CORE Module “Planning and Optimization”

This module is focused on developing the mathematical and engineering skills required to plan for and optimize complex systems such as Intelligent Mobile Systems. It contains two courses on optimization: one focusing on quantitative methods and techniques for effective decision making, and the other dedicated to broader optimization problems, covering topics such as Lagrange multipliers, convex, and nonlinear programming. A third course focuses on planning and decision-making algorithms for autonomous systems.


Operations Research

Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations. By employing techniques such as mathematical modeling, statistical analysis, and mathematical optimization, operations research finds optimal or near-optimal solutions to complex decision-making problems. Operations Research is concerned with determining the maximum (of profit, performance, or yield) or the minimum (of loss, risk, or cost) of some real-world objective. This course introduces students to modelling of decision problems and the use of quantitative methods and techniques for effective decision-making. Familiarity with a programming language (e.g., Python, C++, etc.) is desirable for this course.

  • Semester: Fall (3rd semester)
  • ECTS: 5
  • Instructor: Prof. Dr. Julia Bendul / Prof. Dr. Marcel Oliver

Autonomous Systems

There is an increasing interest and need to generate artificial systems that can carry out complex missions in unstructured environments without permanent human supervision. Intelligent mobile robots are often used as prototype or even defining example of according autonomous systems. But in a more general notion, an autonomous system can be seen as a combination of a computational core, sensors and motors, a finite store for energy, and a suited control allowing, roughly speaking, for flexible stand-alone operation that can deal with situations the designers may not have foreseen when constructing and programming the system. The investigation of autonomous systems is driven from two different perspectives. First, it is driven by the engineering aspects of generating application oriented devices like household, care-giving or security and rescue systems. Second, artificial autonomous systems offer new ways to investigate and constructively understand natural cognition.

  • Semester: Fall (3rd semester)
  • ECTS: 5
  • Instructor: Prof. Dr. Andreas Birk

Optimization

Optimization is a key step in the design of systems and processes. The course starts with classical search techniques like bisection, golden section, Newton’s algorithm, and conjugate gradient. It then discusses constrained problems like linear and quadratic programming based on the Lagrange formalism, and gives a first introduction to the concepts of convex optimization, in particular convex sets, convex functions, optimality conditions and duality. The course comes with a wide variety of examples and applications.

  • Semester: Spring (4th semester)
  • ECTS: 5
  • Instructor: Dr. Mathias Bode