Related papers: A Theoretical Framework of Approximation Error Ana…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The paper presents a solution for the problem of choosing a method for analytical determining of weight factors for a genetic algorithm additive fitness function. This algorithm is the basis for an evolutionary process, which forms a stable…
The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static…
The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
The average convergence rate (ACR) measures how fast the approximation error of an evolutionary algorithm converges to zero per generation. It is defined as the geometric average of the reduction rate of the approximation error over…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…
We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…
Evolutionary algorithms (EAs) are heuristic algorithms inspired by natural evolution. They are often used to obtain satisficing solutions in practice. In this paper, we investigate a largely underexplored issue: the approximation…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
Known as two cornerstones of problem solving by search, exploitation and exploration are extensively discussed for implementation and application of evolutionary algorithms (EAs). However, only a few researches focus on evaluation and…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
The problem of automatic software generation is known as Machine Programming. In this work, we propose a framework based on genetic algorithms to solve this problem. Although genetic algorithms have been used successfully for many problems,…
In Evolutionary Robotics a population of solutions is evolved to optimize robots that solve a given task. However, in traditional Evolutionary Algorithms, the population of solutions tends to converge to local optima when the problem is…
A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is…