1. A Multiobjective Evolutionary Algorithm Using Gaussian Process based Inverse Modeling Ran Cheng 1, Yaochu Jin 1, Kaname Narukawa 2 and Bernhard Sendhof 2 1 Department of Computing, University of Surrey, Guildford, UK 2 Honda Research Institute Europe Offenbach, Germany

2. Multiobjective Optimization

3. Key features of multiobjective problems (MOPs) Involving more than one conflicting objectives to be optimized No one single solution optimizes all the objectives A set of non-dominated solutions are used to present the trade-offs between different objectives Advantages of multiobjective evolutionary algorithms Population based nature Capability to obtain a set of solutions in one single run

4. Multiobjective Optimization Pareto Dominance

5. The proposed IM-MOEA

6. Motivations To investigate the possibility of modeling the inverse mapping from the objective space to the decision space To control the distribution of the solutions by directly sampling the Pareto front To do a posteriori sampling for decision making in the objective space and the corresponding solutions in the decision space can be obtained via the inverse models

7. The proposed IM-MOEA Background “Regularity” property: under KKT condition, for an m- objective problem, both the Pareto front (PF) and the Pareto set (PS) are (m - 1)-D manifolds, i.e., PF and PS are of the same dimensionality The “regularity” property has substantially increased the possibility that the inverse mapping from the (m – 1)-D PF to the (m – 1)-D PS is a “one-to-one” mapping

8. Inverse Modeling for Multiobjective Optimization Inverse Model Decomposition

9. Inverse Modeling for Multiobjective Optimization Independent Sampling on Each Objective

10. Inverse Modeling for Multiobjective Optimization Random Grouping to Capture the Variable Linkages

11. Inverse Modeling for Multiobjective Optimization Inverse Model Decomposition Each univariate model is realized using the Guassian process

12. The proposed IM-MOEA Gaussian process regression training and sampling

13. Inverse Modeling for Multiobjective Optimization Framework of the Inverse Model based MOEA (IM- MOEA)

14. Experimental results

20. Conclusion and future work

21. The proposed IM-MOEA has shown robust performance on a variety of benchmark functions, especially on some complicated functions with variable linkage Its scalability is confirmed by its performance on the 104-D WFG functions It’s a posteriori sampling ability has been confirmed.

22. Conclusion and future work In the future, we would like to : Extend the proposed IM-MOEA for many-objective problems Articulate user preference into the reference vectors

23. That is all ! Thanks for your attention. Reference: Ran Cheng, Yaochu Jin, Kaname Narukawa and Bernhard Sendhoff. A Multiobjective Evolutionary Algorithm using Gaussian Process based Inverse Modeling. IEEE Transactions on Evolutionary Computation, 2015 (accepted)