Karthik Sindhya PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthiksindhyajyufi httpusersjyufikasindhy Objectives ID: 640973
Download Presentation The PPT/PDF document "Non-dominated Sorting Genetic Algorithm ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Non-dominated Sorting Genetic Algorithm (NSGA-II)
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:Understand the basic concept and working of NSGA-IIAdvantages and disadvantagesSlide3
Non-dominated sorting genetic algorithm –II was proposed by Deb et al. in 2000.
NSGA-II procedure has three features:It uses an elitist principleIt emphasizes non-dominated solutions.It uses an explicit diversity preserving mechanismNSGA-II Slide4
NSGA-II
ƒ
1
ƒ
2
Crossover & Mutation
NSGA-IISlide5
Crowded tournament selection operator
A solution xi wins a tournament with another solution xj if any of the following conditions are true:If solution xi has a better rank, that is, ri < rj .If they have the same rank but solution xi has a better crowding distance than solution xj, that is, ri = rj and di > dj .NSGA-II
Objective spaceSlide6
Crowding distance
To get an estimate of the density of solutions surrounding a particular solution.Crowding distance assignment procedureStep 1: Set l = |F|, F is a set of solutions in a front. Set di = 0, i = 1,2,…,l.Step 2: For every objective function m = 1,2,…,M, sort the set in worse order of fm or find sorted indices vector: Im = sort(fm).NSGA-IISlide7
Step 3: For m = 1,2,…,M, assign a large distance to boundary solutions, i.e. set them to ∞ and for all other solutions j = 2 to (l-1),
assign as follows:
ii+1i-1NSGA-IISlide8
Advantages:Explicit diversity preservation mechanism
Overall complexity of NSGA-II is at most O(MN2)Elitism does not allow an already found Pareto optimal solution to be deleted.Disadvantage:Crowded comparison can restrict the convergence.Non-dominated sorting on 2N size.NSGA-II