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