Optimization

Credits
6
Types
Compulsory
Requirements
This subject has not requirements , but it has got previous capacities
Department
EIO;ESAII
he first part of this subject presents a contextualization of the optimization discipline, providing basic knowledge on modeling and solving linear and integer linear optimization problems. The course delves into algorithms for solving linear problems (primal and dual simplex), as well as their application in sensitivity analysis. Regarding the integer linear optimization, the branch and bound enumerative algorithm is described. In this part, the course also includes an introduction to optimization problem solving tools (mathematical programming languages and solvers). The course also presents algorithms based on heuristics and how they are combined with techniques such as simulation to be able to respond to problems that require high computational computation.

Teachers

Person in charge

Others

Weekly hours

Theory
2
Problems
2
Laboratory
0
Guided learning
0
Autonomous learning
6

Competences

Transversal Competences

Transversals

  • CT2 [Avaluable] - Sustainability and Social Commitment. To know and understand the complexity of economic and social phenomena typical of the welfare society; Be able to relate well-being to globalization and sustainability; Achieve skills to use in a balanced and compatible way the technique, the technology, the economy and the sustainability.
  • CT5 [Avaluable] - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.
  • CT6 [Avaluable] - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.

    • Basic

  • CB2 - That the students know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and problem solving within their area of ??study.
  • CB3 - That students have the ability to gather and interpret relevant data (usually within their area of ??study) to make judgments that include a reflection on relevant social, scientific or ethical issues.
  • CB4 - That the students can transmit information, ideas, problems and solutions to a specialized and non-specialized public.

    • Technical Competences

    Especifics

  • CE01 - To be able to solve the mathematical problems that may arise in the field of artificial intelligence. Apply knowledge from: algebra, differential and integral calculus and numerical methods; statistics and optimization.
  • CE20 - To select and put to use techniques of statistical modeling and data analysis, assessing the quality of the models, validating and interpreting.
  • CE21 - To formulate and solve mathematical optimization problems.
  • CE22 - To represent, design and analyze dynamic systems. To acquire concepts such as observability, stability and controllability.
  • CE23 - To design controllers for dynamic systems that represent temporary physical phenomena in a real environment.

    • Generic Technical Competences

    Generic

  • CG2 - To use the fundamental knowledge and solid work methodologies acquired during the studies to adapt to the new technological scenarios of the future.
  • CG4 - Reasoning, analyzing reality and designing algorithms and formulations that model it. To identify problems and construct valid algorithmic or mathematical solutions, eventually new, integrating the necessary multidisciplinary knowledge, evaluating different alternatives with a critical spirit, justifying the decisions taken, interpreting and synthesizing the results in the context of the application domain and establishing methodological generalizations based on specific applications.
  • CG5 - Work in multidisciplinary teams and projects related to artificial intelligence and robotics, interacting fluently with engineers and professionals from other disciplines.
  • CG8 - Perform an ethical exercise of the profession in all its facets, applying ethical criteria in the design of systems, algorithms, experiments, use of data, in accordance with the ethical systems recommended by national and international organizations, with special emphasis on security, robustness , privacy, transparency, traceability, prevention of bias (race, gender, religion, territory, etc.) and respect for human rights.
  • CG9 - To face new challenges with a broad vision of the possibilities of a professional career in the field of Artificial Intelligence. Develop the activity applying quality criteria and continuous improvement, and act rigorously in professional development. Adapt to organizational or technological changes. Work in situations of lack of information and / or with time and / or resource restrictions.

    • Objectives

    1. Be able to apply basic optimization techniques to be able to solve computationally complex problems.
      Related competences: CE23, CG4, CG5, CT5, CT6, CB2, CB3, CB4, CE01, CE21, CE22,
    2. Contextualize the different existing optimization techniques.
      Related competences: CG2, CG5, CG8, CG9, CT2, CT5, CT6, CB2, CB3, CB4, CE20, CE21,

    Contents

    1. Introduction to optimization
      The concept and need for optimization will be presented. Examples and real cases will be shown in which some of the techniques that will be explained during the course have been used.
    2. Discrete optimization
      Introducció a l'optimització discreta, dualitat, SIMPLEX...
    3. Heuristics
      Optimització basada en heurístics.
    4. Linear Dynamical Systems
      Introduction to linear dynamical systems and their representations: ordinal differential equations; Laplace transform; Fourier transform
    5. Discrete Dynamical Systems Models
      Discrete representation of dynamical systems and modelling: AR, MA, ARMA, NARMAX
    6. Control and Optimisation of Dynamical Systems
      Control of dynamical systems and optimisation processes for tuning

    Activities

    Activity Evaluation act


    Introduction to optimization

    Description and classification of the different techniques and approaches to optimization.
    Objectives: 2 1
    Contents:
    Theory
    4h
    Problems
    4h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Linear programming



    Theory
    4h
    Problems
    4h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Introduction to heuristics


    Objectives: 2 1
    Contents:
    Theory
    4h
    Problems
    4h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    15h

    Linear Dynamical Systems



    Theory
    6h
    Problems
    6h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Modelling Discrete Dynamic Systems



    Theory
    4h
    Problems
    6h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Control and Optimization of Dynamic Systems



    Theory
    6h
    Problems
    4h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    15h

    Teaching methodology

    The classes will combine lectures with practical sessions where the students will work on the content of the topics they have covered. The laboratory classes will allow you to develop cases that allow you to apply the knowledge acquired.

    Evaluation methodology

    For the optimization part, two practical works will be developed.
    For the second part there will be a practical exercise and an evaluative written exam.

    For the optimization part, two practical works will be developed.
    For the second part there will be a practical work and an evaluation in the form of a written exam.

    For the optimization part, two practical tasks T01 and T02 will be developed

    For the second part there will be a practical work T03 and an assessment in the form of an EX written exam


    Final Grade= 0.25* T01+0.25*T02+0.25*T03+0.25*EX

    Reassessment: Only those who have failed the final exam may take the reassessment. The maximum grade that can be obtained in the reassessment is 7.

    Bibliography

    Basic

    Previous capacities

    Know the concept of model and system.
    Knowledge of basic statistics.