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Non-dominated Sorting Genetic Algorithm (NSGA-II)

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:

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Non-dominated Sorting Genetic Algorithm (NSGA-II)

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

  2. Objectives The objectives of this lecture isto: • 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 xihas 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 • 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: • 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.

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