# Multicriteria Optimization and Decision Analysis

Vak
2024-2025

Not applicable.

## Description

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.

## Course objectives

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.

## Timetable

The most recent timetable can be found at the Computer Science (MSc) student website.

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

• Lectures

• 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.

## Assessment method

• 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, 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/condensed and peer reviewed version of the lecture notes)

• 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

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Lecturer: dr. Michael Emmerich

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.