NECESSITY FROM CHANCE: SELF-ORGANIZED REPLICATION OF SYMMETRIC PATTERNS THROUGH SYMMETRIC RANDOM INTERACTIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 1185-1225
Author(s):  
ANDRÉ BARBÉ
Keyword(s):  
Random Walk ◽  
Fitness Function ◽  
Basic Algorithm ◽  
Random Interactions ◽  
Self Organized ◽  
Symmetric Configuration ◽  
Geometric Symmetry ◽  
Absorbing States ◽  
State Configuration ◽  
Symmetric Patterns

We present an algorithm, completely random in nature, that, without invoking a fitness function or purposeful design, produces symmetric replicas in a population of so-called cellicules. Cellicules consist of "cells" arranged in a structure with geometric symmetry S. Each cell has one of two possible states, thus defining a state-configuration pattern on a cellicule. The algorithm acts recurrently on a population of cellicules, possibly randomly initialized, through a random "copying interaction" between two randomly selected cellicules that first undergo a random reorientation in accordance with the symmetry S. The dynamics of the algorithm is analyzed in detail for several symmetries. This shows that it is a random walk with absorbing states which correspond to a population in which all cellicules have an identical S-symmetric configuration pattern. We discuss some aspects concerning the evolution of cellicule-populations under mixing and mutation, and some variations on the basic algorithm.

scholarly journals Achieving task allocation in swarm intelligence with bi-objective embodied evolution

2021 ◽  
Author(s):  
Qihao Shan ◽  
Sanaz Mostaghim
Keyword(s):  
Random Walk ◽  
Swarm Intelligence ◽  
Task Allocation ◽  
Fitness Function ◽  
Pareto Frontier ◽  
Weighted Sum ◽  
Objective Functions ◽  
Nsga Ii ◽  
Self Organized ◽  
Baseline Algorithm

AbstractIn this paper, we seek to achieve task allocation in swarm intelligence using an embodied evolutionary framework, which aims to generate divergent and specialized behaviors among a swarm of agents in an online and self-organized manner. In our considered scenario, specialization is encouraged through a bi-objective composite fitness function for the genomes, which is the weighted sum of a local and a global fitness function. The former depends only on the behavior of an agent itself, while the latter depends on the effectiveness of cooperation among all nearby agents. We have tested two existing variants of embodied evolution on this scenario and compared their performances against those of an individual random walk baseline algorithm. We have found out that those two embodied evolutionary algorithms have good performances at the extreme cases of weight configurations, but are not adequate when the two objective functions interact. We thus propose a novel bi-objective embodied evolutionary algorithm, which handles the aforementioned scenario by controlling the proportion of specialized behaviors via a dynamic reproductive isolation mechanism. Its performances are compared against those of other considered algorithms, as well as the theoretical Pareto frontier produced by NSGA-II.

Cooperative Genetic Multi-Objective Optimization Algorithm and Application

2012 ◽  
Vol 220-223 ◽  
pp. 2814-2817
Author(s):  
Li Gao ◽  
Dan Kong
Keyword(s):  
Optimization Algorithm ◽  
Pareto Front ◽  
Fitness Function ◽  
Multi Objective Optimization ◽  
Basic Algorithm ◽  
Multi Objective ◽  
Complicated System ◽  
Present Solution

It is very difficult to find out the best solution for some complicated system problems frequently appear. These problems are mostly of multi-objective. The present solution, however, is short of communication. Based on CO, one of MDO method, this paper gives a new simple kind of multi-objective framework, which will be suitable to multi-subject problems. It can not only organize each disciplinary effectively, but gives the inter-influence between disciplinaries by fitness function as well. Meanwhile, the perfect NSGAⅡ is used as be the basic algorithm, prematurity can be avoided and Pareto front with good distribution is obtained. Micro machined accelerometer example validates the correctness of the framework.

scholarly journals Research on MAS-Based Supply Chain Resilience and Its Self-Organized Criticality

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Liang Geng ◽  
Renbin Xiao ◽  
Xing Xu
Keyword(s):  
Supply Chain ◽  
Fitness Function ◽  
The Self ◽  
Self Organization ◽  
Neighborhood Structure ◽  
Supply Chain System ◽  
Supply Chain Resilience ◽  
Self Organized ◽  
Agglomeration Effect ◽  
Self Organized Criticality

Building resilient supply chain is an effective way to deal with uncertain risks. First, by analyzing the self-organization of supply chain, the supply chain resilience is described as a macroscopic property that generates from self-organizing behavior of each enterprise on the microlevel. Second, a MAS-based supply chain resilience model is established and its local fitness function, neighborhood structure, and interaction rules that are applicable to supply chain system are designed through viewing the enterprise as an agent. Finally, with the help of a case, we find that there is an agglomeration effect and a SOC characteristic in supply chain and the evolution of supply chain is controlled by parameters of MAS. Managers can control the supply chain within the resilient range and choose a good balance between interest and risk by controlling enterprises’ behavior.

scholarly journals A weighted random walk model, with application to a genetic algorithm

2007 ◽  
Vol 39 (2) ◽  
pp. 550-568
Author(s):  
C. Dombry
Keyword(s):  
Genetic Algorithms ◽  
Random Walk ◽  
Fitness Function ◽  
Random Walk Model ◽  
Growth Speed ◽  
Power Type ◽  
Symmetric Random Walk ◽  
Infinite Population ◽  
Deterministic Function ◽  
Selection Dynamics

We consider a weighted random walk model defined as follows. An n-step random walk on the integers with distribution Pn is weighted by giving the path S=(S0,…,Sn) a probability proportional to where the function f is the so-called fitness function. In the case of power-type fitness, we prove the convergence of the renormalized path to a deterministic function with exponential speed. This function is a solution to a variational problem. In the case of the simple symmetric random walk, explicit computations are done. Our result relies on large deviations techniques and Varadhan's integral lemma. We then study an application of this model to mutation-selection dynamics on the integers where a random walk operates the mutation. This dynamics is the infinite-population limit of that of mutation-selection genetic algorithms. We prove that the population grows to ∞ and make explicit its growth speed. This is a toy model for modelling the effect of stronger selection at ∞ for genetic algorithms taking place in a noncompact space.

A note on the inverse problem for reducible Markov chains

1977 ◽  
Vol 14 (03) ◽  
pp. 621-625
Author(s):  
A. O. Pittenger
Keyword(s):  
Inverse Problem ◽  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Physical Process ◽  
Raw Materials ◽  
Transition Probability ◽  
Linear Inequalities ◽  
System Of Linear Inequalities ◽  
Absorbing States

Suppose a physical process is modelled by a Markov chain with transition probability on S 1 ∪ S 2, S 1 denoting the transient states and S 2 a set of absorbing states. If v denotes the output distribution on S 2, the question arises as to what input distributions (of raw materials) on S 1 produce v. In this note we give an alternative to the formulation of Ray and Margo [2] and reduce the problem to one system of linear inequalities. An application to random walk is given and the equiprobability case examined in detail.

Complex Diameter Modulations in Silicon Carbide Nanowire Growth

2004 ◽  
Vol 832 ◽  
Author(s):  
Hideo Kohno ◽  
Hideto Yoshida
Keyword(s):  
Silicon Carbide ◽  
Random Walk ◽  
Power Spectrum ◽  
Power Law ◽  
Spectrum Analysis ◽  
Power Spectrum Analysis ◽  
Nanowire Growth ◽  
Lévy Flight ◽  
Fat Tail ◽  
Self Organized

ABSTRACTSilicon carbide nanowires were grown via a self-organized process. Some of the nanowires showed complex diameter fluctuations. The fluctuation was studied from the viewpoints of random walk and fractal. Power spectrum analysis of a fluctuation revealed that the fluctuation was not periodic and that the spectrum was colored. The distribution of increments had a fat tail which was not Gaussian but obeyed power law. Thus the diameter fluctuation was interpreted as a Lévy Flight. In addition, the fluctuation also showed multiaffine scaling.

Entropy of killed-resurrected stationary Markov chains

2021 ◽  
Vol 58 (1) ◽  
pp. 177-196
Author(s):  
Servet Martínez
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Probability Measure ◽  
Markov Chains ◽  
Stochastic Matrix ◽  
Hitting Times ◽  
Stationary Distributions ◽  
Natural Factors ◽  
Absorbing States ◽  
Stationary Representation

AbstractWe consider a strictly substochastic matrix or a stochastic matrix with absorbing states. By using quasi-stationary distributions we show that there is an associated canonical Markov chain that is built from the resurrected chain, the absorbing states, and the hitting times, together with a random walk on the absorbing states, which is necessary for achieving time stationarity. Based upon the 2-stringing representation of the resurrected chain, we supply a stationary representation of the killed and the absorbed chains. The entropies of these representations have a clear meaning when one identifies the probability measure of natural factors. The balance between the entropies of these representations and the entropy of the canonical chain serves to check the correctness of the whole construction.

scholarly journals Scaling exponents of step-reinforced random walks

2020 ◽  
Author(s):  
Jean Bertoin
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Variable ◽  
Scaling Exponent ◽  
Basic Algorithm ◽  
Real Random Variable ◽  
Scaling Exponents ◽  
Reinforced Random Walks ◽  
Speed Up ◽  
With Memory

Abstract Let $$X_1, X_2, \ldots $$ X 1 , X 2 , … be i.i.d. copies of some real random variable X. For any deterministic $$\varepsilon _2, \varepsilon _3, \ldots $$ ε 2 , ε 3 , … in $$\{0,1\}$$ { 0 , 1 } , a basic algorithm introduced by H.A. Simon yields a reinforced sequence $$\hat{X}_1, \hat{X}_2 , \ldots $$ X ^ 1 , X ^ 2 , … as follows. If $$\varepsilon _n=0$$ ε n = 0 , then $$ \hat{X}_n$$ X ^ n is a uniform random sample from $$\hat{X}_1, \ldots , \hat{X}_{n-1}$$ X ^ 1 , … , X ^ n - 1 ; otherwise $$ \hat{X}_n$$ X ^ n is a new independent copy of X. The purpose of this work is to compare the scaling exponent of the usual random walk $$S(n)=X_1+\cdots + X_n$$ S ( n ) = X 1 + ⋯ + X n with that of its step reinforced version $$\hat{S}(n)=\hat{X}_1+\cdots + \hat{X}_n$$ S ^ ( n ) = X ^ 1 + ⋯ + X ^ n . Depending on the tail of X and on asymptotic behavior of the sequence $$(\varepsilon _n)$$ ( ε n ) , we show that step reinforcement may speed up the walk, or at the contrary slow it down, or also does not affect the scaling exponent at all. Our motivation partly stems from the study of random walks with memory, notably the so-called elephant random walk and its variations.

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