scholarly journals On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism

2019 ◽  
Vol 27 (3) ◽  
pp. 403-433 ◽  
Author(s):  
Edgar Covantes Osuna ◽  
Dirk Sudholt
Keyword(s):  
Distance Function ◽  
Runtime Analysis ◽  
Single Individual ◽  
Powerful Method ◽  
Exponential Time ◽  
Expected Time ◽  
Experimental Approaches ◽  
Phenotypic Distance ◽  
Niching Method ◽  
Theoretical Results

Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis has been focused on experimental approaches that have shown that clearing is a powerful diversity-preserving mechanism. Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic distance function always succeeds in optimising all functions of unitation for small niches in polynomial time, while a genotypic distance function requires exponential time. Finally, we prove that with phenotypic and genotypic distances, clearing is able to find both optima for [Formula: see text] and several general classes of bimodal functions in polynomial expected time. We use empirical analysis to highlight some of the characteristics that makes it a useful mechanism and to support the theoretical results.

scholarly journals Runtime Analysis of Restricted Tournament Selection for Bimodal Optimisation

2021 ◽  
pp. 1-26
Author(s):  
Edgar Covantes Osuna ◽  
Dirk Sudholt
Keyword(s):  
Distance Measure ◽  
Experimental Studies ◽  
Window Size ◽  
Population Diversity ◽  
Single Individual ◽  
Niching Methods ◽  
Size Population ◽  
Tournament Selection ◽  
Theoretical Results ◽  
Shed Light

Abstract Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel and to reduce the effect of genetic drift. We present the first rigorous runtime analyses of restricted tournament selection (RTS), embedded in a (μ+1) EA, and analyse its effectiveness at finding both optima of the bimodal function TwoMax. In RTS, an offspring competes against the closest individual, with respect to some distance measure, amongst w (window size) population members (chosen uniformly at random with replacement), to encourage competition within the same niche. We prove that RTS finds both optima on TwoMax efficiently if the window size w is large enough. However, if w is too small, RTS fails to find both optima even in exponential time, with high probability. We further consider a variant of RTS selecting individuals for the tournament without replacement. It yields a more diverse tournament and is more effective at preventing one niche from taking over the other. However, this comes at the expense of a slower progress towards optima when a niche collapses to a single individual. Our theoretical results are accompanied by experimental studies that shed light on parameters not covered by the theoretical results and support a conjectured lower runtime bound.

scholarly journals Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

scholarly journals On expected durations of birth–death processes, with applications to branching processes and SIS epidemics

2016 ◽  
Vol 53 (1) ◽  
pp. 203-215 ◽  
Author(s):  
Frank Ball ◽  
Tom Britton ◽  
Peter Neal
Keyword(s):  
Asymptotic Expression ◽  
Branching Processes ◽  
Random Variable ◽  
Death Process ◽  
Single Individual ◽  
Expected Time ◽  
Time To Extinction ◽  
Number Of Individuals ◽  
Sis Epidemic ◽  
Birth Death

Abstract We study continuous-time birth–death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size) n is α(n). We focus on two important examples, namely α(n) = λ n being a branching process, and α(n) = λn(N - n) / N which corresponds to an SIS (susceptible → infective → susceptible) epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i.e. in state 1. Let T, An, C, and S denote the (random) time to extinction, the total time spent in state n, the total number of individuals ever alive, and the sum of the lifetimes of all individuals in the birth–death process, respectively. We give expressions for the expectation of all these quantities and show that these expectations are insensitive to the distribution of Q. We also derive an asymptotic expression for the expected time to extinction of the SIS epidemic, but now starting at the endemic state, which is not independent of the distribution of Q. The results are also applied to the household SIS epidemic, showing that, in contrast to the household SIR (susceptible → infective → recovered) epidemic, its threshold parameter R* is insensitive to the distribution of Q.

On the Effect of Populations in Evolutionary Multi-Objective Optimisation

2010 ◽  
Vol 18 (3) ◽  
pp. 335-356 ◽  
Author(s):  
Oliver Giel ◽  
Per Kristian Lehre
Keyword(s):  
Problem Solving ◽  
Evolutionary Algorithms ◽  
Open Problem ◽  
Population Based ◽  
Runtime Analysis ◽  
Single Individual ◽  
Multi Objective ◽  
Important Open Problem ◽  
Population Based Algorithm

Multi-objective evolutionary algorithms (MOEAs) have become increasingly popular as multi-objective problem solving techniques. An important open problem is to understand the role of populations in MOEAs. We present two simple bi-objective problems which emphasise when populations are needed. Rigorous runtime analysis points out an exponential runtime gap between the population-based algorithm simple evolutionary multi-objective optimiser (SEMO) and several single individual-based algorithms on this problem. This means that among the algorithms considered, only the population-based MOEA is successful and all other algorithms fail.

scholarly journals Optimization of Wi-Fi Direct average time to discovery: A Global Channel Randomization Approach

2021 ◽  
Author(s):  
Remy Maxime Mbala ◽  
David Jaures Fotsa-Mbogne ◽  
Jean Michel NLONG ◽  
Olivier Menoukeu-Pamen ◽  
Jean Robert Kala-Kamdjoug
Keyword(s):  
Experimental Tests ◽  
Poisson Processes ◽  
Rapid Evaluation ◽  
Sufficient Condition ◽  
Performance Study ◽  
Comparative Performance ◽  
Expected Time ◽  
Reduction Strategies ◽  
Direct Average ◽  
Theoretical Results

Abstract The main objective of this work is to propose concrete time reduction strategies for discovery of Wi-Fi Direct in Android. To achieve our goals, we perform a fairly general mathematical modeling of the discovery of devices using Poisson processes. Subsequently, under asymptotic invariance hypotheses of certain distributions, we derive formulas for the expected time to discovery. We provide sufficient condition for fast convergence to an invariant distribution and determine key decision parameters (jumps intensities) that minimize the average time to discovery. We also propose a predictive model for rapid evaluation of these optimal discovery parameters. Experimental tests in an emulator are also conducted to validate the theoretical results obtained. A comparative performance study is done with some optimization approaches from literature. Compared with existing methods, the improvement of the average time discovery we obtained with the proposed method is above 98.34%.

COMPUTING ROUNDNESS IS EASY IF THE SET IS ALMOST ROUND

2002 ◽  
Vol 12 (03) ◽  
pp. 229-248 ◽  
Author(s):  
OLIVIER DEVILLERS ◽  
PEDRO A. RAMOS
Keyword(s):  
Local Minimum ◽  
Linear Time ◽  
Slight Modification ◽  
Optimization Approach ◽  
Local Minima ◽  
Partial Explanation ◽  
Worst Case ◽  
Expected Time ◽  
Set Of Points ◽  
Theoretical Results

In this paper we address the problem of computing the thinnest annulus containing a set of points S ⊂ Rd. For d = 2, we show that the problem can be solved in O(n) expected time for a fairly general family of almost round sets, by using a slight modification of Sharir and Welzl's algorithm for solving LP-type problems. We also show that, for points in convex position, the problem can be solved in (O(n) deterministic time using linear programming. For d = 2 and d = 3, we propose a discrete local optimization approach. Despite the extreme simplicity and worst case O(nd+1) complexity of the algorithm, we give empirical evidence that the algorithm performs very well (close to linear time) if the input is almost round. We also present some theoretical results that give a partial explanation of this behavior: although the number of local minima may be quadratic (already for d = 2), almost round configurations of points having more than one local minimum are very unlikely to be encountered in practice.

scholarly journals High load capacity spur gears with conchoidal path of contact

2021 ◽  
Vol 22 ◽  
pp. 47
Author(s):  
Pavlo Tkach ◽  
Pavlo Nosko ◽  
Oleksandr Bashta ◽  
Yurii Tsybrii ◽  
Oleksii Nosko
Keyword(s):  
Energy Efficiency ◽  
Load Capacity ◽  
Active Power ◽  
High Load ◽  
Spur Gears ◽  
Gear Pair ◽  
Test Rig ◽  
Experimental Approaches ◽  
High Load Capacity ◽  
Theoretical Results

The present study is devoted to investigation of spur gears with a conchoidal path of contact and a convex-convex contact between teeth. The load capacity and energy efficiency were evaluated using both theoretical and experimental approaches. The theoretical analysis showed that the conchoidal gear pairs are 5–21% stronger in terms of contact stress and have similar energy efficiency as compared to the involute gear pairs of the same configuration. Experiments were conducted on a gear test rig. Its energy efficiency was determined by measuring the active power of the motor driving the pinion shaft and controlling the torque at the gear shaft. The load capacity of the tested gear pair was estimated by analysing changes in the energy efficiency. It was found that the conchoidal gear pair has more than 20% higher load capacity and slightly higher energy efficiency, which agrees well with the mentioned theoretical results. Thereby, the study concludes a substantially higher load capacity of the conchoidal gears compared to the traditional involute ones.

scholarly journals Near-threshold Rotational and Vibrational Excitation of H2 by Electron Impact: Theory and Experiment

1987 ◽  
Vol 40 (3) ◽  
pp. 239 ◽  
Author(s):  
MA Morrison ◽  
RW Crompton ◽  
Bidhan C Saha ◽  
ZLj Petrovic
Keyword(s):  
Cross Sections ◽  
Vibrational Excitation ◽  
Rotational Excitation ◽  
Threshold Behaviour ◽  
Impact Theory ◽  
Significant Difference ◽  
Excitation Cross Sections ◽  
Experimental Approaches ◽  
Free Interaction ◽  
Theoretical Results

A joint experimental-theoretical attack on low-energy e-H2 scattering is described. The cross sections calculated from a highly converged numerical solution of the nonrelativistic Schrodinger equation, using a parameter-free interaction potential, are first compared with results from swarm experiments, and are later used to improve the accuracy of the swarm analysis at energies above the first vibrational threshold. To provide further perspective, the theoretical results are compared with a variety of other experimental data. The theoretical results for the momentum-transfer and rotational-excitation cross sections are in excellent agreement with the results from swarm experiments, but there is an unresolved and significant difference in the threshold behaviour of the vibrational-excitation cross sections. Both the theoretical and experimental approaches are subjected to close scrutiny in an attempt to uncover possible sources of error that could explain this difference. The failure to locate likely sources points to the need for further independent theoretical and experimental work to resolve a problem that has serious implications.

Learned Placebo Effects in the Immune System

2014 ◽  
Vol 222 (3) ◽  
pp. 148-153 ◽  
Author(s):  
Sabine Vits ◽  
Manfred Schedlowski
Keyword(s):  
Nervous System ◽  
Immune System ◽  
Associative Learning ◽  
Placebo Response ◽  
Immunosuppressive Drug ◽  
Immune Functions ◽  
Placebo Effects ◽  
New Therapeutic Approaches ◽  
Biological Variables ◽  
Experimental Approaches

Associative learning processes are one of the major neuropsychological mechanisms steering the placebo response in different physiological systems and end organ functions. Learned placebo effects on immune functions are based on the bidirectional communication between the central nervous system (CNS) and the peripheral immune system. Based on this “hardware,” experimental evidence in animals and humans showed that humoral and cellular immune functions can be affected by behavioral conditioning processes. We will first highlight and summarize data documenting the variety of experimental approaches conditioning protocols employed, affecting different immunological functions by associative learning. Taking a well-established paradigm employing a conditioned taste aversion model in rats with the immunosuppressive drug cyclosporine A (CsA) as an unconditioned stimulus (US) as an example, we will then summarize the efferent and afferent communication pathways as well as central processes activated during a learned immunosuppression. In addition, the potential clinical relevance of learned placebo effects on the outcome of immune-related diseases has been demonstrated in a number of different clinical conditions in rodents. More importantly, the learned immunosuppression is not restricted to experimental animals but can be also induced in humans. These data so far show that (i) behavioral conditioned immunosuppression is not limited to a single event but can be reproduced over time, (ii) immunosuppression cannot be induced by mere expectation, (iii) psychological and biological variables can be identified as predictors for this learned immunosuppression. Together with experimental approaches employing a placebo-controlled dose reduction these data provide a basis for new therapeutic approaches to the treatment of diseases where a suppression of immune functions is required via modulation of nervous system-immune system communication by learned placebo effects.

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