scholarly journals A New Method for Lower Bounds on the Running Time of Evolutionary Algorithms

2013 ◽  
Vol 17 (3) ◽  
pp. 418-435 ◽  
Author(s):  
Dirk Sudholt
2019 ◽  
Vol 35 (14) ◽  
pp. i417-i426 ◽  
Author(s):  
Erin K Molloy ◽  
Tandy Warnow

Abstract Motivation At RECOMB-CG 2018, we presented NJMerge and showed that it could be used within a divide-and-conquer framework to scale computationally intensive methods for species tree estimation to larger datasets. However, NJMerge has two significant limitations: it can fail to return a tree and, when used within the proposed divide-and-conquer framework, has O(n5) running time for datasets with n species. Results Here we present a new method called ‘TreeMerge’ that improves on NJMerge in two ways: it is guaranteed to return a tree and it has dramatically faster running time within the same divide-and-conquer framework—only O(n2) time. We use a simulation study to evaluate TreeMerge in the context of multi-locus species tree estimation with two leading methods, ASTRAL-III and RAxML. We find that the divide-and-conquer framework using TreeMerge has a minor impact on species tree accuracy, dramatically reduces running time, and enables both ASTRAL-III and RAxML to complete on datasets (that they would otherwise fail on), when given 64 GB of memory and 48 h maximum running time. Thus, TreeMerge is a step toward a larger vision of enabling researchers with limited computational resources to perform large-scale species tree estimation, which we call Phylogenomics for All. Availability and implementation TreeMerge is publicly available on Github (http://github.com/ekmolloy/treemerge). Supplementary information Supplementary data are available at Bioinformatics online.


Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Ke Tang

Evolutionary algorithms (EAs) have been widely applied to solve multi-objective optimization problems. In contrast to great practical successes, their theoretical foundations are much less developed, even for the essential theoretical aspect, i.e., running time analysis. In this paper, we propose a general approach to estimating upper bounds on the expected running time of multi-objective EAs (MOEAs), and then apply it to diverse situations, including bi-objective and many-objective optimization as well as exact and approximate analysis. For some known asymptotic bounds, our analysis not only provides their leading constants, but also improves them asymptotically. Moreover, our results provide some theoretical justification for the good empirical performance of MOEAs in solving multi-objective combinatorial problems.


Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.


2004 ◽  
Vol 220 ◽  
pp. 329-330
Author(s):  
Anne Mathieu

I will present a new method of dynamical modeling of stellar systems based on evolutionary algorithms. the technique will be illustrated with an application to the problem of recovering the gravitational potential of a thin galactic disc from kinematic observables in a non-parametric way.


2004 ◽  
Vol 339 (2) ◽  
pp. 91-94 ◽  
Author(s):  
Stephen S. Gelbart ◽  
Erez M. Lapid ◽  
Peter Sarnak
Keyword(s):  

2019 ◽  
Vol 27 (3) ◽  
pp. 167-175
Author(s):  
Vyacheslav L. Girko

Abstract The lower bounds for the minimal singular eigenvalue of the matrix whose entries have zero means and bounded variances are obtained. The new method is based on the G-method of perpendiculars and the RESPECT method.


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