|
Fitness Proportionate Selection
Fitness proportionate selection, also known as roulette wheel selection, is a genetic operator used in genetic algorithms for selecting potentially useful solutions for recombination. In fitness proportionate selection, as in all selection methods, the fitness function assigns a fitness to possible solutions or chromosomes. This fitness level is used to associate a probability of selection with each individual chromosome. If f_i is the fitness of individual i in the population, its probability of being selected is : p_i = \frac, where N is the number of individuals in the population. This could be imagined similar to a Roulette wheel in a casino. Usually a proportion of the wheel is assigned to each of the possible selections based on their fitness value. This could be achieved by dividing the fitness of a selection by the total fitness of all the selections, thereby normalizing them to 1. Then a random selection is made similar to how the roulette wheel is rotated. While cand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fitness Proportionate Selection Example ...
Fitness may refer to: * Physical fitness, a state of health and well-being of the body * Fitness (biology), an individual's ability to propagate its genes * Fitness (cereal), a brand of breakfast cereals and granola bars * ''Fitness'' (magazine), a women's magazine, focusing on health and exercise * Fitness and figure competition, a form of physique training, related to bodybuilding * Fitness approximation, a method of function optimization evolutionary computation or artificial evolution methodologies * Fitness function, a particular type of objective function in mathematics and computer science * "Fitness", a 2018 song by Lizzo See also * FitNesse, a web server, a wiki, and a software testing tool *Survival of the fittest "Survival of the fittest" is a phrase that originated from Darwinian evolutionary theory as a way of describing the mechanism of natural selection. The biological concept of fitness is defined as reproductive success. In Darwinian terms, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Probability Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Universal Sampling
Stochastic universal sampling (SUS) is a technique used in genetic algorithms for selecting potentially useful solutions for recombination. It was introduced by James Baker. SUS is a development of fitness proportionate selection (FPS) which exhibits no bias and minimal spread. Where FPS chooses several solutions from the population by repeated random sampling, SUS uses a single random value to sample all of the solutions by choosing them at evenly spaced intervals. This gives weaker members of the population (according to their fitness) a chance to be chosen. FPS can have bad performance when a member of the population has a really large fitness in comparison with other members. Using a comb-like ruler, SUS starts from a small random number, and chooses the next candidates from the rest of population remaining, not allowing the fittest members to saturate the candidate space. Described as an algorithm, pseudocode for SUS looks like: SUS(''Population'', ''N'') ''F'' := t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reward-based Selection
Reward-based selection is a technique used in evolutionary algorithms for selecting potentially useful solutions for recombination. The probability of being selected for an individual is proportional to the cumulative reward, obtained by the individual. The cumulative reward can be computed as a sum of the individual reward and the reward, inherited from parents. Description Reward-based selection can be used within Multi-armed bandit framework for Multi-objective optimization to obtain a better approximation of the Pareto front. The newborn a'^ and its parents receive a reward r^, if a'^ was selected for new population Q^, otherwise the reward is zero. Several reward definitions are possible: *1. r^=1, if the newborn individual a'^ was selected for new population Q^. *2. r^ = 1 - \frac \mbox a'^ \in Q^ , where rank(a'^) is the rank of newly inserted individual in the population of \mu individuals. Rank can be computed using a well-known non-dominated sorting procedure. *3. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alias Method
In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by A. J. Walker. That is, it returns integer values according to some arbitrary probability distribution . The algorithms typically use or preprocessing time, after which random values can be drawn from the distribution in time. Operation Internally, the algorithm consults two tables, a ''probability table'' and an ''alias table'' (for ). To generate a random outcome, a fair dice is rolled to determine an index into the two tables. Based on the probability stored at that index, a biased coin is then flipped, and the outcome of the flip is used to choose between a result of and . More concretely, the algorithm operates as follows: # Generate a uniform random variate . # Let and . (This makes uniformly distributed on and uniformly distributed on .) # If , return . This is the biased coin flip. # Otherwise, return . An alterna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big O Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for '' Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Search Algorithm
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, ''a'' and ''b'', which are the minimum and maximum values. The interval can either be closed (e.g. , b or open (e.g. (a, b)). Therefore, the distribution is often abbreviated ''U'' (''a'', ''b''), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable ''X'' under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is: : f(x)=\begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tournament Selection
Tournament selection is a method of selecting an individual from a population of individuals in a genetic algorithm. Tournament selection involves running several "tournaments" among a few individuals (or "chromosomes") chosen at random from the population. The winner of each tournament (the one with the best fitness) is selected for crossover. ''Selection pressure'', a probabilistic measure of a chromosome's likelihood of participation in the tournament based on the participant selection pool size, is easily adjusted by changing the tournament size, the reason is that if the tournament size is larger, weak individuals have a smaller chance to be selected, because, if a weak individual is selected to be in a tournament, there is a higher probability that a stronger individual is also in that tournament. The tournament selection method may be described in pseudo code: choose k (the tournament size) individuals from the population at random choose the best individual from the tou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Operator
A genetic operator is an operator used in genetic algorithms to guide the algorithm towards a solution to a given problem. There are three main types of operators (mutation, crossover and selection), which must work in conjunction with one another in order for the algorithm to be successful. Genetic operators are used to create and maintain genetic diversity (mutation operator), combine existing solutions (also known as chromosomes) into new solutions (crossover) and select between solutions (selection). In his book discussing the use of genetic programming for the optimization of complex problems, computer scientist John Koza has also identified an 'inversion' or 'permutation' operator; however, the effectiveness of this operator has never been conclusively demonstrated and this operator is rarely discussed. Mutation (or mutation-like) operators are said to be '' unary'' operators, as they only operate on one chromosome at a time. In contrast, crossover operators are said to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Universal Sampling
Stochastic universal sampling (SUS) is a technique used in genetic algorithms for selecting potentially useful solutions for recombination. It was introduced by James Baker. SUS is a development of fitness proportionate selection (FPS) which exhibits no bias and minimal spread. Where FPS chooses several solutions from the population by repeated random sampling, SUS uses a single random value to sample all of the solutions by choosing them at evenly spaced intervals. This gives weaker members of the population (according to their fitness) a chance to be chosen. FPS can have bad performance when a member of the population has a really large fitness in comparison with other members. Using a comb-like ruler, SUS starts from a small random number, and chooses the next candidates from the rest of population remaining, not allowing the fittest members to saturate the candidate space. Described as an algorithm, pseudocode for SUS looks like: SUS(''Population'', ''N'') ''F'' := t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncation Selection
In animal and plant breeding, truncation selection is a standard method in selective breeding in selecting animals to be bred for the next generation. Animals are ranked by their phenotypic value on some trait such as milk production, and the top percentage is reproduced. The effects of truncation selection for a continuous trait can be modeled by the standard breeder's equation by using heritability and truncated normal distributions. On a binary trait, it can be modeled easily using the liability threshold model. It is considered an easy and efficient method of breeding. Computer science In computer science, truncation selection is a selection method used in genetic algorithms to select potential candidate solutions for recombination modeled after the breeding method. In truncation selection the candidate solutions are ordered by fitness, and some proportion, ''p'', (e.g. ''p'' = 1/2, 1/3, etc.) of the fittest individuals are selected and reproduced 1/p times. Truncation sele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
