Evaluating the CMA Evolution Strategy on Multimodal Test Functions

By Nikolaus Hansen, Stefan Kern. 2004

882 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Optimization & Training

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Citations in the corpus

SGDR: Stochastic Gradient Descent with Warm Restarts (2016, background): “One way to deal with multimodal functions is to iteratively sample a large number λ of candidate solutions, make a step towards better solutions and slowly shape the sampling distribution to maximize the likelihood of successful steps to appear again (Hansen & Kern, 2004).”
Preference-Based Reinforcement Learning: A Preliminary Survey (2013, methodology): “It also employs an evolutionary strategy for optimizing the parameters of a parametric policy, but CMA-ES [9] was used in this case.”
A restart CMA evolution strategy with increasing population size (2005, methodology): “This result seems to contradict previous results on the Ackley function [3], but it can be explained by the different scaling that is applied here: outside the usual bounds ([-32, 32]n) the Ackley function is almost flat and the composition with a linear transformation with a condition number of 100”
A social learning particle swarm optimization algorithm for scalable optimization (2015, background): “It has been empirically shown that a small swarm size is usually sufficient for uni-modal optimization problems while a bigger swarm size is required for multi-modal optimization problems for more intensive exploration [25,1].”
Covariance Matrix Adaptation for Multi-objective Optimization (2007, methodology): “The (1+ λ )-CMA-ES is compared to the ( µ/µ W , λ )-CMA-ES, the standard CMA-ES with weighted global intermediate ( µ/µ W ) recombination as described by Hansen and Kern (2004).”
Adaptive Designs of Experiments for Accurate Approximation of a Target Region (2010, positive): “In the test problems presented in this chapter, we optimize the criterion on a ﬁne grid for low dimensions, and using the population-based CMA-ES algorithm [Covariance Matrix Adaptation Evolution Strategies, [35]] for higher dimensions.”
Performance evaluation of an advanced local search evolutionary algorithm (2005, methodology): “2 in [4]) is smaller than TolX in all components.”
Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point (2009, methodology): “In prelim-inary experiments for example, we employed the CMA-ES of [12] to derive optimal µ -distributions.”
Parameter Control in Evolutionary Algorithms: Trends and Challenges (2015, methodology): “The IPOP-CMA-ES by Auger and Hansen [13] and the IPOP-αCMA-ES by Hansen and Ros [94] extend the (μw, λ)-CMA-ES [90].”
Preference-based Evolutionary Direct Policy Search (2013, methodology): “We run the implementation of [5] with the Hoeffding race algorithm and CMA-ES [7]; we refer to this implementation as EDPS.”
Optimal gait and form for animal locomotion (2009, methodology): “For further details we refer readers to [Hansen and Kern 2004].”
How to Maximize the Likelihood Function for a DSGE Model (2010, neutral): “The CMA-ES routine is chosen because: i) it should be able to handle a non-convex parameter space, ii) it does well on non-separable multimodal objective functions ( Hansen & Kern (2004) ), and iii) it is better than other evolutionary algorithms on multimodal objective functions (Kern, Muller, Hans”
A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion (2009, neutral): “, were accommodated for use with a large population size in [28].”
DG2: A Faster and More Accurate Differential Grouping for Large-Scale Black-Box Optimization (2017, background): “function is not additively separable [64], which is correctly identified by DG2.”
Grey wolf optimizer: a review of recent variants and applications (2017, background): “genetic algorithm (GA) [11], evolutionary strategies (ES) [37], genetic programming (GP) [59], population-based incremental learning (PBIL) [38], biogeography-based optimizer (BBO) [116] and differential evolution (DE) [120].”
The CMA Evolution Strategy: A Comparing Review (2006, background): “To “estimate” a “better” covariance matrix (7) is modified and the same, weighted selection mechanism as in (3) is used [8].”
SGDR: Stochastic Gradient Descent with Restarts (2016, background): “One way to deal with multimodal functions is to iteratively sample a large number λ of candidate solutions, make a step towards better solutions and slowly shape the sampling distribution to maximize the likelihood of successful steps to appear again (Hansen & Kern, 2004).”