https://www.dagstuhl.de/04461

# Practical Approaches to Multi-Objective Optimization

## Organizers

Jürgen Branke (KIT – Karlsruher Institut für Technologie, DE)
Kalyanmoy Deb (Indian Inst. of Technology – Kanpur, IN)
Kaisa Miettinen (Helsinki School of Economics, FI)
Ralph E. Steuer (University of Georgia, US)

## Summary

As the name suggests, multi-criterion optimization involves optimization in the presence of more than one (conflicting) criteria. Multi-criterion optimization problems arise in a variety of real-world applications and the need for efficient and reliable solution methods is increasing. The main difference between single and multi-criterion optimization is that in case of the latter, there is usually no single optimal solution, but a set of equally good alternatives with different trade-offs, also known as Pareto-optimal solutions. In the absence of any other information, none of these solutions can be said to be better than the other. Usually, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution. Depending on the paradigm used, such knowledge may be introduced before, during, or after the optimization process. Multi-criterion optimization thus has to combine two aspects:optimization and decision support.

So far, there have existed basically two different approaches with corresponding fields of research: the classical approach and the evolutionary algorithm approach. The classical approach has a comparatively long history and subsumes a number of different algorithms, mostly developed by researchers from mathematics and operations research. These algorithms usually generate one solution and then adjust and re-optimize it according to the user's preferences. If they generate a set of alternatives, a small set of alternatives are usually generated sequentially. Many classical methods convert the problem with multiple criteria into one or a series of single criterion problems. On the other hand, evolutionary multi-objective optimization (EMO) is a relatively young research area, and is mostly grounded in computer science and engineering. Since evolutionary algorithms maintain a population of solutions throughout the optimization process, they are naturally suited to search for a large, representative set of Pareto-optimal solutions in parallel. In most cases, these solutions are created whithout the intervention of any decision-maker. Only after the optimization process has been completed, the decision maker chooses from the set of alternative solutions.

Both classical and evolutionary approaches have their merits and demerits, and both fields have become important and emerging topics in the area of informatics and operations research. But while both fields have resulted in number of efficient algorithms and sucessful applications published in dedicated books and major international journals and conferences, interactions among the fields are rarely found.

A major purpose of this seminar therefore was to bring together leading experts from both fields for discussions on the current state-of-the-art methodologies and common interests.

### Proceeding of the Seminar

The seminar was paticipated by 39 persons from 15 countries. It consisted of two tutorials, 27 talks, group discussions an three selscted topics, a panel discussion, and software demonstrations.

### Achievements of the Seminar / Feedback from Participants

The seminar was clearly unique because it brought together scholars from the two sides of the rapidly growing area of multi-criterion optimization. Prior to the seminar, people from the two sides, coming from different disciplines, hardly knew each other. However, as result of the seminar, it is clear that two sides are now considered as comprising the whole of the field of multi-criterion optimization in the most modern interpretation of the term.

The discussions were lively and certainly helped to clarify the terminology used in different groups, which should make reading and understanding each other's research paper easier. Active collaboration between the fields was fostered. As one example, some participants, from both classical and EMO fields even made a head-start to work on a joint project of outlining an interactive multi-criterion optimization method bringing together and hybridizing ideas utilized in the two fields.

At the closing session, the organizers collected feedback about the seminar, which is summarized in the following. All participants found the seminar very successful and were very excited about the idea of bringing together researchers from the two fields of multi-criterion optimization and expressed their interest in participating in such a seminar again. Participants appreciated the excellent opportunity to get to learn about the state-of-the-art, to discuss, to interact, to exchange ideas and to get new ideas. They liked the possibility of meeting many experts and asking them directly on their subjects of interests. It was great how people from classical and EMO fields were able to establish collaborative arrangements that would not have been possible without such a seminar. They also liked the idea of working groups and their results. It was emphasized that we should cooperate as much possible including newsgroups, a paper repository, and website. Some participants even said that this seminar was the most fruitful meeting for a decade for them! Finally, the participants mentioned the Dagstuhl atmosphere as a really significant ingredient in the success of the seminar.

## Book exhibition

Book exhibition in the library, ground floor, during the seminar week.

## Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.