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An Interactive, Preference-Based Multi-objective Evolutionary Algorithm

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josephrobbins
25 diapositives · 331 Views · Jan 03, 2020

This study focuses on multi-objective optimization where conflicting objective functions require finding non-dominated Pareto-optimal solutions. Strategies such as Genetic Algorithms and MOEAs are explored, emphasizing goals like convergence, diversity, and incorporating decision maker preferences. Various successful MOEAs are discussed, along with the proposed algorithm based on ε-MOEA. Preliminary runs on ZDT4 problem illustrate benefits and importance of interactive, preference-based approaches in solving complex optimization problems.

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An Interactive, Preference-Based Multi-objective Evolutionary Algorithm
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  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.