Analysis of Selection Algorithms: A Markov Chain Approach

1996 ◽  
Vol 4 (2) ◽  
pp. 133-167 ◽  
Author(s):  
Uday Kumar Chakraborty ◽  
Kalyanmoy Deb ◽  
Mandira Chakraborty
Keyword(s):  
Genetic Algorithms ◽  
Markov Chain ◽  
Performance Measures ◽  
Finite Population ◽  
Selection Strategy ◽  
Markov Chain Approach ◽  
Population Sizes ◽  
Tournament Selection ◽  
Selection Algorithms ◽  
Compare And Contrast

A Markov chain framework is developed for analyzing a wide variety of selection techniques used in genetic algorithms (GAs) and evolution strategies (ESs). Specifically, we consider linear ranking selection, probabilistic binary tournament selection, deterministic s-ary (s = 3,4, …) tournament selection, fitness-proportionate selection, selection in Whitley's GENITOR, selection in (μ, λ)-ES, selection in (μ + λ)-ES, (μ, λ)-linear ranking selection in GAs, (μ + λ)-linear ranking selection in GAs, and selection in Eshelman's CHC algorithm. The analysis enables us to compare and contrast the various selection algorithms with respect to several performance measures based on the probability of takeover. Our analysis is exact—we do not make any assumptions or approximations. Finite population sizes are considered. Our approach is perfectly general, and following the methods of this paper, it is possible to analyze any selection strategy in evolutionary algorithms.

Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

2019 ◽  
pp. 13-31
Author(s):  
Khalid Alnowibet ◽  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Performance Measures ◽  
Threshold Level ◽  
System Size ◽  
State System ◽  
Markov Chain Approach ◽  
Optimal Value ◽  
Two Phases ◽  
Random Breakdowns

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. The authors assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

2018 ◽  
pp. 1570-1583
Author(s):  
Khalid Alnowibet ◽  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Performance Measures ◽  
Threshold Level ◽  
System Size ◽  
State System ◽  
Markov Chain Approach ◽  
Optimal Value ◽  
Two Phases ◽  
Random Breakdowns

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. We assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

scholarly journals Recombination Can Evolve in Large Finite Populations Given Selection on Sufficient Loci

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2249-2258 ◽  
Author(s):  
Mark M Iles ◽  
Kevin Walters ◽  
Chris Cannings
Keyword(s):  
Experimental Evidence ◽  
Genetic Drift ◽  
Finite Population ◽  
Selective Advantage ◽  
Indirect Selection ◽  
Small Populations ◽  
Finite Populations ◽  
Population Sizes ◽  
Population Recombination

AbstractIt is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.

Estimation of Interregional Trade Flows: A Markov Chain Approach

1986 ◽  
Vol 18 (1) ◽  
pp. 123-132 ◽  
Author(s):  
I Weksler ◽  
D Freeman ◽  
G Alperovich
Keyword(s):  
Markov Chain ◽  
Trade Flows ◽  
Interregional Trade ◽  
Markov Chain Approach

A New Method for Modeling the Behavior of Finite Population Evolutionary Algorithms

2010 ◽  
Vol 18 (3) ◽  
pp. 451-489 ◽  
Author(s):  
Tatsuya Motoki
Keyword(s):  
Markov Chain ◽  
Evolutionary Algorithms ◽  
Finite Population ◽  
Fitness Landscape ◽  
Markov Chain Model ◽  
Search Space ◽  
Chain Model ◽  
Transition Matrices ◽  
Memory Space ◽  
Exact Model

As practitioners we are interested in the likelihood of the population containing a copy of the optimum. The dynamic systems approach, however, does not help us to calculate that quantity. Markov chain analysis can be used in principle to calculate the quantity. However, since the associated transition matrices are enormous even for modest problems, it follows that in practice these calculations are usually computationally infeasible. Therefore, some improvements on this situation are desirable. In this paper, we present a method for modeling the behavior of finite population evolutionary algorithms (EAs), and show that if the population size is greater than 1 and much less than the cardinality of the search space, the resulting exact model requires considerably less memory space for theoretically running the stochastic search process of the original EA than the Nix and Vose-style Markov chain model. We also present some approximate models that use still less memory space than the exact model. Furthermore, based on our models, we examine the selection pressure by fitness-proportionate selection, and observe that on average over all population trajectories, there is no such strong bias toward selecting the higher fitness individuals as the fitness landscape suggests.

Change point dynamics for financial data: an indexed Markov chain approach

2018 ◽  
Vol 15 (2) ◽  
pp. 247-266 ◽  
Author(s):  
Guglielmo D’Amico ◽  
Ada Lika ◽  
Filippo Petroni
Keyword(s):  
Markov Chain ◽  
Change Point ◽  
Financial Data ◽  
Markov Chain Approach

Analysis of an M/G/1 queue with two types of impatient units

1995 ◽  
Vol 27 (03) ◽  
pp. 840-861 ◽  
Author(s):  
M. Martin ◽  
J. R. Artalejo
Keyword(s):  
Markov Chain ◽  
Performance Measures ◽  
Mathematical Analysis ◽  
Service System ◽  
Probability Distributions ◽  
Embedded Markov Chain ◽  
Renewal Processes ◽  
Stationary Probability ◽  
Markov Renewal Processes ◽  
Specific Performance

This paper deals with a service system in which the processor must serve two types of impatient units. In the case of blocking, the first type units leave the system whereas the second type units enter a pool and wait to be processed later. We develop an exhaustive analysis of the system including embedded Markov chain, fundamental period and various classical stationary probability distributions. More specific performance measures, such as the number of lost customers and other quantities, are also considered. The mathematical analysis of the model is based on the theory of Markov renewal processes, in Markov chains of M/G/l type and in expressions of ‘Takács' equation' type.

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