Non-dominated Sorting Genetic Algorithm (NSGA-II) Karthik Sindhya, PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthik.sindhya@jyu.fi http://users.jyu.fi/~kasindhy/

Objectives The objectives of this lecture is to: Understand the basic concept and working of NSGA-II Advantages and disadvantages

NSGA-II Non-dominated sorting genetic algorithm –II was proposed by Deb et al. in 2000. NSGA-II procedure has three features: It uses an elitist principle It emphasizes non-dominated solutions. It uses an explicit diversity preserving mechanism

NSGA-II NSGA-II Crossover & Mutation ƒ2 ƒ1

NSGA-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

NSGA-II Crowding distance Crowding distance assignment procedure To get an estimate of the density of solutions surrounding a particular solution. Crowding distance assignment procedure Step 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-II 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: i-1 i i+1

NSGA-II Advantages: Disadvantage: 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.