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Hybird - PowerPoint Presentation

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Hybird - PPT Presentation

Evolutionary Multiobjective Algorithms Karthik Sindhya PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthiksindhyajyufi ID: 525237

emo hybrid search algorithm hybrid emo algorithm search local termination optimal pareto criterion concurrent convergence function algorithms speed front

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Slide1

Hybird Evolutionary Multi-objective Algorithms

Karthik

Sindhya, PhD

Postdoctoral ResearcherIndustrial Optimization GroupDepartment of Mathematical Information TechnologyKarthik.sindhya@jyu.fihttp://users.jyu.fi/~kasindhy/Slide2

Objectives

The objectives of this lecture is to:Obtain an idea about hybrid algorithmsSlide3

Hybrid

EMO algorithmWhat 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 PriusSlide4

Global search+local search

= HybridGlobal search – Gasoline engineLocal search – Battery powerGlobal search – EMO algorithm & Local search – Locally improve solutions in a population.Local search: Optimizing a scalarized function of a MOP using a suitable mathematical programming

technique.Hybrid EMO algorithmSlide5

Hybrid EMO algorithms:Increase

in convergence speed.Guaranteed convergence to the Pareto optimal front.An efficient termination criterion.Classification:Concurrent hybrid EMO algorithmSerial hybrid EMO algorithmHybrid EMO algorithmSlide6

Hybrid

EMO algorithm

Concurrent hybrid EMO algorithm:EMO algorithmLocal searchTermination criterion ?

Local searchPareto optimal front

No

YesSlide7

Concurrent hybrid EMO algorithm

(cont’d):Locally improving a few solutions in a generation. Convergence speed can be increased.A local search on final population is done to guarantee Pareto optimality. Examples:Hybrid MOGA (Ishibuchi and Murata, 1998)MOGLS (Jaszkiewicz, 2002) etc.

Hybrid EMO algorithmSlide8

Serial hybrid EMO algorithm

(cont’d):Local search applied only after the termination of an EMO algorithm.Convergence speed is not improved.Pareto optimality of the final population is guaranteed.No clear termination criterion for stopping an EMO algorithm.Examples:MSGA-LS1 & LS3 (Levi et al., 2000)Hybrid algorithm using PDM method (Harada et al., 2006)

Hybrid EMO algorithmSlide9

Serial hybrid EMO algorithm:

Hybrid EMO algorithmEMO algorithmTermination criterion ?

Local searchNoYes

Pareto optimal frontSlide10

Increase in convergence speed

only possible in a concurrent hybrid EMO algorithm.Issues exist for a good implementation of a concurrent hybrid EMO algorithm:Type of a scalarizing function:Several scalarizing functions exist – Weighted sum method (Gass, Saaty, 1955), achievement scalarizing function (Wierzbicki, 1980) etc.

Hybrid EMO algorithmSlide11

Hybrid

EMO algorithmSlide12

Frequency

of local search

Cyclic probability of local search Plocal.Balancing exploration and exploitationExploration – Crossover and mutation operators (global search).Exploitation – local search.Periodically Plocal reduced to zero to allow global search.

Generations

Probability of local search

P

local

0

Hybrid

EMO

algorithmSlide13

Termination criterionUsing the

optimal value of an ASF:Using criterion of maximum number of function evaluations does not indicate proximity of solutions to the Pareto optimal front.The optimal value of an ASF can be used to devise a new termination criterion for a hybrid EMO algorithm.The optimal value of an ASF Ω at every generation t is stored in an archive.Average of Ω (Ωavg) after t+φ generations are

calculated.If Ωavg ≤ σ (σ – small postive scalar), hybrid algorithm is terminated.Hybrid EMO algorithmSlide14

Hybrid

EMO algorithmSlide15

Hybrid

EMO algorithmsHybrid

Original NSGA-II

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