Related papers: Evolutionary Design of Numerical Methods: Generati…
Existing multi-strategy adaptive differential evolution (DE) commonly involves trials of multiple strategies and then rewards better-performing ones with more resources. However, the trials of an exploitative or explorative strategy may…
In recent years, Evolutionary Strategies were actively explored in robotic tasks for policy search as they provide a simpler alternative to reinforcement learning algorithms. However, this class of algorithms is often claimed to be…
This paper explores the critical role of differentiation approaches for data-driven differential equation discovery. Accurate derivatives of the input data are essential for reliable algorithmic operation, particularly in real-world…
The logistic equation has been extensively used to model biological phenomena across a variety of disciplines and has provided valuable insight into how our universe operates. Incorporating time-dependent parameters into the logistic…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set…
Evolutionary Computation is a group of biologically inspired algorithms used to solve complex optimisation problems. It can be split into Evolutionary Algorithms, which take inspiration from genetic inheritance, and Swarm Intelligence…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
In this paper we propose a novel method for learning how algorithms perform. Classically, algorithms are compared on a finite number of existing (or newly simulated) benchmark datasets based on some fixed metrics. The algorithm(s) with the…
Differential evolution (DE) is a simple but powerful evolutionary algorithm, which has been widely and successfully used in various areas. In this paper, an event-triggered impulsive control scheme (ETI) is introduced to improve the…
We study the application of the generalized convolution quadrature (gCQ) based on Runge--Kutta methods to approximate the solution of an important class of sectorial problems. The gCQ generalizes Lubich's original convolution quadrature…
Classification is one of the most studied tasks in data mining and machine learning areas and many works in the literature have been presented to solve classification problems for multiple fields of knowledge such as medicine, biology,…
A new class of third order Runge-Kutta methods for stochastic differential equations with additive noise is introduced. In contrast to Platen's method, which to the knowledge of the author has been up to now the only known third order…
Differential evolution(DE) is a conventional algorithm with fast convergence speed. However, DE may be trapped in local optimal solution easily. Many researchers devote themselves to improving DE. In our previously work, whale swarm…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However,…
In this paper a new Runge-Kutta type scheme is introduced for nonlinear stochastic partial differential equations (SPDEs) with multiplicative trace class noise. The proposed scheme converges with respect to the computational effort with a…
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differential equations have invariants, and numerical schemes for…
Differential evolution is one of the most prestigious population-based stochastic optimization algorithm for black-box problems. The performance of a differential evolution algorithm depends highly on its mutation and crossover strategy and…