An Interactive, Preference-Based Multi-objective Evolutionary Algorithm

1. İbrahim Karahan Middle East Technical University An Interactive, Preference-BasedMulti-objective Evolutionary Algorithm

2. Multi-objective Optimization

3. Multi-objective Optimization • Objective functions are conflicting • There does not exist a single solution that optimizes all objectives • The search is for finding the “non-dominated” (Pareto-optimal) solutions

4. Non-dominated Solutions A solution i is non-dominated if: there is no solution j that is at least as good as solution i in all objective values and is better than solution i in at least one objective

5. An Illustration

6. An Illustration

7. An Illustration

8. An Illustration

9. How to Solve? • Classical Methods: • Weighted sum method • ε-Constraint Method • Value function method • Goal programming methods • Interactive methods • Evolutionary methods

10. Genetic Algorithms • Population based algorithms • Converges to the optimal solutions by using principles borrowed from nature, such as: • Reproduction • Crossover • Mutation

11. Genetic Algorithms • Each solution is represented by a chromosome • A fitness function is utilized to evaluate solutions • New offspring are created using crossover and mutation operators

12. Flowchart

13. Multi-objective Evolutionary Algorithms (MOEAs) • The aim is more than finding a single solution • An approximation to the entire or partial Pareto-optimal frontier is desired • Not only convergence, but also diversity among the solutions is important

14. MOEAs Goals of Multiobjective EAs: • Convergence to Pareto-optimal frontier • Diversity to have an adequate representation of entire frontier

15. Successful MOEAs • SPEA2 (Zitzler et al., 2001) • NSGA-II (Deb et al., 2002) • IBEA (Zitzler et al., 2004) • ε-MOEA (Deb et al., 2005) • SMS-MOEA (Beume et al., 2007) • EMAPS (Köksalan et al., 2007)

16. MOEAs • Most of MOEAs approximate the entire Pareto-optimal frontier • Approximating the entire frontier becomes harder as the number of objectives increases • Coello Coello (2000) states that this does not help decision making at all Coello Coello, Carlos A, Handling preferences in evolutionary multiobjective optimization: A survey, The 2000 Congress on Evolutionary Computation CEC 00; California, CA; USA; 16 July-19 July 2000. pp. 30-37. 2000

17. Preference Incorporation • Introducing DM’s preference leads to solutions which are of higher relevance to DM • There are a number of approaches that introduces DM’s preferences, such as STEM, GDF, Visual Interactive Approach

18. Preference Incorporation • Instead of finding a single solution near the region of interest, it is better to generate a set of solutions to assist decision making • It is even better to generate solutions from multiple regions of interest simultaneously

19. MOEAs Additional Goal for Preference-Based Multiobjective EAs: • Generate solutions which are on those segments of the efficient frontier that will appeal to the DM

20. Proposed Algorithm • Based on ε-MOEA (Deb et al., 2005) • A preference-based, interactive approach • Offspring acceptance procedure is altered for: • Better diversity • Preference incorporation

21. Preliminary Runs Test Problem ZDT4 (Zitzler et al., 2000)

22. Preliminary Runs

23. Preliminary Runs

24. Benefits • More solutions are found when a particular region is focused • Multiple regions can be simultaneously explored • DM can act while the algorithm is in progress

25. Thank you for your listening…Questions and comments are welcome.