## Self Adaptation in Evolutionary Algorithms (1998)

Citations: | 12 - 1 self |

### BibTeX

@TECHREPORT{Smith98selfadaptation,

author = {James Edward Smith},

title = {Self Adaptation in Evolutionary Algorithms},

institution = {},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

Evolutionary Algorithms are search algorithms based on the Darwinian metaphor of “Natural Selection”. Typically these algorithms maintain a population of individual solutions, each of which has a fitness attached to it, which in some way reflects the quality of the solution. The search proceeds via the iterative generation, evaluation and possible incorporation of new individuals based on the current population, using a number of parameterised genetic operators. In this thesis the phenomenon of Self Adaptation of the genetic operators is investigated. A new framework for classifying adaptive algorithms is proposed, based on the scope of the adaptation, and on the nature of the transition function guiding the search through the space of possible configurations of the algorithm. Mechanisms are investigated for achieving the self adaptation of recombination and mutation operators within a genetic algorithm, and means of combining them are investigated. These are shown to produce significantly better results than any of the combinations of fixed operators tested, across a range of problem types. These new operators reduce the need for the designer of an algorithm to select

### Citations

8066 |
Genetic Algorithms
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(Show Context)
Citation Context ...e gives fH ( ) dH ( ) m( H, t + 1) ≥ mHt ( , ) ⋅ ----------- ⋅ 1 – ⎛pc⋅----------- ⎞ – p (1) f ⎝ l – 1⎠ m ⋅ oH ( ) This is the Schema Theorem. A related concept is the Building Block Hypothesis (see [=-=Goldberg, 1989-=- pp 41-45] for a good description). Simply put, this is the idea that Genetic Algorithms work by discovering low order schemata of high fitness (building blocks) and combining them via recombination t... |

2985 |
Adpatation in Natural and Artificial Systems
- Holland
- 1975
(Show Context)
Citation Context ...ary Algorithms can (broadly speaking) be distinguished by the nature of the alphabet used to represent the search space and the specialisation of the various operators used, e.g. Genetic Algorithms ([=-=Holland, 1975-=-]: binary or finite discrete representations), Evolution Strategies ([Rechenberg, 1973, Schwefel, 1981]: real numbers) Evolutionary Programming ([Fogel et al., 1966]: real numbers), and Genetic Progra... |

1295 |
The Selfish Gene
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- 1976
(Show Context)
Citation Context ...and what benefits it confers, have long been studied by Evolutionary Biologists (see [Maynard-Smith, and Szathmary, 1995 chapter 9] for a good overview). From the point of view of the “selfish gene” [=-=Dawkins, 1976-=-], it would initially appear that “parthenogenesis” (asexual reproduction) would appear to confer an advantage, since all of an organism’s genes are guaranteed (saving mutation) to survive into the ne... |

809 |
The Genetical Theory of Natural Selection
- Fisher
- 1930
(Show Context)
Citation Context ...is similar to the Building Block hypothesis, and shows that in changing environments populations using recombination are able to accumulate and combine successful mutations faster than those without [=-=Fisher, 1930-=-]- this is sometimes known as “hybrid vigour”. 2.2. Recombination Biases Considerable effort has been put into deriving expressions which describe the amount and type of schema disruption caused by va... |

705 |
Evolutionsstrategie. Optimierung technischer Systeme nach Prinzipien der biologischen Evolution
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(Show Context)
Citation Context ...t used to represent the search space and the specialisation of the various operators used, e.g. Genetic Algorithms ([Holland, 1975]: binary or finite discrete representations), Evolution Strategies ([=-=Rechenberg, 1973-=-, Schwefel, 1981]: real numbers) Evolutionary Programming ([Fogel et al., 1966]: real numbers), and Genetic Programming ([Cramer, 1985, Koza, 1989]: tree based representation of computer programs). Th... |

624 |
The Origins of Order
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(Show Context)
Citation Context ... range of widely used crossover operators are presented, and the effect of changing other search parameters is investigated. In Chapter Four, Kauffman’s NK-family of search landscapes are introduced [=-=Kauffman, 1993-=-]. These are a set of tunable landscapes with well known statistical characteristics. An analysis is then given of the recombination strategies which evolve on different types of landscapes, in the li... |

546 |
Uniform crossover in genetic algorithms
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(Show Context)
Citation Context ...basis of which decisions could be reliably made depends on the size of the search space. The next few years of research saw a variety of new operators proposed, some of which (e.g. Uniform Crossover [=-=Syswerda, 1989-=-]) forced a reappraisal of the Schema Theory and led to the Page 11sfocusing on two important concepts. The first of these, Crossover Bias [Eshelman et al., 1989], refers to the differing ways in whic... |

430 | editors. Handbook of Evolutionary Computation - Bäck, Fogel, et al. - 1997 |

419 |
Optimization of Control Parameters for Genetic Algorithms
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(Show Context)
Citation Context ...fied a suite of test functions and proposed a set of parameters which it was hoped would work well across a variety of problem types. However later studies using a “meta-ga” to learn suitable values [=-=Grefenstette, 1986-=-] or using exhaustive testing [Schaffer et al., 1989] arrived at different conclusions. Meanwhile theoretical analysis on optimal population sizes [Goldberg, 1985] started to formalise the (obvious?) ... |

413 | A comparative analysis of selection schemes used in genetic algorithms
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(Show Context)
Citation Context ... as effectively increasing the selection pressure towards more highly fit individuals, and it has been argued that it is this factor rather than any other which accounts for differences in behaviour [=-=Goldberg and Deb, 1991-=-]. In fact since the algorithm is iterative, the two selection distributions are applied consecutively, and so they can be treated as a single operator U with a p.d.f. given by p s (a i t ) = pr (a i ... |

349 |
Reducing Bias and Inefficiency in the Selection Algorithm
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- 1987
(Show Context)
Citation Context ...fference in the selection pressure due to the incremental selection of parents in the SSGA as opposed to the selection of a whole population in the GGA. For the latter Baker’s SUS algorithm was used [=-=Baker 1987-=-]. As for the “roulette wheel” this assigns an expected number of members to each member of the population and then performs stochastic selection to create a parental gene-pool. However the SUS algori... |

248 | Genetic Algorithms, Noise, and the Sizing of Populations
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(Show Context)
Citation Context ...tween relations and their instances (schemata). It has been shown that the size of the population needed to solve a problem increases with the order of the highest relations that must be chosen e.g. [=-=Goldberg et al., 1992-=-], [Kargupta and Goldberg, 1994] Hence if the mean population linkage increases, implying a selective advantage towards preserving longer blocks, so will the order and number of possible schemata that... |

234 | A survey of evolution strategies - Bäck, Schwefel - 1991 |

230 |
A representation for the adaptive generation of simple sequential programs
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- 1985
(Show Context)
Citation Context ...y or finite discrete representations), Evolution Strategies ([Rechenberg, 1973, Schwefel, 1981]: real numbers) Evolutionary Programming ([Fogel et al., 1966]: real numbers), and Genetic Programming ([=-=Cramer, 1985-=-, Koza, 1989]: tree based representation of computer programs). This thesis is primarily concerned with Genetic Algorithms (GAs) based on a binary problem representation, since these can be used to re... |

211 | Fitness distance correlation as a measure of problem difficulty for genetic algorithms
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- 1995
(Show Context)
Citation Context ...unction of the epistasis, and so increasing the size of the landscape increases their separation. 5. Analysis into the use of fitness-distance correlation as a measure of problem difficulty for GA’s [=-=Jones and Forrest, 1995-=-] shows that the correlation between fitness and distance drops rapidly with increasing epistasis, from -1.0 at K= 0 to 0.0 at K = N -1. In [Weinberger, 1990] an examination was made of the autocorrel... |

207 | The royal road for genetic algorithms: Fitness landscapes and GA performance
- Mitchell, Forrest, et al.
- 1991
(Show Context)
Citation Context ...ratio diminished over time for mutation and increased over time for Uniform Crossover, but the former had a far better mean best performance in terms of discovering optima. The Royal Road landscapes [=-=Mitchell et al., 1992-=-, Forrest and Mitchell, 1992] were created with building blocks specifically designed to suit the constructive powers of crossover. Mitchell et al. compared results from algorithms using both crossove... |

198 |
Numerische Optimierung von Computer-modellen mittels der Evolutionsstrategie
- Schwefel
- 1977
(Show Context)
Citation Context ...ion pressure. These considerations, when coupled with interactions with other Evolutionary Algorithm communities who were already using adaptive operators (e.g. the (1+1) [Rechenberg, 1973] and (μλ) [=-=Schwefel, 1977-=-, 1981] Evolutionary Strategies), has led to an ever increasing interest in the possibilities of developing algorithms which are able to adapt one or more of their operators or parameters in order to ... |

197 |
An analysis of the behaviour of a class of genetic adaptive systems, Doctoral thesis
- Jong
- 1975
(Show Context)
Citation Context ...g. 1 for GGAs). This variance decreases with larger populations, but was the basis behind early recommendations for generational algorithms (e.g. Holland’s original work and the empirical studies in [=-=DeJong, 1975-=-]) where small populations were used. It was also found that the use of strategies such as “delete-oldest” (a.k.a. FIFO) reduced the observed variance in behaviour whilst not affecting the theoretical... |

188 |
Adapting operator probabilities in genetic algorithms
- Davis
- 1989
(Show Context)
Citation Context ...robabilities of application for a few simple operators (uniform crossover, averaging crossover, mutation, “big creep” and “little creep”) depending on their performance over the last few generations [=-=Davis, 1989-=-]. Many later authors have proposed variants on this approach, using a number of different learning methods as will be seem later. A similar approach which changes the population updating mechanism by... |

179 |
A study of control parameters affecting online performance of genetic algorithms for function optimization
- Schaffer, Caruana, et al.
- 1989
(Show Context)
Citation Context ... of parameters which it was hoped would work well across a variety of problem types. However later studies using a “meta-ga” to learn suitable values [Grefenstette, 1986] or using exhaustive testing [=-=Schaffer et al., 1989-=-] arrived at different conclusions. Meanwhile theoretical analysis on optimal population sizes [Goldberg, 1985] started to formalise the (obvious?) point that the value of μ on the basis of which deci... |

173 | A Co-operative Coevolutionary Approach to Function Optimisation
- Potter, Jong
- 1994
(Show Context)
Citation Context ...re sections are read from the n parents successively. This will exhibit positional bias to a degree dependant on the arity. The idea of co-evolving separate populations of sub-components was used in [=-=Potter and DeJong, 1994-=-] as an approach to function optimisation, with similar findings that the efficiency of the approach is lessened as the amount of epistasis increases, but that if the problem decomposition is suitable... |

124 |
Hierarchical Genetic Algorithm Operating on Populations of Computer Programs
- Koza
- 1989
(Show Context)
Citation Context ...screte representations), Evolution Strategies ([Rechenberg, 1973, Schwefel, 1981]: real numbers) Evolutionary Programming ([Fogel et al., 1966]: real numbers), and Genetic Programming ([Cramer, 1985, =-=Koza, 1989-=-]: tree based representation of computer programs). This thesis is primarily concerned with Genetic Algorithms (GAs) based on a binary problem representation, since these can be used to represent a wi... |

120 | Optimal mutation rates in genetic search - Back - 1993 |

118 | Self-adaptation in genetic algorithms
- Bäck
- 1992
(Show Context)
Citation Context ... mutations likely in the production of a copy of the converged solution. It can be shown that the mutation rates will eventually converge towards zero using a Markov Chain analysis. This was done in [=-=Bäck, 1992-=-b], but a simple version is sketched here for completeness. The reader is referred to e.g [Hoel et al.,1972] for a full discussion of the convergence of Markov Chains. A converged population is assume... |

118 | The genetic algorithm and the structure of the fitness landscape - Manderick, Weger, et al. - 1991 |

117 |
Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms
- Srinivas, Patnaik
- 1994
(Show Context)
Citation Context ... rely on endogenous control and self-adaptation. As with population level adaptations, a number of other algorithms can be used to control the behaviour of individuals. A typical example is found in [=-=Srinivas and Patnaik, 1994-=-] where the probabilities of applying mutation or crossover to an individual depend on its relative fitness, and the degree of convergence (of fitnesses) of the population. This fitness-dependant cont... |

102 |
Biases in the crossover landscape
- Eshelman, Caruana, et al.
- 1989
(Show Context)
Citation Context ...posed, some of which (e.g. Uniform Crossover [Syswerda, 1989]) forced a reappraisal of the Schema Theory and led to the Page 11sfocusing on two important concepts. The first of these, Crossover Bias [=-=Eshelman et al., 1989-=-], refers to the differing ways in which the p.d.f.’s arising from various crossover operators maintain hyperplanes of high estimated fitness during recombination, as a function of their order and def... |

96 | Genetic Algorithms for Tracking Changing Environments
- Cobb, Grefenstette
- 1993
(Show Context)
Citation Context ...atter is similar to many strategies for tracking changing environments, where a drop in the performance of the best member of the current generation is used to trigger a higher rate of mutation e.g. [=-=Cobb and Grefenstette, 1993-=-]. In [Lee and Takagi, 1993] fuzzy rules are learned and used to control various parameters based on the relative performance of the best, worst and mean of the current population. This concept of obs... |

96 | The Gene Expression Messy Genetic Algorithm
- Kargupta
- 1996
(Show Context)
Citation Context ...aken to mean the combination of a particular allele (bit) value in a particular locus (position)). Subsequent variants (the “fast messy GA” [Goldberg et al., 1993] and the “Gene Expression Messy GA” [=-=Kargupta, 1996-=-]) rely on first order statistics to identify the blocks of linked genes that they manipulate, as do a number of other schemes e.g. [van Kemenade,1996]. An alternative scheme was proposed in [Harik an... |

95 |
GENITOR: a different genetic algorithm
- Whitley
(Show Context)
Citation Context ...n of the population in any given iteration (known as generations). At the opposite end of the spectrum to generational GAs lie “steady state” genetic algorithms (SSGAs) such as the GENITOR algorithm [=-=Whitley and Kauth, 1988-=-]. These replace only a single member of the population at any given time (λ = 1). It can be shown that under the right conditions, the two algorithms display the same behaviour. In an empirical compa... |

93 |
The interaction of mutation rate, selection, and self-adaptation within a genetic algorithm
- Bäck
- 1992
(Show Context)
Citation Context ... of the population increases, the proportion of genes with the optimal value increases, and so the chance that a randomly distributed mutation will be beneficial is decreased. This was formalised in [=-=Bäck, 1992-=-a, 1993] where an exact form for the Safety Ratio was derived for a mutation probability p. This could not be solved analytically, but was optimised numerically and 1 found to be well fitted by a curv... |

92 |
An Adaptive Crossover Distribution Mechanism for Genetic Algorithms
- Schaffer, Morishima
- 1987
(Show Context)
Citation Context ...re subsumed into δ. A second class of adaptive GA’s can be distinguished as changing the actual action of the operator(s) over time. An early example of this was the “Punctuated Crossover” mechanism [=-=Schaffer and Morishima, 1987-=-] which added extra bits to the representation to encode for crossover points. These were allowed to evolve over time to provide a 2 parent N-point recombination mechanism, where N was allowed to vary... |

88 |
Preventing Premature Convergence in Genetic Algorithms by Preventing Incest
- Eshelman, Schaffer
- 1991
(Show Context)
Citation Context ...e the convergence of the population to alter the thresholds governing incest prevention, and the time spent without improvement to govern the probability of restarting the GA using vigorous mutation [=-=Eshelman and Schaffer, 1991-=-]. This latter is similar to many strategies for tracking changing environments, where a drop in the performance of the best member of the current generation is used to trigger a higher rate of mutati... |

86 | Adaptive and Self-Adaptive Evolutionary Computation,” in Marimuthu Palaniswami et al
- Angeline
- 1995
(Show Context)
Citation Context ...5] can be seen in this restructuring light, as can the Adaptive Penalty Functions of [Eiben and van der Hauw, 1997, Eiben et al. 1998]. 1.3.2. What is the Scope of the Adaptation? The terminology of [=-=Angeline, 1995-=-] defines three distinct levels at which adaptation can occur in evolutionary algorithms. Population-level adaptations make changes which affect the p.d.f. contribution from each member of the current... |

80 | The Major Transitions in Evolution - Maynard-Smith, Szathmàry - 1997 |

79 |
The relation of recombination to mutational advance
- Muller
- 1964
(Show Context)
Citation Context ...cted that a gene for parthenogenesis that arose by mutation in a sexually reproducing population would soon dominate. However, when a finite population is considered, the effects of Muller’s Ratchet [=-=Muller, 1964-=-] come into play. Simply stated, this is the effect that deleterious mutations will tend to accumulate in a population of fixed size. In practice this tendency is counteracted by selection, so that an... |

76 | On the virtues of parameterized uniform crossover
- Spears, Dejong
- 1991
(Show Context)
Citation Context ...to the landscape induced by the problem encoding. These findings have been confirmed by more formal analysis on the relative merits of various recombination mechanisms [DeJong and Spears, 1990, 1992, =-=Spears and DeJong, 1991-=-]. The second concept was that of Safety Ratios [Schaffer and Eshelman, 1991] i.e. of the ratio of probability that a new point generated by the application of reproductive operators would be fitter t... |

73 | Crossover or Mutation
- Spears
- 1993
(Show Context)
Citation Context ...is almost entirely converged, crossover has a greater ability to construct higher order schemata from good lower order ones (the Building Block hypothesis). This ability is modelled theoretically in [=-=Spears, 1992-=-] where it is shown that crossover has a higher potential than mutation. The nature (in terms of order and defining length) of lower order schema that will be combined depends on the form of the cross... |

69 |
What have you done for me lately? Adapting operator probabilities in a steady-state genetic algorithm on genetic algorithms
- Julstrom
- 1995
(Show Context)
Citation Context ...more parameters dynamically in accordance with the performance of the algorithm or some measured quantity of the population. A well known, and popular approach (e.g. [Davis, 1989, Corne et al., 1994, =-=Julstrom, 1995-=-]) is to keep statistics on the performance of offspring generated by various reproductive operators relative to their parents. Periodically “successful” operators are rewarded by increasing their pro... |

68 | An analysis of the interacting roles of population size and crossover in genetic algorithms. Parallel Problem Solving from Nature, 38–47. (Also AIC
- Jong, Spears
- 1990
(Show Context)
Citation Context ... by the recombination operator to the landscape induced by the problem encoding. These findings have been confirmed by more formal analysis on the relative merits of various recombination mechanisms [=-=DeJong and Spears, 1990-=-, 1992, Spears and DeJong, 1991]. The second concept was that of Safety Ratios [Schaffer and Eshelman, 1991] i.e. of the ratio of probability that a new point generated by the application of reproduct... |

65 | Genetic Algorithms with Multi-Parent Recombination
- Eiben, Rau´e, et al.
- 1994
(Show Context)
Citation Context ...er for a>2 this class is no longer isomorphic to Syswerda’s original specification. An alternative representation, which is more easily generalised to models with arity a, such as Scanning Crossover [=-=Eiben et al. 1994-=-], is for the elements of x to be drawn from the set {0...a-1} according to some probability distribution. This might be uniform, fitness proportionate, or parameterised as above. The generalised repr... |

65 | Adapting crossover in evolutionary algorithms
- Spears
- 1995
(Show Context)
Citation Context ...a set of rules are applied based on the relative fitness of offspring and parents, which update the state of each automata. An alternative method for controlling recombination strategies was used in [=-=Spears, 1995-=-] where a single bit was added to the genotype and used to decide whether two-point or uniform crossover would be used when an individual reproduced. Again self-adaptation was used for the transition.... |

64 | Learning linkage
- Harik, Goldberg
- 1997
(Show Context)
Citation Context ...ta, 1996]) rely on first order statistics to identify the blocks of linked genes that they manipulate, as do a number of other schemes e.g. [van Kemenade,1996]. An alternative scheme was proposed in [=-=Harik and Goldberg, 1996-=-], which attempted to co-evolve the positions and values of genes using a representation which consider loci as points on a circle, with the (real-valued) distance between points representing their li... |

61 |
Crossover’s niche
- Eshelman, Schaffer
- 1993
(Show Context)
Citation Context ...re 34 sub- optima scoring 18 at Hamming distances from one of the optima of between two and ten. In addition to being multi-modal, this problem has high local epistasis of order two. The analysis in [=-=Eshelman and Schaffer, 1993-=-] suggests that the difficulty of the problem for the more disruptive operators will depend on the speed with which the search drops one of the two possible solutions. One point crossover would be exp... |

57 |
A study of reproduction in generational and steady state genetic algorithms
- Syswerda
- 1991
(Show Context)
Citation Context ...e replace only a single member of the population at any given time (λ = 1). It can be shown that under the right conditions, the two algorithms display the same behaviour. In an empirical comparison [=-=Syswerda, 1991-=-] the two variants, were shown to exhibit near identical growth curves, provided that a suitable form of p u was used to define U for the SSGA. In this case random deletion was used i.e. t pu( ai) n –... |

55 | Dynamic Control of Genetic Algorithm Using Fuzzy Logic Techniques
- Lee, Takagi
- 1993
(Show Context)
Citation Context ...s for tracking changing environments, where a drop in the performance of the best member of the current generation is used to trigger a higher rate of mutation e.g. [Cobb and Grefenstette, 1993]. In [=-=Lee and Takagi, 1993-=-] fuzzy rules are learned and used to control various parameters based on the relative performance of the best, worst and mean of the current population. This concept of observing the fitness distribu... |

51 |
Towards an Optimal Mutation Probability for Genetic Algorithms. Proceedings of 1st workshop : Parallel problem solving from nature
- Hesser, &Männer
- 1991
(Show Context)
Citation Context ...nsition function Γ. Page 15sThere are a number of theoretical results which provide support for this kind of approach, e.g. regarding the time-variance of the optimal mutation rate [Mühlenbein, 1992, =-=Hesser and Manner, 1991-=-] (see also the discussions Bäck’s results, and of Schaffer & Eshelman’s experimental results regarding the time dependencies of Safety Ratios for mutation and crossover, on page 12). In [Fogarty, 198... |

51 | Adaptation in Evolutionary Computation: A Survey
- Hinterding, Michalewicz, et al.
- 1997
(Show Context)
Citation Context ...e common usage than “tightly coupled” algorithms is the term Self Adaptation. The three classes of algorithms distinguished on the basis of the transition function differ significantly from those of [=-=Hinterding et al., 1997-=-], who agree on the category of Self Adaptation, but split all other adaptive algorithms into two classes according to whether they utilise any feedback (of any kind) from the GA or not. Into the latt... |

48 | Strategy adaptation by competing subpopulations - Schlierkamp-Voosen, Mühlenbein - 1994 |

44 |
Recombination distributions for genetic algorithms
- Booker
- 1993
(Show Context)
Citation Context ...exploitation of “good” building blocks. This has been explored in terms of positional and distributional biases, experimentally [Eshelman et al., 1989, Eshelman and Schaffer, 1994] and theoretically [=-=Booker, 1992-=-, Spears and DeJong, 1990, 1991]. In brief, an operator is said to exhibit positional bias if the probability of disrupting schema H of a given order o(H) is a function of the defining length d(H). Th... |