Optimization

Code:

PRDEIG007

Acronym:

OPTI

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2596
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Doctoral Program in Engineering and Industrial Management

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEGI	3	Syllabus since 2015/16	1	-	6	42	162

Teaching language

English

Objectives

The main objective of this course is to build skills for creating models for combinatorial optimization problems and to solve them through exact techniques.

Learning outcomes and competences

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 CPLEX through OPL Studio interface to solve optimization problems and get insights on the solutions;
• use ILOG Solver to solve constraint programming models for combinatorial problems.

Working method

Presencial

Program

• Linear programing formulations for continuous linear optimization problems.


• Geometrical analysis of optimization problems.


• Solving linear programming problems.


• Sensitivity analysis.


• Duality in linear programming.


• Integer programming models.


• Solution methods for integer programming


• Using IBM ILOG CPLEX Optimization Studio.


• Constraint programming.

Mandatory literature

IBM ILOG CPLEX ; IBM ILOG CPLEX Optimization Studio (available on-line)
Bradley, Hax, and Magnanti; Applied Mathematical Programming, Addison-Wesley, 1977 (downloadable from http://web.mit.edu/15.053/www/)
Kim Marriott and Peter J. Stuckey; Programming with constraints. ISBN: 0-262-13341-5

Complementary Bibliography

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

Teaching methods and learning activities

Before each one of the classes the students should study the corresponding chapter in the book

Some of the classes will start with a quiz on the book chapters discussed in previous classes. The new chapter will then be presented and some exercises will be solved in class.

The learning process will be consolidated through two assignments that will be based on the use of software for solving linear problems (CPLEX) and constraint programming problems (ILOG Solver), that will be presented in class.

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

Designation	Weight (%)
Teste	50,00
Trabalho escrito	50,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	95,00
Frequência das aulas	42,00
Trabalho de campo	25,00
Total:	162,00

Eligibility for exams

not applicable

Calculation formula of final grade

The final score will be calculated according to the following:

• 3 quizzes (closed book), from which the best 2 are chosen (2 x 25%);
• 2 individual assignments (15% + 20%);
• 1 presentation (15%).

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