Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
Introduction to Algorithms
Multiple Objective Optimization with Vector Evaluated Genetic Algorithms
Proceedings of the 1st International Conference on Genetic Algorithms
A Variant of Evolution Strategies for Vector Optimization
PPSN I Proceedings of the 1st Workshop 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
Design and Analysis of Experiments
Design and Analysis of Experiments
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms
IEEE Transactions on Evolutionary Computation
The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making
IEEE Transactions on Evolutionary Computation - Special issue on preference-based multiobjective evolutionary algorithms
Using an adaptation of a binary search tree to improve the NSGA-II nondominated sorting procedure
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Towards a deeper understanding of trade-offs using multi-objective evolutionary algorithms
EvoApplications'12 Proceedings of the 2012t European conference on Applications of Evolutionary Computation
Generalizing the improved run-time complexity algorithm for non-dominated sorting
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Pareto Optimal Pairwise Sequence Alignment
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
International Journal of Data Mining and Bioinformatics
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We present a new non-dominated sorting algorithm to generate the non-dominated fronts in multi-objective optimization with evolutionary algorithms, particularly the NSGA-II. The non-dominated sorting algorithm used by NSGA-II has a time complexity of O(MN2) in generating non-dominated fronts in one generation (iteration) for a population size N and M objective functions. Since generating non-dominated fronts takes the majority of total computational time (excluding the cost of fitness evaluations) of NSGA-II, making this algorithm faster will significantly improve the overall efficiency of NSGA-II and other genetic algorithms using non-dominated sorting. The new non-dominated sorting algorithm proposed in this study reduces the number of redundant comparisons existing in the algorithm of NSGA-II by recording the dominance information among solutions from their first comparisons. By utilizing a new data structure called the dominance tree and the divide-and-conquer mechanism, the new algorithm is faster than NSGA-II for different numbers of objective functions. Although the number of solution comparisons by the proposed algorithm is close to that of NSGA-II when the number of objectives becomes large, the total computational time shows that the proposed algorithm still has better efficiency because of the adoption of the dominance tree structure and the divide-and-conquer mechanism.