Algorithmic Methods for Mathematical Models

Credits
6
Types
Compulsory
Requirements
This subject has not requirements , but it has got previous capacities
Department
DAC;CS
The task of building mathematical models that represent real-world problems and using existing tools for solving such models is an ubiquitous task in computer science. Knowledge about such tools and algorithms allows one to weigh up the balance between how precisely we formalize the problem and how tractable the resulting model is.

With an special emphasis on their application to concrete computer science problems, this course will review some of these mathematical models and algorithms. First of all, we will review the basics of linear and non-linear programming. Then, metaheuristic algorithms will be presented as an alternative to the previous methods for combinatorial optimization problems.

Teachers

Person in charge

Others

Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0
Autonomous learning
7.12

Competences

Technical Competences of each Specialization

Computer networks and distributed systems

  • CEE2.1 - Capability to understand models, problems and algorithms related to distributed systems, and to design and evaluate algorithms and systems that process the distribution problems and provide distributed services.

    • Advanced computing

  • CEE3.2 - Capability to use a wide and varied spectrum of algorithmic resources to solve high difficulty algorithmic problems.

    • Generic Technical Competences

    Generic

  • CG1 - Capability to apply the scientific method to study and analyse of phenomena and systems in any area of Computer Science, and in the conception, design and implementation of innovative and original solutions.
  • CG3 - Capacity for mathematical modeling, calculation and experimental designing in technology and companies engineering centers, particularly in research and innovation in all areas of Computer Science.

    • Transversal Competences

    Teamwork

  • CTR3 - Capacity of being able to work as a team member, either as a regular member or performing directive activities, in order to help the development of projects in a pragmatic manner and with sense of responsibility; capability to take into account the available resources.

    • Reasoning

  • CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.

    • Objectives

    1. Modelling in various mathematical formalisms the problems arising in different computer science disciplines
      Related competences: CG1, CG3, CEE2.1, CTR3, CTR6,
    2. Becoming familiar with state-of-the-art tools used to solve various mathematical models
      Related competences: CG3, CEE2.1, CEE3.2, CTR3, CTR6,
    3. Understanding the basics of the algorithms used for solving various mathematical models
      Related competences: CEE2.1, CEE3.2,

    Contents

    1. Linear Programming
      Basics on linear programming. Modelling examples. The simplex algorithm. Duality.
    2. Integer linear programming
      Modelling examples. Branch-and-bound, cuts and branch-and-cut.
    3. Non-linear programming
      Basics on non-linear programming. Modelling examples.
    4. Metaheuristics
      Constructive procedures. Local search. Metaheuristics: GRASP, Simulated Annealing, Tabu Search, Genetic algorithms, Ant Colony, Path Relinking, etc.

    Activities

    Activity Evaluation act


    Linear programming


    Objectives: 1 3
    Contents:
    Theory
    12h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    11h

    Integer Linear Programming


    Objectives: 1 3
    Contents:
    Theory
    8h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    12h

    Linear Programming Laboratory


    Objectives: 2
    Contents:
    Theory
    0h
    Problems
    0h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    9h

    Non-linear programming


    Objectives: 1 3
    Contents:
    Theory
    4h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    3h

    Metaheuristics


    Objectives: 1 3
    Contents:
    Theory
    16h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    12h

    Metaheuristics Laboratory


    Objectives: 2
    Contents:
    Theory
    0h
    Problems
    0h
    Laboratory
    6h
    Guided learning
    0h
    Autonomous learning
    9h

    Project


    Objectives: 1 2
    Week: 16
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Exam


    Objectives: 1 2 3
    Week: 18
    Theory
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Teaching methodology

    Since the goal of the course is to provide the students with the necessary expertise to use different formalisms and tools to solve concrete problems, the teaching methodology will take that into account. Theory classes will always use motivating examples. In these sessions, students will solve simple exercises that will be key ingredients of more complicated algorithms.

    In the laboratory sessions the students will become familiar with tools for solving problems computationally.

    In the development of the project the students will be supervised by the instructors.

    Evaluation methodology

    The final grade of the course will take into account:

    A) A practical work (project): 40%

    B) A final exam: 60%

    Bibliography

    Basic

    Complementary

    Previous capacities

    Students should be familiar with basic concepts in linear algebra: vector, matrix, rank, matrix inverse and solving systems of linear equations.