Optimization Models and Methods

Know the mathematical models and techniques for solving optimization problems, as well as their applications: linear and integer programming problems, network analysis, problems in the context of machine learning.

Solve practical cases by using appropriate computer tools.

Unit 1. General foundations of mathematical optimization.
Unit 2. Linear programming.
Unit 3. Integer programming.
Unit 4. Network optimization.
Unit 5. Optimization and machine learning.

Basic
- Bazaraa, M., Jarvis, J. y Sherali, H. (2010): “Linear Programming and Network Flows”, Wiley and Sons. Available online through USC.
(Versión en castellano, más antigua: Bazaraa, M., Jarvis, J. y Sherali, H. (2005): “Programación lineal y flujo en redes”, Limusa).
- Ahuja, R. K.; Magnanti, T. L.; Orlin, J. B. (1993): “Network Flows. Theory, Algorithms and Applications”. Prentice-Hall.
- Hillier, F.; Lieberman, G. (2002): “Investigación de operaciones”, McGraw-Hill.

Complementary
- Salazar González, J.J. (2001). “Programación Matemática”. Díaz de Santos.

In this matter the basic, general and transversal competences collected in the memory of the title will be worked on. The specific competences that will be promoted in this area are indicated below:
- Knowledge of operational research techniques that can be used in the development of algorithms for solving engineering problems.
- CG8. Knowledge of the basic subjects and technologies that enable them to learn and develop new methods and technologies, as well as those that give them great versatility to adapt to new situations.
- CG9. Ability to solve problems with initiative, decision making, autonomy and creativity. Ability to know how to communicate and transmit the knowledge, abilities and skills of the profession of Technical Engineer in Computer Science.
- TR1. Instrumental: Capacity for analysis and synthesis. Organizational and planning skills. Oral and written communication in Galician, Spanish and English. Ability to manage information. Problem resolution. Decision making
- TR2. Personal: Teamwork. I work in a multidisciplinary and multilingual team. Skills in interpersonal relationships. Critical thinking. Ethical commitment
- TR3. Systemic: Autonomous learning. Adaptation to new situations. Creativity. Initiative and entrepreneurial spirit. Motivation for quality. Sensitivity towards environmental issues
- FB1. Ability to solve mathematical problems that may arise in engineering.
- FB3. Ability to understand and master the basic concepts of computational complexity, and its application for solving engineering problems.
- RI6. Knowledge and application of the basic algorithmic procedures of computer technologies to design solutions to problems by analyzing the suitability and complexity of the proposed algorithms.
- RI15. Knowledge and application of the fundamental principles and basic techniques of intelligent systems and their practical application.
- TI5. Ability to select, deploy, integrate and manage information systems that meet the needs of the organization, with identified cost and quality criteria.

The competences mentioned above will be worked on in the expository classes, where the theoretical contents of the subject and the procedures for solving practical problems will be learned; and also in the interactive classes, which will be in the computer room, where the handling of computer programs for the execution of mathematical optimization techniques will be learned, emphasizing the practical application of theoretical concepts. The reference software will be R (http://www.r-project.org) and also AMPL (https://ampl.com/).

In particular, to achieve the TR1 and FB1 competencies, activities will be proposed for the students, which will consist of solving questions, exercises and examples related to the modeling and resolution of applied optimization problems. These activities will be part of the final evaluation.

The USC Virtual Campus will also be used as a tool to provide material to students and as a possible discussion forum.

Continuous evaluation: the continuous evaluation will be carried out throughout the four-month period. It will consist of the resolution of exercises or works in which the student will use the techniques and knowledge acquired in the classes.
Final exam: the final exam will consist of theoretical and practical questions on the contents of the subject.
The final grade, both in the first and in the second opportunity, will be the maximum between: a) the grade of the final theoretical-practical exam and b) the weighted average between the continuous evaluation (25%) and the grade of the theoretical-practical exam (75%).

It is recommended to dedicate at least an hour and a half of additional work for each hour of expository and interactive class, in addition to the hours of tutoring.

To successfully pass the subject, it is highly recommended to regularly attend the expository, interactive and tutoring classes. Also, the completion of the proposed tasks should serve to achieve the objectives of the course.

In cases of fraudulent performance of exercises or tests, the provisions of the “Regulations for the evaluation of student academic performance and the review of grades” will apply.