.
Academic Dishonesty
The exams and home-works must be done individually by each student.
Course Schedule
Topic
Class Organization
DVD – Waste Management case
Discussion of OR, LP, IP
Nature of Discrete Optimization
Lumpy LPs and Fixed Charges, Modeling Tricks
Excel Solver
Knapsack, Capital Budgeting, Set Covering/Partitioning
Assignment and Matching Models, Clustering
Complexity theory: P, NP, NPC
Complexity Analysis
TSP
TSP, (MS Visual C++ Introduction)
Constructive Heuristics for Discrete Optimization
Improving Heuristics for Discrete Optimization, Lin-kerninghan
Simulated Annealing
Genetic Algorithm
Tabu Search, Ant-Colony
Hybrid meta heuristic – TSPTW case
Mid Term Exam
Exam Review, Vehicle Routing Problems
VRP in Waste Industry
Project 중간보고
Facilities Location and Network Design
Processor Scheduling
POSCO scheduling problem
Solving by Total Enumeration
Elementary Relaxations
Strengthening LP Relaxations
Lagrangian Relaxations
Branch and Bound
Valid Inequalities
Branch and Cut, Gomory cut
Holiday(석가탄신일)
Dantzig & Wolfe Decomposition
Column generation(Cutting Stock Problem)
Bender’s decomposition algorithm
Shortest Path Models, Dijkstra, Floyd-Warshall, Bellman-Ford
Data structure, A* one-to-one algorithm
Longest Paths and CPM
Dynamic Programming
Network Flow Models
Minimum cost network flow, Multicommodity flow
Gain/Loss flow, Network simplex algorithms
Review
Project Presentation(Project Report Due)
Final Exam
Section
Week
Date
1
3/6
3/8
2.5
11.1
2
11.2-3
11.4
3
4
11.5
11.5
12.8
12.6
12.7
12.7
5
6
7
8
11.5
9
11.6
11.7
10
12.1
12.2
12.3
11
3/13
3/15
3/20
3/22
3/27
3/29
4/3
4/5
4/10
4/12
4/17
4/19
4/24
4/26
5/1
5/3
5/8
5/10
5/15
5/17
12.4
12.5
9.1-7
12
5/22
13
5/24
5/29
14
5/31
6/5
9.6-7
9.8
10.1-8
6/7
15
-
16
6/12
6/14
6/19