Optimization Techniques

Code:

PDEEC0045

Acronym:

OT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 2S

Active?	Yes
Web Page:	http://www.fe.up.pt/~mac/ensino/OT20112012.html
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Doctoral Program in Electrical and Computer Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PDEEC	10	Syllabus since 2007/08	1	-	7,5	70	200

Teaching language

English

Objectives

It is expected to endow the students with skills to:
- identify, analyse and structure optimization problems;
- build models for optimization problems;
- obtain solutions for continuous linear optimization problems using the simplex method and duality theory;
- analyse the robustness of continuous linear optimization problems solutions using sensitivity analysis;
- build solutions for mixed integer and binary optimization problems using tree-search algorithms;
- use decomposition techniques to solve hard optimization problems;
- identify the best techniques to solve a particular problem;
- use CPLEX through OPL Studio interface to solve optimization problems and get insights on the solutions;
- use ILOG Solver to solve constraint models for combinatorial problems.

Program

(2 x 3 hours)
Mathematical Programming
Linear programing formulations for continuous linear optimization problems
Geometrical analysis of optimization problems

(1 x 3 hours)
Solving Linear Programs | The Simplex Algorithm

(1 x 3 hours)
Sensitivity analysis

(1 x 3 hours)
Duality in Linear Programming

(1 x 3 hours)
Integer Programming (Branch-and-Bound)

(2 x 3 hours)
Using IBM ILOG CPLEX Optimization Studio

(5 x 3 hours)
Constraint Programming

Mandatory literature

IBM ILOG CPLEX Optimization Studio (available on-line)
Bradley, Hax, and Magnanti; Applied Mathematical Programming, Addison-Wesley, 1977
Kim Marriott and Peter J. Stuckey; Programming with constraints. ISBN: 0-262-13341-5

Complementary Bibliography

Hillier, Frederick S.; Introduction to operations research. ISBN: 007-123828-X

Teaching methods and learning activities

Attendance of classes will suppose that the student has previous read the correspondent book chapter.
Each class will start with a quiz on the book chapter discussed in the previous class.
Afterwards, the new chapter will be presented and some exercises, for group resolution, proposed.
Assignments in the use of software to solve linear programming problems and constraint programming problems will consolidate the learning process.

Software

IBM ILOG CPLEX Optimization Studio

keywords

Physical sciences > Computer science > Cybernetics > Artificial intelligence
Physical sciences > Mathematics > Applied mathematics > Operations research

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	42,00
Linear programming assignment	Trabalho escrito	20,00		2012-04-18
Constraint programming assigment	Trabalho escrito	40,00		2012-06-07
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Autonomous study	Estudo autónomo	100	2012-05-31
	Total:	100,00

Eligibility for exams

not applicable

Calculation formula of final grade

The components for student evaluation are the assignments that will be graded in percentage.
The final score will be calculated according to the following:

5 quizzes (5 x 10%)
2 group assignments (20% + 30%)

Examinations or Special Assignments

Two group assignments
------------------------

Special assessment (TE, DA, ...)

These students will be subject to all evaluation procedures of regular students, i.e., they must deliver their assignments specified during the course plus any special works also specified, the only difference towards regular students being that they are not required to attend classes and deliver assignments in the same dates as regular students, in the cases the law specifically states it.

Classification improvement

not applicable