Evolutionary Multi-Objective Optimization

--- Results of the EMO exam from 10th February ---

The results of the final exam are online. You can see your grade in the LSF system. The exam review will take place in the beginning of the next semester: April 8 from 12:00 to 13:00. Please write an email to the tutors in order to review your exam.


In our daily lives we are inevitably involved in optimization. How to get to the university in the least time is a simple optimization problem that we encounter every morning. Just looking around ourselves we can see many examples of optimization problems even with conflicting objectives and higher complexities. It is natural to want everything to be as good as possible, in other words optimal. The difficulty arises when there are conflicts between different goals and objectives. Indeed, there are many real-world optimization problems with multiple conflicting objectives in science and industry, which are of great complexity. We call them Multi-objective Optimization Problems.
Over the past decade, lots of new ideas have been investigated and studied to solve such optimization problems as any new development in optimization which can lead to a better solution of a particular problem is of considerable value to science and industry. Among these methods, evolutionary algorithms are shown to be quite successful and have been applied to many applications.

This course addresses the basic and advanced topics in the area of evolutionary multi-objective optimization and contains the following content:

  • Introduction to single-objective optimization (SO) and multiobjective optimization (MO), classical methods for solving MO, definitions of Pareto-optimality and other theoretical foundations for MO
  • Basics of evolutionary algorithms (algorithms, operators, selection mechanisms, coding and representations)
  • Evolutionary multi-objective algorithms (NSGA-II, EMO scalarization methods such as MOEA/D)
  • Large-scale EMO: large scale decision space and many objective optimization (such as NSGA-III)
  • Constraint handling in SO and MO, robust optimization in EMO, surrogate methods for expensive function evaluations
  • Dynamic EMO
  • Evaluation mechanisms (Design of experiments, test problems, metrics, visualization)






The lectures take place: Thursdays 13:00 -14:30 in G29-307. The first lecture will take place on 4th April.





Recorded lectures

Dear students, As I already said in the first lecture, we do not guarantee to be able to upload the recordings every week. Very often the recordings do not work, due to technical issues. Since the recordings are meant to capture the live lectures, those will be missing. I recommend to visit the lectures, make notes, and do not fully rely on the recordings. 







For the lecture there will be weekly tutorials. In order to write the exam at the end of the lecture, you must attend and actively participate in one of the tutorial groups. New assignments will be published here every week. To attend, you must first apply for a spot in one of the groups (see below).

Participation in the tutorials consists of preparing answers to the written assignments at home as well as coming to the tutorials and presenting your solutions to your fellow students. At the beginning of each tutorial, we will ask you to volunteer for those assignments that you prepared. You pass the tutorial (and are allowed to write the exam) only if you volunteer for at least 2/3 of all assignments and presented a solution at least two times (Update: you only need to present a solution 1 time instead of 2). You must also pass the mid-term exam (see below).



  Day Time Location 1st Tutorial  2nd Tutorial 3rd Tutorial 4th Tutorial 5th Tutorial
Group 1 Tue 15:15 - 16:45 G22A - 112 16.04. 07.05. 21.05. 11.06. 25.06.
Group 2  Wed   13:15 - 14:45    G22A - 110    17.04.  08.05. 22.05. 12.06. 26.06.
Group 3  Wed   15:15 - 16:45    G22A - 112    17.04.  08.05. 22.05. 12.06. 26.06.
Group 4  Thu   15:15 - 16:45    G22A - 112    18.04.  09.05.  23.05. 13.06.  27.06.
Group 5 Tue  15:15 - 16:45  G22A - 112   23.04. 14.05.  04.06. 18.06.  02.07.
Group 6 Wed 13:15 - 14:45 G22A - 110  24.04. 15.05.  05.06. 19.06.  03.07.
Group 7 Wed 15:15 - 16:45 G22A - 112  24.04. 15.05. 05.06 19.06.  03.07.
Group 8 Thu 15:15 - 16:45 G22A - 112  25.04. 16.05.  06.06.  20.06.  04.07.


In order to attend a tutorial group, you will need to apply for a spot in one of the groups. This done via the LSF system from 1st April to 10th April. Please use this link to see the tutorial information in the LSF system. After you log in with your student account, you can register for the tutorials and give preferences for each of the four groups. We will assign the free spots in the groups based on the preferences you gave for each group. Important: There is only limited space per tutorial group and we can only offer four tutorial groups. Therefore, if there are too many applicants, it might be that not every applicant can attend this lecture and the tutorials. Note that the final assignment of the free spots will be done after the application deadline is over, and you will be informed via email if you can participate in this course or not.

The first tutorials will take place in the third and fourth weeks of the semester, from 16th to 25th of April (see above).

Note: Each week, one assignent sheet will be discussed. You only volunteer and present for assignments in the respective week where these assignments are scheduled to be discussed. Further, you should only volunteer and present in your own tutorial group. Visiting the other tutorial groups is possible, but it should remain an exception (e.g. because of illness or other important appointments) and should be announced beforehand. The submission of assignments via email is not possible, with the only exception of illness. You should notify your TA about your absence beforehand. You can then attend another tutorial group in that week or submit via email. If you have a certificate of illness from your physician, the respective assignment sheet will not be counted when calculating your percentage of solved assignments in the end.

There will be mid-term exam, which we plan for 24th of May at 3pm in Hörsaal 1 (G26-H1). In order to be allowed to the final exam, every student must pass this short (45 minutes) exam on that day. This mid-term exam helps you to prepare for the contents of the course during the semester, and will make it easier for you to pass the final exam.


----- Announcement: ----

The EMO lecture had a very large amount of student applying for the tutorials. It is our aim not to exclude anyone who wants to attend, and at the same time, we want to ensure a high quality of the tutorials.
Therefore, the only option is to split the four offered groups into 8 groups, where each of them is offered only every second week. That means that the times and rooms that were announced previously are now used in one week for groups 1 - 4 and the week after that for groups 5 - 8. The resulting new 8 groups are numbered anew and are visible in the LSF system as well as below on his website. Every student who is admitted to one of these groups will receive an email stating exactly wich group number he or she is assigned to. Please visit only this group (see group numbers and times below).

Another change regards a mid-term exam, which we plan for 24th of May at 3pm. In order to be allowed to the final exam, every student must pass this short (45 minutes) exam on that day. Since the reduced amount of tutorial session per student (see above) does not allow us to check your progress in the way we originally intended, this mid-term exam helps you to prepare for the contents of the course during the semester, and will make it easier for you to pass the final exam. The mid-term exam will take place on Friday, 24th May at 3:00 pm (s.t.). The exam will take place in Hörsaal 1 (G26-H1). The exam time is 45 minutes. No tools or calculators are allowed. Please bring your student id card.




  • Assignments 1 (discussed in tutorials from 16th May to 25th April)
  • Assignments 2 (discussed in tutorials from 6th May to 17th May)
  • Assignments 3 (discussed in tutorials from 20th May to 7th June)
  • Assignments 4 (discussed in tutorials from 10th June to 21st June)
  • Assignments 5 (discussed in tutorials from 24th June to 5th July)



------ Results of the Mid-term Exam ------

The mid-term exam has been corrected. You will receive an email with your result and further information from us. In the following, you can see the distribution of achieved points overall. In the exam, we stated that 8 out of 12 points were necessary to pass the exam. If we had applied this limit, only 24% of all students who took the exam could pass. Therefore, we decided to lower the limit to 5.5 points, which results in 51% of students passing the exam. As an opportunity to prepare for the final exam, we have uploaded the exam questions here and here. In case you have failed the exam, we welcome you to participate again next year in summer 2020.



--- Results of the EMO exam from 8th July ---

The results of the final exam are online. You can see your grade in the LSF system. In the following you see the distribution of grades among the 61 participants. The exam review will take place on  Wednesday (16th October) from 13:00 to 16:00 o'clock. Once you write to us, we will assign you a time slot and inform you about the time and place.





  •  Deb, Kalyanmoy. Multi-Objective Optimization Using Evolutionary Algorithms, Wiley, 2001.
  • Coello, Carlos A. Coello, Gary B. Lamont, and David A. Van Veldhuizen. Evolutionary algorithms for solving multi-objective problems. Vol. 5. New York: Springer, 2007.
  • Miettinen, Kaisa. Nonlinear multiobjective optimization. Vol. 12. Springer Science & Business Media, 2012.
  • Ehrgott, Matthias. Multicriteria optimization. Vol. 491. Springer Science & Business Media, 2005.
  • Kruse, Rudolf, et al. Computational intelligence: a methodological introduction. Springer, 2016.


Last Modification: 17.01.2024 - Contact Person: Webmaster