This course is about advanced computational optimization methods that can handle constraints and multiple objective functions, and as such deals with topics on the boundary of computer science and applied mathematics. Moreover, we discuss the principles of decision analysis with multiple conflicting criteria, where also some aspects of understanding human psychology (how we make choices) play a role.
We will discuss the basic methodology and terminology of Operational Research, Nonlinear Mathematical Programming, and Decision Theory. We will emphasize the cutting edge research topics in the direction of multiobjective optimization and decision analysis (MODA). This emerging field of computational science has applications in various fields of technology, where balanced solutions are to be found in the presence of multiple conflicting objectives and constraints: These applications range across a broad range of topics, including economics, engineering/product design, machine learning, scheduling, economics, environmental sciences, drug discovery, and medical sciences.
At the end of the class the student should be able to:
Formulate and identify different types of mathematical programming problems, including formulations with constraints and multiple objectives. Understand basic terminology and modelling techniques in operational research.
Comprehend the axiomatic foundations of (partial) orderings. Be able to compare different ordered sets and analyze their properties; understand the interpretation of ordered sets Cartesian space as a concept governed by dominance regions, which often can be modeled by means of polyhedral cones.
Analytically solve simple Pareto optimization problems that are special cases for the application of Karush Kuhn Tucker conditions and the Lagrange multiplier theorem.
Know different aggregation methods, with their pros and cons, and apply basic heuristic algorithms for computing optimal point sets, such as SMS-EMOA, NSGA-II, epsilon-constraint methods, and numerical continuation.
Get acquainted with the concept of set-oriented optimization and set-gradients for finding efficient manifolds.
Understand and be able to apply methods in multicriteria decision making in practice in real world problem domains.
The most recent timetable can be found at the Computer Science (MSc) student website.
Mode of instruction
Exercises with solutions (non-graded)
Hours of study: 168 hrs. (= 6 EC)
Lectures: 33:00 hrs.
Practical work: 16:00 hrs.
Tutoring: 6:00 hrs.
Examination: 3:00 hrs.
Other (self-study): 110:00 hrs.
Exam (written), 3 hours.
Final Grade = Grade Written Exam.
Two graded homeworks (can be handed in individually or in group of two or three).
Grade of exam must be greater or equal to 6 (5.5 will be rounded up to 6, all grades below 5.5 will be non-passing grades)
Final grade: 0.1 Grade Homework1 + 0.1 Homework2 + 0.8 Exam
Pass: Final grade >= 5.5
The teacher will inform the students how the inspection of and follow-up discussion of the exams will take place.
Michael Emmerich and André Deutz: Multicriteria Optimization and Decision Making: Principles, Algorithms, and Applications, LIACS, 2017(Course Lecture nodes, will be made available on Brightspace)
Emmerich, Michael TM, and André H. Deutz. "A tutorial on multiobjective optimization: fundamentals and evolutionary methods." Natural computing 17.3 (2018): 585-609. (open access)
https://link.springer.com/article/10.1007/s11047-018-9685-y (this is a compact version of the lecture notes, that was published open access)
Further reading, background literature:
Matthias Ehrgott: Multicriteria Optimization, Springer 2005
Kaisa Miettinen: Nonlinear Multiobjective Optimization, Kluwer, 199
Diwekar, Urmila: Introduction to Applied Optimization, Springer, 2010
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Lecturer: dr. Michael Emmerich