Presentation on theme: "Non-dominated Sorting Genetic Algorithm (NSGA-II)"— Presentation transcript:
1Non-dominated Sorting Genetic Algorithm (NSGA-II) Karthik Sindhya, PhDPostdoctoral ResearcherIndustrial Optimization GroupDepartment of Mathematical Information Technology
2Objectives The objectives of this lecture is to: Understand the basic concept and working of NSGA-IIAdvantages and disadvantages
3NSGA-IINon-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 mechanism
5NSGA-II 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 .Objective space
6NSGA-II Crowding distance Crowding distance assignment procedure 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).
7NSGA-IIStep 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:i-1ii+1
8NSGA-II Advantages: Disadvantage: Explicit diversity preservation mechanismOverall 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.