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A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 1917)


Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN 3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN 2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA—two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II’s low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come.


  • Multiobjective Optimization
  • Sharing Parameter
  • Binary Tournament Selection
  • Simulated Binary Crossover
  • Niched Pareto Genetic Algorithm

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Deb, K., Agrawal, S., Pratap, A., Meyarivan, T. (2000). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. In: Schoenauer, M., et al. Parallel Problem Solving from Nature PPSN VI. PPSN 2000. Lecture Notes in Computer Science, vol 1917. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41056-0

  • Online ISBN: 978-3-540-45356-7

  • eBook Packages: Springer Book Archive