Historical milestones in MCDM and LIACS Projects

1. Historical milestones in MCDMand LIACS Projects

2. Georg Cantor and Felix Haussdorff • The origins of the mathematical foundations of multiobjective optimization can be traced back to the period that goes from 1895 to 1906. During that period, Georg Cantor and Felix Hausdorff laid the foundations of infinite dimensional ordered spaces. • Haussdorff gave the first example for complete orderings • Cantor introduced equivalence classes and gave the first example of a utility function

3. Francis Ysidro Edgeworth and Wilfredo Pareto Having several objective functions, the notion of “optimum” changes, because in MOPs, we are really trying to find good compromises (or “trade-offs”) rather than a single solution as in global optimization. The notion of “optimum” that is most commonly adopted is that originally proposed by Francis Ysidro Edgeworth in 1881. This notion was later generalized by Vilfredo Pareto (in 1896). Although some authors call Edgeworth-Pareto optimum to this notion, the most commonly accepted term remains Pareto optimum.

4. Albert W.Tucker Leonid Hurwitz Nevertheless, multiobjective optimization theory remained relatively undeveloped during the 1950s. It was until the 1960s that the foundations of multiobjective optimization were consolidated and taken seriously by pure mathematicians when Leonid Hurwicz generalized the results of Kuhn & Tucker to topological vector spaces. • Albert Tucker was the first who systematically worked on vector optimization • Kuhn and Tucker analyzed local Pareto optimality and stated conditions for local optimal based on differential geometry of the vector valued function

5. John Nash/ John von Neumann Foundations of game theory: Many players in conflicting and cooperative games Game theory is today an important field that is closely related multiobjective optimization, as interests of different players can be viewed as multiple objectives.

6. TC. Koopmans and S.A. Marglin The application of multiobjective optimization to domains outside economics began with the work by Koopmans (1951) in production theory and with the work of Marglin (1967) in water resources planning.

7. Kaiza Miettinen and Matthias Ehrgott Kaiza Miettinen summed up state-of-the-art on seterministic methods in MCDM and mathematicall programming Ehrgott generalized many combinatorial Algorithms to multiobjective versions.

8. Kalyanmoy Deb and Carlos Coello Coello (C3) Web Repository On Metaheuristics, Thesis and Test-Problems Deb Introduced Large Scale Multi-objective Optimization algorithms Based on Evolutionary Algorithms http://www.lania.mx/~ccoello/EMOO/

9. Many more researchers … • International Society of MCDM Awards: • MCDM Gold Medal, • Edgeworth-Pareto Award, and • Georg Cantor Award http://www.terry.uga.edu/mcdm/index.html

10. LIACS Contributions to MCDM Evolutionary Strategies for MCO (Bäck, Willmes, Emmerich 2002, 2004) SMS-EMOA: Algorithm proposed first on EMO 2005 conference, now is one of the state-of-the-art techniques used in the field. Recently: CMA-SMS-EMOA and S-Gradient Method have been developed an published in 2007 Pareto Optimization for Optimization with time consuming evaluation functions (Emmerich, Naujoks) Niching Methods in EMOA (Emmerich, Shir, Preuss) 2006: Rigorous analysis of spherical target problems using superellipsoid theory (Deutz, Emmerich) 2004: Interval-based orders in Pareto Optimization (Emmerich, Naujoks) – University of Dortmund Various Applications: Airfoil optimization, Turbine Blade Optimization, Laser Pulse Shaping, High Purity Silicon Production, and many more, Grid Computing, Building Design …(TU Eindhoven, TU Aachen, TU Dortmund, Fraunhofer UMSICHT, Bayer, DEGUSSA) Gradient-Based S-Metric Maximization

11. Current Research:S-Gradient (Hybrid Metaheuristics 2007) Idea: Gradient-Based Maximization of the S-Metric First Paper: HM 2007, Hybrid-EMO/Gradient

12. Current Research:Exploring the Chemical Universe LACDR Cooperation for Medical Drug Design Multi-objective Search for Drug-like Molecules

13. Current Research:Robust Design Optimization Noisy Objective Functions, Fuzzy Constraints => Interval Ordered Spaces Applications in Building Performance Design

14. Current Research:Grid-Scheduling Finding optimal Scheduling Strategies Each User-Group defines Objective

15. Some Recent Research Fields Optimization of Interval-Ordered Sets Complexity/Reliability Theory for Algorithms S-Metric and Indicator Based Approaches Geometrical Analysis of Partially-Ordered Landscapes Many-Objective Optimization Combination of Mathematical Programming and Metaheuristics Multi-objective Robust Design Optimization Multi-objectivization in Combinatorial Optimization Geometrical Classification of Conflicts Long term goal: Reliable, flexible, efficient methods for Pareto Optimization Optimal support of human decision making