Multidimensional divide-and-conquer
Communications of the ACM
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
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
An efficient non-dominated sorting method for evolutionary algorithms
Evolutionary Computation
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
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
Multi-objective path planning in discrete space
Applied Soft Computing
Revisiting the NSGA-II crowding-distance computation
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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This paper generalizes the "Improved Run-Time Complexity Algorithm for Non-Dominated Sorting" by Jensen, removing its limitation that no two solutions can share identical values for any of the problem's objectives. This constraint is especially limiting for discrete combinatorial problems, but can also lead the Jensen algorithm to produce incorrect results even for problems that appear to have a continuous nature, but for which identical objective values are nevertheless possible. Moreover, even when values are not meant to be identical, the limited precision of floating point numbers can sometimes make them equal anyway. Thus a fast and correct algorithm is needed for the general case. The paper shows that generalizing the Jensen algorithm can be achieved without affecting its time complexity, and experimental results are provided to demonstrate speedups of up to two orders of magnitude for common problem sizes, when compared with the correct baseline algorithm from Deb.