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Runtime Analyses of NSGA-III on Many-Objective Problems
NSGA-II and NSGA-III are two of the most popular evolutionary multi-objective algorithms used in practice.
A Tight $O(4^k/p_c)$ Runtime Bound for a ($μ$+1) GA on Jump$_k$ for Realistic Crossover Probabilities
This yields an improved and tight time bound of $O(\mu n \log(k) + 4^k/p_c)$ for a range of~$k$ under the mild assumptions $p_c = O(1/k)$ and $\mu \in \Omega(kn)$.
Analysing the Robustness of NSGA-II under Noise
To our knowledge, this is the first proof that NSGA-II can outperform GSEMO and the first runtime analysis of NSGA-II in noisy optimisation.
Analysing Equilibrium States for Population Diversity
We give an exact formula for the drift of population diversity and show that it is driven towards an equilibrium state.
Crossover Can Guarantee Exponential Speed-Ups in Evolutionary Multi-Objective Optimisation
We provide a theoretical analysis of the well-known EMO algorithms GSEMO and NSGA-II to showcase the possible advantages of crossover: we propose classes of "royal road" functions on which these algorithms cover the whole Pareto front in expected polynomial time if crossover is being used.
Differentiability Properties of Log-Analytic Functions
We show that the derivative of a log-analytic function is log-analytic.
Logic Algebraic Geometry Classical Analysis and ODEs 03C64, 14P15, 26A09, 26E05, 26E10, 32B20
