1,601 research outputs found
Lyapunov design of a simple step-size adaptation strategy based on success
A simple success-based step-size adaptation rule for singleparent Evolution Strategies is formulated, and the setting of the corresponding parameters is considered. Theoretical convergence on the class of strictly unimodal functions of one variable that are symmetric around the optimum is investigated using a stochastic Lyapunov function method developed by Semenov and Terkel [5] in the context of martingale theory. General expressions for the conditional expectations of the next values of step size and distance to the optimum under (1 +, λ)-selection are analytically derived, and an appropriate Lyapunov function is constructed. Convergence rate upper bounds, as well as adaptation parameter values, are obtained through numerical optimization for increasing values of λ. By selecting the number of offspring that minimizes the bound on the convergence rate with respect to the number of function evaluations, all strategy parameter values result from the analysis
Convergence of the Continuous Time Trajectories of Isotropic Evolution Strategies on Monotonic C^2-composite Functions
The Information-Geometric Optimization (IGO) has been introduced as a unified
framework for stochastic search algorithms. Given a parametrized family of
probability distributions on the search space, the IGO turns an arbitrary
optimization problem on the search space into an optimization problem on the
parameter space of the probability distribution family and defines a natural
gradient ascent on this space. From the natural gradients defined over the
entire parameter space we obtain continuous time trajectories which are the
solutions of an ordinary differential equation (ODE). Via discretization, the
IGO naturally defines an iterated gradient ascent algorithm. Depending on the
chosen distribution family, the IGO recovers several known algorithms such as
the pure rank-\mu update CMA-ES. Consequently, the continuous time
IGO-trajectory can be viewed as an idealization of the original algorithm. In
this paper we study the continuous time trajectories of the IGO given the
family of isotropic Gaussian distributions. These trajectories are a
deterministic continuous time model of the underlying evolution strategy in the
limit for population size to infinity and change rates to zero. On functions
that are the composite of a monotone and a convex-quadratic function, we prove
the global convergence of the solution of the ODE towards the global optimum.
We extend this result to composites of monotone and twice continuously
differentiable functions and prove local convergence towards local optima.Comment: PPSN - 12th International Conference on Parallel Problem Solving from
Nature - 2012 (2012
Markov Chain Analysis of Evolution Strategies on a Linear Constraint Optimization Problem
This paper analyses a -Evolution Strategy, a randomised
comparison-based adaptive search algorithm, on a simple constraint optimisation
problem. The algorithm uses resampling to handle the constraint and optimizes a
linear function with a linear 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 path length control. We exhibit for each case a Markov chain
whose stability analysis would allow us to deduce the divergence of the
algorithm depending on its internal parameters. We show divergence at a
constant rate when the step-size is constant. We sketch that with step-size
adaptation geometric divergence takes place. Our results complement previous
studies where stability was assumed.Comment: Amir Hussain; Zhigang Zeng; Nian Zhang. IEEE Congress on Evolutionary
Computation, Jul 2014, Beijing, Chin
進化的及び樹状突起のメカニズムを考慮したソフトコンピューティング技術の提案
富山大学・富理工博甲第117号・宋振宇・2017/03/23富山大学201
A logistic map approach to economic cycles I. The best adapted companies
A birth-death lattice gas model about the influence of an environment on the
fitness and concentration evolution of economic entities is analytically
examined. The model can be mapped onto a high order logistic map. The control
parameter is a (scalar) "business plan". Conditions are searched for growth and
decay processes, stable states, upper and lower bounds, bifurcations, periodic
and chaotic solutions. The evolution equation of the economic population for
the best fitted companies indicates "microscopic conditions" for cycling. The
evolution of a dynamic exponent is shown as a function of the business plan
parameters.Comment: 10 pages, 5 postscript figure
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