21,524 research outputs found
Cumulative Step-size Adaptation on Linear Functions
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation,
where the step size is adapted measuring the length of a so-called cumulative
path. The cumulative path is a combination of the previous steps realized by
the algorithm, where the importance of each step decreases with time. This
article studies the CSA-ES on composites of strictly increasing functions with
affine linear functions through the investigation of its underlying Markov
chains. Rigorous results on the change and the variation of the step size are
derived with and without cumulation. The step-size diverges geometrically fast
in most cases. Furthermore, the influence of the cumulation parameter is
studied.Comment: arXiv admin note: substantial text overlap with arXiv:1206.120
Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES
The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely
accepted as a robust derivative-free continuous optimization algorithm for
non-linear and non-convex optimization problems. CMA-ES is well known to be
almost parameterless, meaning that only one hyper-parameter, the population
size, is proposed to be tuned by the user. In this paper, we propose a
principled approach called self-CMA-ES to achieve the online adaptation of
CMA-ES hyper-parameters in order to improve its overall performance.
Experimental results show that for larger-than-default population size, the
default settings of hyper-parameters of CMA-ES are far from being optimal, and
that self-CMA-ES allows for dynamically approaching optimal settings.Comment: 13th International Conference on Parallel Problem Solving from Nature
(PPSN 2014) (2014
Parameter Inference in Differential Equation Models of Biopathways using Time Warped Gradient Matching
Parameter inference in mechanistic models of biopathways based on systems
of coupled differential equations is a topical yet computationally challenging problem,
due to the fact that each parameter adaptation involves a numerical integration of the
differential equations. Techniques based on gradient matching, which aim to minimize
the discrepancy between the slope of a data interpolant and the derivatives predicted
from the differential equations, offer a computationally appealing shortcut to the inference
problem. However, gradient matching critically hinges on the smoothing scheme
for function interpolation, with spurious wiggles in the interpolant having a dramatic
effect on the subsequent inference. The present article demonstrates that a time warping
approach aiming to homogenize intrinsic functional length scales can lead to a signifi-
cant improvement in parameter estimation accuracy. We demonstrate the effectiveness
of this scheme on noisy data from a dynamical system with periodic limit cycle and a
biopathway
Experimental Comparisons of Derivative Free Optimization Algorithms
In this paper, the performances of the quasi-Newton BFGS algorithm, the
NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm
Optimizers (PSO) are compared experimentally on benchmark functions reflecting
important challenges encountered in real-world optimization problems.
Dependence of the performances in the conditioning of the problem and
rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund :
Germany (2009
Markov Chain Analysis of Cumulative Step-size Adaptation on a Linear Constrained Problem
This paper analyzes a (1, )-Evolution Strategy, a randomized
comparison-based adaptive search algorithm, optimizing a linear function with a
linear constraint. The algorithm uses resampling to handle the constraint. Two
cases are investigated: first the case where the step-size is constant, and
second the case where the step-size is adapted using cumulative step-size
adaptation. We exhibit for each case a Markov chain describing the behaviour of
the algorithm. Stability of the chain implies, by applying a law of large
numbers, either convergence or divergence of the algorithm. Divergence is the
desired behaviour. In the constant step-size case, we show stability of the
Markov chain and prove the divergence of the algorithm. In the cumulative
step-size adaptation case, we prove stability of the Markov chain in the
simplified case where the cumulation parameter equals 1, and discuss steps to
obtain similar results for the full (default) algorithm where the cumulation
parameter is smaller than 1. The stability of the Markov chain allows us to
deduce geometric divergence or convergence , depending on the dimension,
constraint angle, population size and damping parameter, at a rate that we
estimate. Our results complement previous studies where stability was assumed.Comment: Evolutionary Computation, Massachusetts Institute of Technology Press
(MIT Press): STM Titles, 201
Predicting cortical bone adaptation to axial loading in the mouse tibia
The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms
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