Adaptive Ranking Based Constraint Handling for Explicitly Constrained Black-Box Optimization

A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.Comment: 9 page

Magnon scattering processes and low temperature resistivity in CMR manganites

Low temperature resistivity of CMR manganites is investigated. At the ground state, conduction electrons are perfectly spin polarized, which is called half-metallic. From one-magnon scattering processes, it is discussed that the resistivity of a half metal as a function of temperature scales as rho(T) - rho(0) propto T^3. We take (Nd,Tb,Sr)MnO_3 as an example to compare theory and experiments. The result is in a good agreement.Comment: To appear in Proc. ICM 200

Distributional behavior of time averages of non-L1L^1 observables in one-dimensional intermittent maps with infinite invariant measures

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of $L^1(m)$ functions, i.e., integrable functions with respect to an infinite invariant measure. The other is characterized by the generalized arc-sine distribution for time averages of non-$L^1(m)$ functions. Here, we provide another distributional behavior of time averages of non-$L^1(m)$ functions in one-dimensional intermittent maps where each has an indifferent fixed point and an infinite invariant measure. Observation functions considered here are non-$L^1(m)$ functions which vanish at the indifferent fixed point. We call this class of observation functions weak non-$L^1(m)$ function. Our main result represents a first step toward a third distributional limit theorem, i.e., a distributional limit theorem for this class of observables, in infinite ergodic theory. To prove our proposition, we propose a stochastic process induced by a renewal process to mimic a Birkoff sum of a weak non-$L^1(m)$ function in the one-dimensional intermittent maps.Comment: 24 pages, 6 figure

Kinetic effects in strong Langmuir turbulence

Kinetic effects with regard to a one dimensional Langmuir soliton-like pulse are investigated. Though thus far mainly transit-time accelerations have been investigated regarding strong Langmuir turbulence, it is found that ponderomotive reflections (generalized nonlinear Landau damping) may play important roles also. The former may diffuse fast electrons up to relativistic energies, while the latter reflects slow electrons as well as ions that have speeds comparable with the group velocity of the pulse, and tend to form flat-top electron distributions at and around the quasi-soliton.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

On the definition of equilibrium and non-equilibrium states in dynamical systems

We propose a definition of equilibrium and non-equilibrium states in dynamical systems on the basis of the time average. We show numerically that there exists a non-equilibrium non-stationary state in the coupled modified Bernoulli map lattice.Comment: 4 pages, 2 figure