1. Non-dominated Sorting Genetic Algorithm (NSGA-II)
Karthik Sindhya, PhD
Postdoctoral Researcher
Industrial Optimization Group
Department of Mathematical Information Technology

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

3. 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

4. NSGA-II
NSGA-II
Crossover & Mutation ƒ2 ƒ1

5. 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

6. 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).

7. 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

8. 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.