The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Evolutionary Computation
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Generalizing the improved run-time complexity algorithm for non-dominated sorting
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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This paper improves upon the reference NSGA-II procedure by removing an instability in its crowding distance operator. This instability stems from the cases where two or more individuals on a Pareto front share identical fitnesses. In those cases, the instability causes their crowding distance to either become null, or to depend on the individual's position within the Pareto front sequence. Experiments conducted on nine different benchmark problems show that, by computing the crowding distance on unique fitnesses instead of individuals, both the convergence and diversity of NSGA-II can be significantly improved.