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Hybird Evolutionary Multi-objective Algorithms. Karthik Sindhya , PhD. Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology [email protected] http://users.jyu.fi/~kasindhy/. Objectives The objectives of this lecture is to: - PowerPoint PPT Presentation
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Hybird Evolutionary Multi-objective Algorithms
Karthik Sindhya, PhDPostdoctoral Researcher
Industrial Optimization GroupDepartment of Mathematical Information Technology
[email protected]://users.jyu.fi/~kasindhy/
Objectives
The objectives of this lecture is to:• Obtain an idea about hybrid algorithms
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
• Global search+local search = Hybrid– Global search – Gasoline engine– Local search – Battery power
• Global 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 algorithm
• Hybrid EMO algorithms:– Increase in convergence speed.– Guaranteed convergence to the Pareto optimal
front.– An efficient termination criterion.
• Classification:– Concurrent hybrid EMO algorithm– Serial hybrid EMO algorithm
Hybrid EMO algorithm
Hybrid EMO algorithm
• Concurrent hybrid EMO algorithm:
EMO algorithm Local search
Termination criterion ?
Local search
Pareto optimal front
No
Yes
• 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 algorithm
• 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 algorithm
• Serial hybrid EMO algorithm:
Hybrid EMO algorithm
EMO algorithm
Termination criterion ?
Local search
No
Yes
Pareto optimal front
• 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 algorithm
Hybrid EMO algorithm
– Frequency of local search• Cyclic probability of local
search Plocal.• Balancing exploration and
exploitation– Exploration – Crossover and
mutation operators (global search).
– Exploitation – local search.
• Periodically Plocal reduced to zero to allow global search.
GenerationsPr
obab
ility
of l
ocal
sear
ch
Plocal
0
Hybrid EMO algorithm
– Termination criterion• Using 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 algorithm
Hybrid EMO algorithm
Hybrid EMO algorithms
HybridOriginal NSGA-II