# Multicriteria Optimization and Decision Analysis

Vak
2023-2024

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.

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of instruction

• Lectures

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.

• 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)

• Matthias Ehrgott: Multicriteria Optimization, Springer 2005

• Kaisa Miettinen: Nonlinear Multiobjective Optimization, Kluwer, 199

• Diwekar, Urmila: Introduction to Applied Optimization, Springer, 2010

## Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.

## Contact

Lecturer: dr. Michael Emmerich