The course's aim and contents are described at
Chalmers
student portal
The course
(i) and exercise
(ii) books are available in both
Swedish and English and sold by Cremona.
Complementary material
(iii) (mainly from the book
Optimization in
Operations Research by R. L. Rardin, published by Prentice-Hall, 1998)
will be handed out during the course.
-
English version:
-
Optimization (i) by J. Lundgren, M. Rönnqvist, and P. Värbrand, published by Studentlitteratur, 2010.
-
Optimization. Exercises (ii) by M. Henningsson, J. Lundgren,
M. Rönnqvist, and P. Värbrand, published by Studentlitteratur, 2010.
-
Swedish version:
-
Optimeringslära (i) by J. Lundgren, M. Rönnqvist, and P.
Värbrand, published by Studentlitteratur, 2008.
-
Optimeringslära. Övningsbok (ii) by M. Henningsson, J.
Lundgren, M. Rönnqvist, and P. Värbrand, published by Studentlitteratur, 2008.
The course plan below is preliminary and may be adjusted!!
Lecture notes will be published prior to the respective lectures in the
Activity column below.
The exercises indicated for the problem solving sessions 1-7 are preliminary.
Week 12 (March 17-21)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Lecture 1
|
Chapters in (i): 1, 2.1-5, 3
|
Introduction; course map; modelling
optimization applications; graphic solution
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-15
|
Computer exercise on linear programming
|
Thursday 10.00-11.45
|
Problem solving session 1
|
Exercises in
(ii): 3.4, 3.6, 3.10
|
Exercises on linear optimization modelling
|
Friday 10.00-10.45
|
Lecture 2a
|
|
AMPL and CPLEX, Computer exercise on linear programming Zuzana Šabartová
|
Friday 11.00-11.45
|
Lecture 2b
|
|
Supply chain
(Assignment 1) Zuzana Šabartová
|
Friday 13.15-17.00
|
Computers reserved
|
Teachers present 13.30-16.30
|
Computer exercise on linear programming
|
Week 13 (March 24-28)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Lecture 3
|
Chapters in (i): 2.4, 4.1-7, (7.1), 4.8-10
|
Convexity; basic feasible solution; the simplex method; (self study: degeneracy; unbounded solution; infeasibility; starting solutions)
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-15.00
|
Computer exercise on linear programming
|
Wednesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on linear programming
|
Thursday 10.00-11.45
|
Problem solving session 2
|
Exercises in
(ii): 4.5, 4.6, 4.13
|
Exercises on
linear optimization theory and algorithms
|
Friday 10.00-11.45
|
Lecture 4
Revised version
|
Chapters in (i): 6, (7.2-5),
5.1-5, (5.6)
|
Linear programming duality; economic
interpretation; post-optimal and sensitivity analysis
|
Week 14 (March 31-April 4)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Lecture 5
|
Chapters in (i): 13, 2.6
|
Discrete optimization models and applications; complexity
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on linear programming
|
Wednesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on linear programming
|
Thursday 10.00-11.45
|
Problem
solving session 3
|
Exercises in
(ii): 5.5, 6.8, 6.10
|
Exercises on
linear optimization duality and sensitivity analysis
|
Friday 10.00-10.45
|
Lecture 6a
|
Chapters in (i): 14.1-3, 15.1-3
|
Theory and algorithms for discrete
optimization models
|
Friday 11.00-11.45
|
Lecture 6b
|
|
Maintenance
scheduling optimization (Assignment 2)
|
Week 15 (April 7-11)
Day
|
Activity
|
Literature
|
Contents
|
Monday 23.59
|
Deadline
|
|
Hand in report of Assignment 1
|
Tuesday 10.00-11.45
|
Lecture
7
|
Chapters in (i): 14.4-5,
(14.6), 16.1-2, 17.1-2, (17.3-4) 13.10-11, 15.4, (15.5)
|
Discrete optimization: theory and
algorithms
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer programming
|
Wednesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer programming
|
Thursday 10.00-11.45
| Problem
solving session 4
|
Exercises in
(ii): 13.5, 13.6, 15.6
|
Exercises on integer linear optimization modelling and algorithms
|
Friday 9.00-9.45
|
Course evaluation meeting 2
|
|
|
Friday 10.00-11.45
|
Lecture 8
|
Chapters in (i): 16, 8.3
|
Combinatorial optimization theory and algorithms
|
Easter break
Week 18 (April 28-May 2)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-10.45
|
Lecture 9a
Revised version
|
(iii): Hand-outs
|
Multi-objective optimization
|
Tuesday 11.00-11.45
|
Lecture 9b
|
|
The traveling
salesperson problem (Assignment 3a) Emil Gustavsson
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-15.00
|
Computer exercise on integer programming
|
Friday 10.00-10.45
|
Lecture 10a
|
|
Wind power
investment and generation (Assignment 3b) Ola Carlson
|
Friday 11.00-11.45
|
Lecture 10b
Revised version
|
(iii): Hand-outs
|
Multi-objective optimization
|
Friday 23.59
|
Deadline
|
|
Hand in report of Assignment 2
|
Week 19 (May 5-9)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Lecture 11
|
Chapters in (i):, 8.1-2, 8.4, (8.5), 18.1-5, (18.6-7), 13.5
|
Network optimization: Shortest paths, dynamic programming, linear programming formulations of flows
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer and linear programming
|
Wednesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer and linear programming
|
Wednesday 23.59
|
Deadline
|
|
Hand in opposition report of Assignment 2
|
Thursday 10.00-11.45
|
Problem
solving session 5
|
Exercises in (ii): 14.4, 14.8, 17.9
|
Exercises on integer linear optimization theory and algorithms
|
Friday 10.00-11.45
|
Lecture 12
|
Chapters in (i): 8.6-7
|
Linear programming formulations and algorithms for minimum cost network flows
|
Week 20 (May 12-16)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Lecture 13
|
Chapters in (i): 2.5.1, 9-12
|
Overview of non-linear optimization
|
Tuesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer and linear programming
|
Wednesday 13.15-15.00
|
Computers reserved
|
Teachers present 13.30-14.30
|
Computer exercise on integer and linear programming
|
Thursday 10.00-11.45
|
Problem
solving session 6
|
Exercises in
(ii): 8.10, 8.12, 8.17a
|
Exercises on network flows
|
Friday 10.00-11.45
|
Problem
solving session 7
|
Exercises in
(ii): 9.8, 9.10, 11.4
|
Exercises on
non-linear optimization
|
Friday 23.59
|
Deadline
|
|
Hand in report of Assignment 3
|
Week 21 (May 19-23)
Day
|
Activity
|
Literature
|
Contents
|
Tuesday 10.00-11.45
|
Seminar 1
|
|
Students' presentations of Assignment 3
|
Thursday 10.00-11.45
|
Seminar 2
|
|
Students' presentations of Assignment 3
|
Friday 10.00-11.45
|
Seminar 3
|
|
Students' presentations of Assignment 3
|
Weeks 22 (May 26-28) and 23 (June 2-3)
Hours
|
Activity
|
Description
|
9.00-15.00
|
Oral examination for higher grades
|
Students having accomplished reports and presentations of high
enough quality may book a time slot for the oral examination.
|
- Linear optimization and software
In order to prepare for the assignments, you are recommended to do this
computer exercise on linear optimization and software.
-
Also use this
Matlab scriptfile to set paths for Cplex
Reference literature for matlab:
Tobin A. Driscoll, Learning MATLAB, ISBN: 978-0-898716-83-2
(The book is published by SIAM)
Integer linear optimization software
A
java-applet
for learning the branch-and-bound algorithm for solving integer optimization problems.
- Be aware that this is a beta-version!
- To run on Linux:
Download the file and place it in a suitable folder.
Open a terminal window and move to the folder where the jar-file is placed.
Give the command:
> java -jar BandBWithTSP.jar
- Comments and questions can be posed to ramle -at- student.chalmers.se
- AMPL-CPLEX User's Guide
can be downloaded from
here.
The following exercise numbers refer to the course book
(ii) above.
- 2.3, 2.4, 2.6
- 3.1, 3.4, 3.6, 3.10, 3.14, 3.15
- 4.2, 4.3, 4.4, 4.5, 4.6, 4.8, 4.9, 4.11, 4.15
- 5.1, 5.2, 5.4, 5.5, 5.8, 5.13
- 6.1, 6.2, 6.3, 6.6, 6.8, 6.10, 6.14, 6.15
- 13.3, 13.4, 13.5, 13.6, 13.8, 13.9, 13.13, 13.15
- 14.1, 14.3, 14.4, 14.5, 14.6, 14.7, 14.8, 14.9
- 15.3, 15.4, 15.6, 15.7, 15.12, 15.14, 15.15
- 17.8, 17.9, 17.14, 17.15, 17.17, 17.20
The randomly selected course representatives are:
Jessica Fredby (TKTEM, fredbyj -AT- student.chalmers.se),
Jonas Jagers (TKTEM, jagersj -AT- student.chalmers.se),
Johan Karlsson (MPENM, jokarls -AT- student.chalmers.se),
Joacim Linder (TKTEM, ljoacim -AT- student.chalmers.se), and
Alexander Lyckell (MPSYS, lyckell-AT- student.chalmers.se).
Being a student representative means that you are responsible for
evaluating the course together with the examiner/course responsible
and the program board of the program that gives the course. The
evaluation process consists of three parts:
-
The student representatives and the teacher are expected to have two
informal meetings during the course. The first one should be in the
first study week, the second one after approximately half the
course. The first meeting is mostly for you to get acquainted, the
second one are for the student representatives to give feedback to the
teacher on the progress of the course.
-
After the course an evaluation questionnaire is sent out. The examiner
will get a chance to add extra questions to the standard
questionnaire.
-
After the course, there will be an evaluation meeting where the
student representatives and the examiner/course responsible for the
course have a meeting together with the program board of the program
who gives the course, discussing the courses' advantages and potential
for improvement. This meeting will be held in study week 3-6 in the
study period after the examination. The examiner invites the
participants to this meeting.
The second meeting with the course representatives will be held on Friday the
11th of April at 9.00 in room MV:L11.