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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] |
Evolutionary Algorithm
In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators. Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real applications of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-armed Bandit
In probability theory and machine learning, the multi-armed bandit problem (sometimes called the ''K''- or ''N''-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. This is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. The name comes from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each mach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-objective Optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multi-objective optimization problem, no single solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Efficiency
Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" for t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypervolume Indicator
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled ''x'', ''y'', and ''z''). The idea of adding a fourth dimension began with Jean le Rond d'Alembert's "Dimensions" being published in 1754, was followed by Joseph-Louis Lagrange in the mid-1700s, and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann. In 1880, Charles Howard Hinton popularized these insights in an essay titled "What is the Fourth Dimension?", which explained the concept of a " four-dimensional cube" with a step-by-step generalization of the properties of lines, squares, and cubes. The simplest form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 candi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selection (genetic Algorithm)
Selection is the stage of a genetic algorithm in which individual genomes are chosen from a population for later breeding (using the crossover operator). A generic selection procedure may be implemented as follows: #The fitness function is evaluated for each individual, providing fitness values, which are then normalized. Normalization means dividing the fitness value of each individual by the sum of all fitness values, so that the sum of all resulting fitness values equals 1. #Accumulated normalized fitness values are computed: the accumulated fitness value of an individual is the sum of its own fitness value plus the fitness values of all the previous individuals; the accumulated fitness of the last individual should be 1, otherwise something went wrong in the normalization step. #A random number ''R'' between 0 and 1 is chosen. #The selected individual is the first one whose accumulated normalized value is greater than or equal to ''R''. For many problems the above algorithm m ... [...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'' := to ... [...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] |
Footnotes
A note is a string of text placed at the bottom of a page in a book or document or at the end of a chapter, volume, or the whole text. The note can provide an author's comments on the main text or citations of a reference work in support of the text. Footnotes are notes at the foot of the page while endnotes are collected under a separate heading at the end of a chapter, volume, or entire work. Unlike footnotes, endnotes have the advantage of not affecting the layout of the main text, but may cause inconvenience to readers who have to move back and forth between the main text and the endnotes. In some editions of the Bible, notes are placed in a narrow column in the middle of each page between two columns of biblical text. Numbering and symbols In English, a footnote or endnote is normally flagged by a superscripted number immediately following that portion of the text the note references, each such footnote being numbered sequentially. Occasionally, a number between brack ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Algorithms
In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators. Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real applications o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
