Multi-objective optimization and decision making: Principles, Algorithms and Case Studies

Dr. Michael T. M. Emmerich (UD)


Time: Tuesdays 11:15 - 13:00, Room 412
Speaking hour: Tuesday 13:30-14:30, Room 128




Course Description

Real world decision and optimization problems usually involve conflicting criteria. Ideal solutions are rather the exception than the rule. In this course we will deal with algorithmic methods for solving multi-objective optimization and decision making problems. The rich mathematical structure of such problems as well as their high relevance in various application fields led recently to a significant increase of research activities. In particular algorithms that make use of fast, parallel computing technologies are envisaged for tackling hard combinatorial and/or nonlinear application problems.
In the course we will discuss the theoretical foundations of multi-objective optimization problems and their solution methods, including order and decision theory, analytical, interactive and meta-heuristic solution methods as well as state-of-the-art tools for their performance-assessment. Also an overview on decision aid tools and formal ways to reason about conflicts will be provided. All theoretical concepts will be accompanied by illustrative hand calculations and graphical visualizations during the course. In the second part of the course, discussed approaches will be exemplified by the presentation of case studies from literature, including various application domains of decision making, e.g. economy, engineering, medicine or social science. The course will cover topics of ongoing research at LIACS and there will be opportunities for master projects and thesis on these topics after finishing the course.

Assignments

Download Assignment 1
Download Assignment 2
A pattern solution for some of the tasks in the assignment is here: download

Topics

  • 1 Introduction
  • 2 Order theory
  • 3 Pareto optimality conditions
  • 4 Shapes of Pareto fronts and search landscapes
  • 5 Scalarization Methods
  • 7 Heuristic Algorithms
  • 8 Performance Assessment
  • 9 Branch and Bound
  • 10 History

    • Book:



    Introduction to Multiobjective Optimization (Reader)
    Mathias Ehrgott: Multicriteria Optimization: Springer, Berlin 2005

    'People talk about the middle of the road as though it were unacceptable. Actually, all human problems, excepting morals, come into the gray areas. Things are not all black and white. There have to be compromises.' (D. Eisenhower)

    last modified: 1.9.2005 14:41:02 MET 2000