Search

Differential evolution (DE) is one of the most efficient evolution algorithms (ES) for dealing with nonlinear, complicated and difficult global optimization problems. The main contribution of this paper can be summarized in three directions: Firstly, a novel crossover rate (CR) generation scheme based on the zscore value of fitness, named fcr, is introduced. For a minimization problem, the proposed CR generation strategy always assigns a smaller CR value to individual with smaller fitness value. Therefore, the parameters of individuals with better fitness are inherited by their offspring with high probability. In the second direction, the control parameters are adjusted by unused bimodal settings in which each parameter setting is selected according to the evolution status of individual. The third direction of our work is introducing the L1 norm distance as the weights for updating the mean value of crossover rate and scale factor. Theoretically, compared with L2 norm, L1-norm is more efficient to suppress outliers in the difference vector. These modifications are first integrated with the mutation strategy of JADE, then a modified version, named JADEfcr, is proposed. In addition, to improve the optimization ability further, another variant LJADEfcr by using a linear population reduction mechanism is considered. So as to confirm and examine the performance of JADEfcr and LJADEfcr, numerical experiments are conducted on 29 optimization problems defined by CEC2017 benchmark. For JADEfcr, its experimental results are made a comparison with twelve state-of-the-art algorithms. The comparative study demonstrates that in terms of robustness, stability and solution quality, JADEfcr are better and highly competitive with these well-known algorithms. For LJADEfcr, its results are compared with JADEfcr and other nine powerful algorithms including four recent algorithms and five top algorithms on CEC2017 competition. Experimental results indicate that LJADEfcr is superior and statistically competitive with these excellent algorithms in terms of robustness, stability and the quality of the obtained solutions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized discrete Lotka-Volterra equation and explore its connections with symmetric orthogonal polynomials, Hankel determinants and convergence acceleration algorithms. Firstly, we extend the fully discrete Lotka-Volterra equation to a generalized one with a sequence of given constants { u 0 (n) } and derive its solution in terms of Hankel determinants. Then, it is shown that the discrete equation of motion is transformed into a discrete Riccati system for a discrete Stieltjes function, hence leading to a complete linearization. Besides, we obtain its Lax pair in terms of symmetric orthogonal polynomials by generalizing the Christoffel transformation for the symmetric orthogonal polynomials. Moreover, a generalization of the famous Wynn's ε-algorithm is also derived via a Miura transformation to the generalized discrete Lotka-Volterra equation. Finally, the numerical effects of this generalized ε-algorithm are discussed by applying to some linearly, logarithmically convergent sequences and some divergent series. [ABSTRACT FROM AUTHOR]

Firstly, a new sequence transformation that can be expressed in terms of a ratio of two pfaffians is derived based on a special kernel. It can be regarded as a direct generalization of Aitken's Δ2 process from the point of view of pfaffians and then the corresponding convergence acceleration algorithm is constructed. Numerical examples with applications of this algorithm are also presented. Secondly, we find a way to generalize the Shanks transformation via pfaffians so that a larger class of new sequence transformations are derived. The corresponding recursive algorithms are also proposed. [ABSTRACT FROM AUTHOR]

We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorithm and of Osada's generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series. [ABSTRACT FROM AUTHOR]

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algebraic method to construct non-autonomous discrete integrable systems. The method starts from constructing generalizations of convergence acceleration algorithms related to discrete integrable systems. Then the non-autonomous version of the corresponding integrable systems are derived. The molecule solutions of the systems are also obtained. As an example of the application of the method, we propose a generalization of the multistep ϵ-algorithm, and then derive a non-autonomous discrete extended Lotka–Volterra equation. Since the convergence acceleration algorithm from the lattice Boussinesq equation is just a particular case of the multistep ϵ-algorithm, we have therefore arrived at a generalization of this algorithm. Finally, numerical experiments on the new algorithm are presented. [ABSTRACT FROM PUBLISHER]

The molecule solution of an extended discrete Lotka–Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability. Some numerical examples are also presented. [ABSTRACT FROM AUTHOR]

In this paper, the confluent form of the multistep ɛ-algorithm is proposed. The molecule solution of this system is derived by using determinantal identities. A new continuous prediction algorithm based on this confluent form is constructed. It also shows that this algorithm is a special case of the extended Lotka-Volterra system. [ABSTRACT FROM AUTHOR]

This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura ( Inverse Problems 2009; :015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A q-difference lattice Boussinesq equation and its confluent form are proposed. With the help of determinant identity, their molecule solutions are constructed. It is shown that the q-difference lattice Boussinesq equation can be used as a numerical convergence acceleration algorithm to compute the approximation limt → ∞f(t). Numerical examples with the application of this algorithm are presented. [ABSTRACT FROM AUTHOR]

In earthquake monitoring, an important aspect of the operational effect of earthquake intensity rapid reporting and earthquake early warning networks depends on the density and performance of the deployed seismic sensors. To improve the resolution of seismic sensors as much as possible while keeping costs low, in this article the use of multiple low-cost and low-resolution digital MEMS accelerometers is proposed to increase the resolution through the correlation average method. In addition, a cost-effective MEMS seismic sensor is developed. With ARM and Linux embedded computer technology, this instrument can cyclically store the continuous collected data on a built-in large-capacity SD card for approximately 12 months. With its real-time seismic data processing algorithm, this instrument is able to automatically identify seismic events and calculate ground motion parameters. Moreover, the instrument is easy to install in a variety of ground or building conditions. The results show that the RMS noise of the instrument is reduced from 0.096 cm/s2 with a single MEMS accelerometer to 0.034 cm/s2 in a bandwidth of 0.1–20 Hz by using the correlation average method of eight low-cost MEMS accelerometers. The dynamic range reaches more than 90 dB, the amplitude–frequency response of its input and output within −3 dB is DC −80 Hz, and the linearity is better than 0.47%. In the records from our instrument, earthquakes with magnitudes between M2.2 and M5.1 and distances from the epicenter shorter than 200 km have a relatively high SNR, and are more visible than they were prior to the joint averaging. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the related generalization of the rs-algorithm is equivalent to a generalized qd-algorithm. Applications of the generalization of the G-transformation to the computation of infinite integrals are also given. [ABSTRACT FROM AUTHOR]

Deep Reinforcement Learning (deep RL) has been successfully applied to solve various decision-making problems in recent years. However, the observations in many real-world tasks are often high dimensional and include much task-irrelevant information, limiting the applications of RL algorithms. To tackle this problem, we propose LCER, a representation learning method that aims to provide RL algorithms with compact and sufficient descriptions of the original observations. Specifically, LCER trains representations to retain the controllable elements of the environment, which can reflect the action-related environment dynamics and thus are likely to be task-relevant. We demonstrate the strength of LCER on the DMControl Suite, proving that it can achieve state-of-the-art performance. LCER enables the pixel-based SAC to outperform state-based SAC on the DMControl 100 K benchmark, showing that the obtained representations can match the oracle descriptions (i. e. the physical states) of the environment. We also carry out experiments to show that LCER can efficiently filter out various distractions, especially when those distractions are not controllable. [ABSTRACT FROM AUTHOR]