Advanced Numerical Computation

Lecturer (Coordinator):
Vicente Martín
Esther Dopazo
José Luis Rosales


Second semester




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.


  1. Introduction to optimization
    1. Problem statement. Types and examples
    2. Basic optimization concepts
  2. Methods of optimization
    1. Optimization with and without constraints: traditional methods
    2. Heuristic optimization: algorithms based on ideas borrowed from natural processes: simulated annealing, evolutionary algorithms, immune networks, etc. Practical examples
  3. 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:
  • S. M. Sait, H. Youssef: "Iterative Computer Algorithms with Applications in Engineering". Ed. IEEE Computer Society (1999)
  • Kolda, Lewis, Torczon: "Optimization by Direct Search". SIAM Review 45, 385-482, 2003.


  • Basic numerical calculus
  • Basic knowledge of computer architecture

Assessment Method

Students will be graded on the oral presentation and written report on a project that they have to complete as part of the subject. Students shall be assigned projects individually. Projects shall address any part of the subject content and cover theoretical and practical aspects of the learning contents. Before developing their project, students shall have to submit a topic proposal and work plan for discussion with the instructor.

Tuition language


Lecture Room

R 5208

Subject-Specific Competences

Code, description and proficiency level for each subject-specific competence
Code Competence Proficiency Level
CEM2 Analysis and synthesis of solutions to problems requiring innovative approaches to the definition of the computational infrastructure, processing and analysis of heterogeneous data types A
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, description and proficiency level for each subject learning outcome
Code Learning Outcome Associated competences Proficiency level
RA-APDI-1 Be familiar with examples of real applications and research trends and lines CEM2, CEM7 A
RA-APDI-2 Select and apply optimization methods to specific problems CEM2, CEM8 S
RA-APDI-3 Be familiar with the theory of classical optimization methods and heuristics CEM2, CEM8 S
RA-APDI-103 Be familiar with and apply the optimization methods in production management CEM7, CEM8 S

Learning Guide

Learning Guide: Advanced Numerical Computation