相关论文: Lower Bounds for Non-Elitist Evolutionary Algorith…

One of the key difficulties in using estimation-of-distribution algorithms is choosing the population size(s) appropriately: Too small values lead to genetic drift, which can cause enormous difficulties. In the regime with no genetic drift,…

In this paper, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness…

With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is…

We propose and analyze a self-adaptive version of the $(1,\lambda)$ evolutionary algorithm in which the current mutation rate is part of the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark…

The paper is devoted to upper bounds on run-time of Non-Elitist Genetic Algorithms until some target subset of solutions is visited for the first time. In particular, we consider the sets of optimal solutions and the sets of local optima as…

We study stochastic nonconvex optimization under heavy-tailed noise. In this setting, the stochastic gradients only have bounded $p$-th central moment ($p$-BCM) for some $p \in (1,2]$. Building on the foundational work of Arjevani et al.…

The fitness level method is a widely used technique for estimating the mean hitting time of elitist evolutionary algorithms on level-based fitness functions. However, this paper identifies its main limitation: the linear lower bound derived…

We consider the question of the stability of evolutionary algorithms to gradual changes, or drift, in the target concept. We define an algorithm to be resistant to drift if, for some inverse polynomial drift rate in the target function, it…

In this article a tool for the analysis of population-based EAs is used to derive asymptotic upper bounds on the optimization time of the algorithm solving Royal Roads problem, a test function with plateaus of fitness. In addition to this,…

Runtime analysis, as a branch of the theory of AI, studies how the number of iterations algorithms take before finding a solution (its runtime) depends on the design of the algorithm and the problem structure. Drift analysis is a…

Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes. In this work, we argue that stochastic domination is a notion that should be used more frequently in this…

We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p_n = c/n finds the optimum of a linear objective function over bit strings of length n in expected time Theta(n log n). Previously, this was only…

One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed…

We consider the expected runtime of non-elitist evolutionary algorithms (EAs), when they are applied to a family of fitness functions with a plateau of second-best fitness in a Hamming ball of radius r around a unique global optimum. On one…

We give a lower bound on the growth of a subshift based on a simple condition on the set of forbidden patterns defining that subshift. Aubrun et Al. showed a similar result based on the Lov\'asz Local Lemma for subshift over any countable…

This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible…

The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…

It may seem very intuitive that for the maximization of the OneMax problem $\OM(x):=\sum_{i=1}^n{x_i}$ the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator…

A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is…

This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations…