Advanced Numerical Computation
- Lecturer (Coordinator):
- Vicente Martín
- vicente@fi.upm.es
- Lecturer:
- Esther Dopazo
- edopazo@fi.upm.es
- Profesor:
- Juan Pedro Brito
- jp.brito@fi.upm.es
- Lecturer:
- José Luis Rosales
- jose.rosales@fi.upm.es
Semester
Second semester
Credits
4 ECTS
Outline
The studied numerical techniques focus on optimization methods and are addressed from an essentially practical viewpoint. They include classical methods for problems with and without constraints, stochastic methods like simulated annealing and techniques based on biological systems like evolutionary computing or artificial immune systems, and foraging and swarm strategies. Finally, students will look at their application to production line problems in industry.
Learning Goals
Familiarity with applied advanced numerical calculus techniques and their implementation in high-performance computing in order to solve new problems and generally tackle and research questions related to this line of work.
Syllabus
- Introduction to optimization
- Problem statement. Types and examples
- Basic optimization concepts
- Methods of optimization
- Optimization with and without constraints: traditional methods
- Heuristic optimization: algorithms based on ideas borrowed from natural processes: simulated annealing, evolutionary algorithms, immune networks, etc. Practical examples
- Application of optimization techniques to industrial problems
Recommended reading
- M. A. Bhatti: "Practical Optimization Methods". Springer-Verlag (2000).
- A. E. Eiben, J. E. Smith: "Introduction to Evolutionary Computing". Springer (2003). Additional documentation at: http://www.bit.uwe.ac.uk/~jsmith/ecbook/ecbook.html.
- S. M. Sait, H. Youssef: "Iterative Computer Algorithms with Applications in Engineering". IEEE Computer Society (1999)
- T. G. Kolda, R. M. Lewis, V. Torczon: "Optimization by Direct Search". SIAM Review 45, 385-482, 2003.
Prerequisites
- Basic numerical calculus
- Basic knowledge of computer architecture
Tuition language
Spanish
Subject-Specific Competences
| Code | Competence | Proficiency Level |
|---|---|---|
| CEM7 | Evaluation and application of diverse mathematical and statistical theories, and available knowledge extraction and discovery processes, methods and techniques for large data volumes | C |
| CEM8 | Application of the theoretical and mathematical foundations of heterogeneous functions and data processing and analysis and evaluation and design of related methods for application in practical domains | S |
Learning Outcomes
| Code | Learning Outcome | Associated competences | Proficiency level |
|---|---|---|---|
| RA-APDI-1 | Be familiar with examples of real applications and research trends and lines | CEM7 | A |
| RA-APDI-2 | Select and apply optimization methods to specific problems | CEM8 | S |
| RA-APDI-3 | Be familiar with the theory of classical optimization methods and heuristics | CEM8 | S |
| RA-APDI-7 | To know, apply and be critic about the research bibliography so it can be used as a starting point for a research | CEM7, CEM8 | C |
| RA-APDI-12 | Be familiar with examples of real applications and research trends and lines | CEM7, CEM8 | C |
| RA-APDI-12 | Select and apply optimization methods to specific problems | CEM7, CEM8 | A |
| RA-APDI-103 | Be familiar with and apply the optimization methods in production management | CEM7, CEM8 | S |