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Elitist Non-dominated Sorting Genetic Algorithm: NSGA-II Tushar Goel (Kalyanmoy Deb) One of most popular MOGA algorithms. Used in Matlabs gamultobj

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tusharg@ufl.edu 2 Pareto optimal front Usual approaches: weighted sum strategy, multiple-constraints modeling Alternative: Multi- objective GA Algorithm requirements: Convergence Spread Min f 2 Min f 1

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tusharg@ufl.edu 3 Ranking Children and parents are combined. Non-dominated points belong to first rank. The non-dominated solutions from the remainder are in second rank, and so on. f2f2 f1f1

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tusharg@ufl.edu 4 Elitism Elitism: Keep the best individuals from the parent and child population f2f2 f1f1 Parent Child

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tusharg@ufl.edu 5 Niching for last rank Niching is an operator that gives preference to solutions that are not crowded Crowding distance c = a + b Solutions from last rank are selected based on niching f2f2 f1f1 a b

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tusharg@ufl.edu 6 Flowchart of NSGA-II Begin: initialize population (size N) Evaluate objective functions Selection Crossover Mutation Evaluate objective function Stopping criteria met? Yes No Child population created Rank population Combine parent and child populations, rank population Select N individuals Elitism Report final population and Stop

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Problems NSGA-II Sort all the individuals in slide 4 into ranks, and denote the rank on the figure in the slide next to the individual. Describe how the 10 individuals were selected, and check if any individuals were selected based on crowding distance. tusharg@ufl.edu7