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Hybird Evolutionary Multi-objective Algorithms

Hybird Evolutionary Multi-objective Algorithms. Karthik Sindhya , PhD. Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthik.sindhya@jyu.fi http://users.jyu.fi/~kasindhy/. Objectives The objectives of this lecture is to:

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Hybird Evolutionary Multi-objective Algorithms

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  1. Hybird Evolutionary Multi-objective Algorithms KarthikSindhya, PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthik.sindhya@jyu.fi http://users.jyu.fi/~kasindhy/

  2. Objectives The objectives of this lecture is to: • Obtain an idea about hybrid algorithms

  3. Hybrid EMO algorithm • What is hybrid? • The hybrid Prius runs on battery power up to 42 mph and while idling. When the car is moving above 42 mph, the gasoline engine kicks in. Toyota Prius

  4. Hybrid EMO algorithm • Globalsearch+localsearch = Hybrid • Globalsearch – Gasolineengine • Localsearch – Batterypower • Globalsearch – EMO algorithm & Localsearch – Locallyimprovesolutions in a population. • Localsearch: Optimizing a scalarizedfunction of a MOP using a suitablemathematicalprogrammingtechnique.

  5. Hybrid EMO algorithm • Hybrid EMO algorithms: • Increase in convergencespeed. • Guaranteedconvergence to the Paretooptimalfront. • An efficientterminationcriterion. • Classification: • Concurrenthybrid EMO algorithm • Serial hybrid EMO algorithm

  6. Hybrid EMO algorithm • Concurrenthybrid EMO algorithm: EMOalgorithm Local search Terminationcriterion ? No Yes Local search Pareto optimal front

  7. Hybrid EMO algorithm • Concurrenthybrid EMO algorithm (cont’d): • Locallyimprovinga fewsolutions in a generation. • Convergencespeedcanbeincreased. • A localsearchon finalpopulation is done to guaranteeParetooptimality. • Examples: • Hybrid MOGA (Ishibuchi and Murata, 1998) • MOGLS (Jaszkiewicz, 2002) etc.

  8. Hybrid EMO algorithm • Serial hybrid EMO algorithm (cont’d): • Localsearchappliedonlyafter the termination of an EMO algorithm. • Convergencespeed is notimproved. • Paretooptimality of the finalpopulation is guaranteed. • No clearterminationcriterion for stopping an EMO algorithm. • Examples: • MSGA-LS1 & LS3 (Levi et al., 2000) • Hybridalgorithmusing PDM method (Harada et al., 2006)

  9. Hybrid EMO algorithm • Serial hybrid EMO algorithm: EMOalgorithm Terminationcriterion ? No Yes Local search Pareto optimal front

  10. Hybrid EMO algorithm • Increase in convergencespeedonlypossible in a concurrenthybrid EMO algorithm. • Issuesexist for a goodimplementation of a concurrenthybrid EMO algorithm: • Type of a scalarizingfunction: • Severalscalarizingfunctionsexist – Weightedsummethod (Gass, Saaty, 1955), achievementscalarizingfunction (Wierzbicki, 1980) etc.

  11. Hybrid EMO algorithm

  12. Hybrid EMO algorithm • Frequency of localsearch • Cyclicprobability of localsearchPlocal. • Balancingexploration and exploitation • Exploration – Crossover and mutationoperators (globalsearch). • Exploitation – localsearch. • PeriodicallyPlocalreduced to zero to allowglobalsearch. Plocal Probability of local search 0 Generations

  13. Hybrid EMO algorithm • Terminationcriterion • Using the optimalvalue of an ASF: • Using criterion of maximumnumber of functionevaluationsdoesnotindicateproximity of solutions to the Paretooptimalfront. • The optimal value of an ASF can be used to devise a new termination criterion for a hybrid EMO algorithm. • The optimalvalue of an ASF Ω at everygenerationt is stored in an archive. • Average of Ω (Ωavg) aftert+φgenerationsarecalculated. • IfΩavg ≤ σ (σ – smallpostivescalar), hybridalgorithm is terminated.

  14. Hybrid EMO algorithm

  15. Hybrid EMO algorithms Original NSGA-II Hybrid

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