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Dagstuhl Seminar 15031

Understanding Complexity in Multiobjective Optimization

( Jan 11 – Jan 16, 2015 )


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Please use the following short url to reference this page: https://www.dagstuhl.de/15031

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Motivation

This seminar carries on a series of four previous Dagstuhl Seminars (04461, 06501, 09041 and 12041) that were focused on Multiobjective Optimization. Our major goal is to further strengthen the links between the Evolutionary Multiobjective Optimization (EMO) and Multiple Criteria Decision Making (MCDM) communities, and to advance our understanding of different aspects concerning complexity in multiobjective optimization.

The need for a better understanding of complexity is pressing and timely, as recent work has sometimes shown opposing views regarding how problems scale and grow in difficulty, and their inherent challenges. On the one hand, we know that multiobjective optimization problems are complex problems by their very nature; optimization problems that are easy to solve in the single objective case are often intractable and highly complex already in the biobjective case. Moreover, recent work has pointed to further fundamental limitations in multiobjective optimization as we scale up to many objectives.

On the other hand, a multiobjective perspective can in a sense also help reduce complexity. For example, it often leads to a better understanding of a problem and hence supports the decision making process. Moreover, adding objectives to a problem does not always make it harder, because decomposing it can reduce the presence of local optima. And multiobjective approaches can also be used to support constraint handling, to model robustness criteria, or to approach bilevel optimization problems, simplifying these aspects. Further afield, too, in the machine learning community, we are seeing that the multiobjective optimization perspective is being used to get at the root of ill-posed problems in dimensionality reduction, pattern recognition and classification.

From the MCDM point of view, we observe that there is an intrinsic complexity in the process of understanding the optimization problem and building preferences on the solutions proposed by the multiobjective optimization. At the beginning of the decision process the Decision Maker (DM) has a rather vague idea of the decision problem at hand and, consequently, also the preferences are incomplete, approximate, uncertain or fuzzy.

Thus, better understanding complexity in multiobjective optimization is of central importance for the two communities, MCDM and EMO, and several related disciplines. It would enable us to wield existing methodologies with greater knowledge, control and effect, and should, more importantly, provide the foundations and impetus for the development of new, principled methods, in this area. Taking into account the above remarks, complexity in multiobjective optimization, as the main theme of the seminar, will be focused around three topics:

Focus 1: Complexity in preference: This topic is mainly concerned with elicitation, representation and exploitation of the preference of one or more users, for example:

  • Discovering and building preferences that are dynamic and unstable
  • Group preference
  • Complex structure of criteria
  • Non-standard preferences
  • Learning in multiobjective optimization (c.f. Seminar 12041)

Focus 2: Complexity in optimization: This topic is mainly concerned with the generation of alternative candidate solutions, given some set of objective functions and feasible space. The following topics are examples for the wide range of issues in this context:

  • High-dimensional problems
  • Complex optimization problems
  • Simulation-based optimization and expensive functions
  • Uncertainty and robustness (c.f. Seminar 09041)
  • Interrelating decision and objective space information

Focus 3: Complexity in applications: An all-embracing goal is to achieve a better understanding of complexity in practical problems. Many fields in the Social Sciences, Economics, Engineering Sciences are relevant: E-government, Finance, Environmental Assessment, E-commerce, Public Policy Evaluation, Risk Management and Security issues are all examples for areas where the findings of this seminar could apply.

We intend that discussions around these three topics will provide a strong basis for progress in both the theory and practice of handling complexity in multiobjective optimization in all its guises.


Summary

Understanding complexity in multiobjective optimization is of central importance for the two communities, MCDM and EMO, and several related disciplines. It enables us to wield existing methodologies with greater knowledge, control and effect, and should, more importantly, provide the foundations and impetus for the development of new, principled methods, in this area.

We believe that a strong route to further progress in multiobjective optimization is a determination to understand more about the various ways that complexity manifests itself in multiobjective optimization. We observe that in several fields, ranging from engineering to medicine to economics to homeland security, real-world problems are very often characterized by a high degree of complexity deriving from the presence of many competitive objectives to be optimized, many stakeholders expressing conflicting interests and the presence of many technical parameters being unstable in time and for which we have imperfect knowledge. These very complex problems require a specific methodology, mainly based on multiobjective optimization, that, using high computational capacities, takes into account robustness concerns and allows an effective participation of the several stakeholders in the decision process.

The seminar took place January 11th--16th 2015. The main goals of the seminar were the exploration and elucidation of complexity in three fundamental domains:

Focus 1: Complexity in preference

This topic is mainly concerned with elicitation, representation and exploitation of the preference of one or more users, for example: discovering and building preferences that are dynamic and unstable, group preference, complex structure of criteria,non-standard preferences, learning in multiobjective optimization.

Focus 2: Complexity in optimization

This topic is mainly concerned with the generation of alternative candidate solutions, given some set of objective functions and feasible space. The following topics are examples for the wide range of issues in this context: high-dimensional problems, complex optimization problems, simulation-based optimization and expensive functions, uncertainty and robustness, interrelating decision and objective space information.

Focus 3: Complexity in applications

An all-embracing goal is to achieve a better understanding of complexity in practical problems. Many fields in the Social Sciences, Economics, Engineering Sciences are relevant: E-government, Finance, Environmental Assessment, E-commerce, Public Policy Evaluation, Risk Management and Security issues are among the possible application areas.

During the seminar the program was updated on a daily basis to maintain flexibility in balancing time slots for talks, discussions, and working groups. The working groups were established on the first day in highly interactive fashion: at first each participant was requested to write her/his favorite topic on the black board, before a kind of collaborative clustering process was applied for forming the initial five working groups, some of them splitting into subgroups later. Participants were allowed to change working groups during the week, but the teams remained fairly stable throughout. Abstracts of the talks and extended abstracts of the working groups can be found in subsequent chapters of this report.

Further notable events during the week included: (i) a session devoted to discuss the results and the perspectives of this series of seminars after ten years of the first one, (ii) a hike within a time slot with worst weather conditions during the week, (iii) a presentation session allowing us to share details of upcoming events in our research community, and (iv) a wine and cheese party made possible by a donation of UCL's EPSRC Centre for Innovative Manufacturing in Emergent Macromolecular Therapies represented by Richard Allmendinger.

Outcomes

The outcomes of each of the working groups can be seen in the sequel. Extended versions of their findings will be submitted to a Special Issue on "Understanding Complexity in Multiobjective Optimization" in the Journal of Multi-Criteria Decision Analysis guest-edited by the organizers of this Dagstuhl seminar.

This seminar resulted in a very insightful, productive and enjoyable week. It has already led to first new results and formed new cooperation, research teams and topics. In general, the relations between the EMO and MCDM community were further strengthened after this seminar and we can expect that thanks to the seminar a greater and greater interaction will be developed in the next few years.

Acknowledgements. Many thanks to the Dagstuhl office and its helpful and patient staff; huge thanks to the organizers of the previous seminars in the series for setting us up for success; and thanks to all the participants, who worked hard and were amiable company all week. In the appendix, we also give special thanks to Salvatore Greco as he steps down from the organizer role.

Copyright Salvatore Greco, Kathrin Klamroth, Joshua D. Knowles, and Günter Rudolph

Participants
  • Richard Allmendinger (University College London, GB) [dblp]
  • Jürgen Branke (University of Warwick, GB) [dblp]
  • Dimo Brockhoff (INRIA - University of Lille 1, FR) [dblp]
  • Carlos A. Coello Coello (CINVESTAV - Mexico, MX) [dblp]
  • Salvatore Corrente (Università di Catania, IT) [dblp]
  • Matthias Ehrgott (Lancaster University, GB) [dblp]
  • Gabriele Eichfelder (TU Ilmenau, DE) [dblp]
  • Michael Emmerich (Leiden University, NL) [dblp]
  • José Rui Figueira (IST - Lisbon, PT) [dblp]
  • Carlos M. Fonseca (University of Coimbra, PT) [dblp]
  • Xavier Gandibleux (University of Nantes, FR) [dblp]
  • Martin Josef Geiger (Helmut-Schmidt-Universität - Hamburg, DE) [dblp]
  • Salvatore Greco (University of Catania, IT & University of Portsmouth, GB) [dblp]
  • Jussi Hakanen (University of Jyväskylä, FI) [dblp]
  • Carlos Henggeler Antunes (University of Coimbra, PT) [dblp]
  • Hisao Ishibuchi (Osaka Prefecture University, JP) [dblp]
  • Johannes Jahn (Universität Erlangen-Nürnberg, DE) [dblp]
  • Andrzej Jaszkiewicz (Poznan University of Technology, PL) [dblp]
  • Yaochu Jin (University of Surrey, GB) [dblp]
  • Milosz Kadzinski (Poznan University of Technology, PL) [dblp]
  • Kathrin Klamroth (Universität Wuppertal, DE) [dblp]
  • Joshua D. Knowles (University of Manchester, GB) [dblp]
  • Renaud Lacour (Bergische Universität Wuppertal, DE) [dblp]
  • Manuel López-Ibáñez (Free University of Brussels, BE) [dblp]
  • Luis Marti (PUC - Rio de Janeiro, BR) [dblp]
  • Kaisa Miettinen (University of Jyväskylä, FI) [dblp]
  • Sanaz Mostaghim (Universität Magdeburg, DE) [dblp]
  • Vincent Mousseau (Ecole Centrale Paris, FR) [dblp]
  • Mauro Munerato (ESTECO SpA - Trieste, IT)
  • Boris Naujoks (FH Köln, DE) [dblp]
  • Luís Paquete (University of Coimbra, PT) [dblp]
  • Silvia Poles (Noesis Solutions - Leuven, BE) [dblp]
  • Robin Purshouse (University of Sheffield, GB) [dblp]
  • Patrick M. Reed (Cornell University, US) [dblp]
  • Enrico Rigoni (ESTECO SpA - Trieste, IT) [dblp]
  • Günter Rudolph (TU Dortmund, DE) [dblp]
  • Stefan Ruzika (Universität Koblenz-Landau, DE) [dblp]
  • Serpil Sayin (Koc University - Istanbul, TR) [dblp]
  • Pradyumn Kumar Shukla (KIT - Karlsruher Institut für Technologie, DE) [dblp]
  • Roman Slowinski (Poznan University of Technology, PL) [dblp]
  • Ralph E. Steuer (University of Georgia, US) [dblp]
  • Michael Stiglmayr (Bergische Universität Wuppertal, DE) [dblp]
  • Heike Trautmann (Universität Münster, DE) [dblp]
  • Tea Tusar (Jozef Stefan Institute - Ljubljana, SI) [dblp]
  • Daniel Vanderpooten (University Paris-Dauphine, FR) [dblp]
  • Simon Wessing (TU Dortmund, DE) [dblp]
  • Margaret M. Wiecek (Clemson University, US) [dblp]
  • Xin Yao (University of Birmingham, GB) [dblp]

Related Seminars
  • Dagstuhl Seminar 04461: Practical Approaches to Multi-Objective Optimization (2004-11-07 - 2004-11-12) (Details)
  • Dagstuhl Seminar 06501: Practical Approaches to Multi-Objective Optimization (2006-12-10 - 2006-12-15) (Details)
  • Dagstuhl Seminar 09041: Hybrid and Robust Approaches to Multiobjective Optimization (2009-01-18 - 2009-01-23) (Details)
  • Dagstuhl Seminar 12041: Learning in Multiobjective Optimization (2012-01-22 - 2012-01-27) (Details)
  • Dagstuhl Seminar 18031: Personalized Multiobjective Optimization: An Analytics Perspective (2018-01-14 - 2018-01-19) (Details)
  • Dagstuhl Seminar 20031: Scalability in Multiobjective Optimization (2020-01-12 - 2020-01-17) (Details)
  • Dagstuhl Seminar 23361: Multiobjective Optimization on a Budget (2023-09-03 - 2023-09-08) (Details)

Classification
  • modelling / simulation
  • optimization / scheduling
  • soft computing / evolutionary algorithms

Keywords
  • multi-criteria optimization
  • multiple criterion decision making
  • evolutionary multiobjective optimization
  • MCDM
  • EMO
  • hybrid methods
  • complexity