Learning in Multiobjective Optimization

Motivation

This seminar follows the three previous, highly successful, Dagstuhl Seminars on Multi-objective Optimization (04461, 06501 and 09041). The first two seminars established for the first time a link between the two communities of Multiple Criteria Decision Making (MCDM) and Evolutionary Multi-Criterion Optimization (EMO), while the last seminar in January 2009 focused on the development of novel robust techniques joining the methods from both realms (hybridization). We aim at continuing this seminar series, building on the now more integrated MCDM and EMO communities, by putting a theme in the center that is relevant to the whole field of multi-objective optimization and decision making. This theme is learning, and we intend that this topic can lead to a new coherence and common vision in our field that can bring about advances in both basic methods and our approach to practical applications.

Learning is an important subject in multi-objective optimization because it aims at guiding the decision maker, in an efficient and effective manner, to a preferred solution that is Pareto optimal. The expectation is that an effective learning process would lead to increased satisfaction with and confidence in a decision, as well as a better understanding of the underlying rationale. Therefore, on the one hand, a multi-objective optimization procedure should aim at permitting the decision maker (DM) to learn about the optimization problem, while, on the other hand it should aim at permitting a formal model to be found, to include information about preferences of the DM, which can be interpreted as a learning process from the point of view of the formal model. Therefore, we can say that the quality of a multi-objective optimization process is related to what the DM and the model learn. Consequently, a fundamental aspect of a multi-objective optimization method is the set of procedures that permit both the DM, and the model, to learn. From this perspective, many questions arise:

• How can individual learning be characterized?
• How can individual learning be supported?
• How can different types of model learn about the preferences of the DM?
• What type of interdependence is there between the DM's learning and the model's learning?

Learning as the main theme of the seminar will be focused around three topics:

1. User preferences This topic takes mainly the perspective of the optimization process that interacts with the user and tries to infer formal information to guide the search and adapt the model. The key questions here are "What can and should be learnt from user interactions and how can user preferences be inferred?". Under the term preferences, all additional information related to the underlying optimization problem is understood. This information is usually implicitly reflected by the choices of the decision maker(s). How to extract and exploit this information is the main question here. Let us observe that also a good multi-objective optimization process should enable decision makers to learn about their own preferences, which in general are not well established at the beginning of the process. From this point of view, there have been several suggestions to pay attention to behavioural issues and the work of the Behavioural Decision Theory community should be taken into account.
2. Problem understanding This topic covers all aspects that aim at gaining insight about the underlying optimization problem. The consideration is related to the DM who wants to obtain some information about the problem, in particular about the Pareto-optimal set (but not necessarily restricted to it). For instance, one may be interested in identifying structurally similar regions in the decision space close to the Pareto front in the objective space. Therefore this topic considers the question "What can be learnt about the problem structure and how can useful information for the DM be extracted?"
3. The problem solving process This topic is driven by the application-side where the entire process from the optimization model to the final solution is in the center; clearly, the two first topics are essential for this perspective, but here the process as such is the focus. Therefore, this topic considers the question "In what respect is the problem solving process a learning process?" In more detail, this topic will try to find an answer to questions such as: "What does a decision maker learn?", "How do we know if a decision maker has learnt?", "How does a decision maker learn?", "What factors influence how and what a decision maker learns?". One should point out that in all this, human-computer interaction is essential because transferring information from the optimization model to the DM and preference information from the DM to the multi-objective optimization solution procedure cannot be successful without interfaces that are intuitive and genuinely support the tasks in question.

From this seminar, we expect a fresh analysis of existing multi-objective procedures to take place with respect to their learning aspects, and that this will lead to several proposals to improve them. Moreover, we expect that new paradigms of learning-oriented multi-objective optimization will be proposed and elaborated. These should be the basis of a new generation of multi-objective optimization methodologies. We expect also that several collaborative projects in this direction can start among the participants of the seminar.