Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
A fast and effective method for pruning of non-dominated solutions in many-objective problems
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
DEMO: differential evolution for multiobjective optimization
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
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
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
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Nondominated sorting and diversity estimation procedures are an essential part of many multiobjective optimization algorithms. In many cases these procedures are the computational bottleneck of the entire algorithm. We present the methods to decrease the cost of these procedures for multiobjective differential evolution (DE) algorithms. Our approach is to compute domination ranks and crowding distances for the population at the beginning of the algorithm and use a combination of well known data structures to efficiently update these attributes. Experiments show that the cost of improved nondominated sorting is sub-quadratic in the number of individuals. In practice using our methods the overall DE algorithm can run 2 to 100 times faster.