D. E. Goldberg. Optimal initial population size for binary-coded genetic algorithms. Technical Report TCGA-850001, University of Alabama, November 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....De Jong suggested a population size of 50 100, based on his suite of test functions. Grefenstette [40] took the novel approach of using a GA to determine optimal GA performance parameters and suggested a population size of only 30. In one of the first analytical investigations, Goldberg [31] proposed an optimal population size based on the length , in number of bits, of the chromosome: P = 1:65 Theta 2 0:21 (4.2) Schaffer et. al [79] later proposed an empirically optimal P of 20 30, and Goldberg in a more recent analytical work suggested that with a few simplifying ....

D. E. Goldberg. Optimal initial population size for binary-coded genetic algorithms. Technical Report TCGA-850001, University of Alabama, November 1985.

....of premature convergence to a poor solution. On the other hand, larger populations allow the exploration of fewer generations per unit of computational effort, and if the available computational effort is limited, may preclude convergence at all. Some research has been reported on this problem in [Goldberg, 1985]. Using the criterion that we should try to maximise the expected number of new schemata per individual, this work indicates that the optimal size for binary coded strings grows exponentially with the length of the string n. Some refinements of this work are reported in [Goldberg, 1989a] but they ....

D.E.Goldberg (1985) Optimal initial population size for binary-coded genetic algorithms. TCGA Report 85001, University of Alabama, Tuscaloosa.

....the number of classes. It is clear that the GA technique can be improved to better and more precisely determine the number of classes. The number of individuals in the population needs to be reexamined. It is possible that the number of individuals in the population is too small. Dave Goldberg [4] has determined the optimal initial population size for individuals represented as bit strings with a length of up to 60 bits. For individuals of length 60, the optimal population size is 10,000. The individuals in the GA considered in this paper contained 200 bits, yet the size of the population ....

D. E. Goldberg, "Optimal initial population size for binary-coded genetic algorithms", TCGA Report Number 8500001, The Clearinghouse for Genetic Algorithms, Department of Engineering Mechanics, University of Alabama, Tuscaloosa, Alabama, November 1985.

....will converge to a local optimum very fast with insufficient processing of too few schemata. On the other hand, if the population is too large, though it has the benefit of finding a global optimum by having a large sampling of the space, the convergence will be too slow for practical use. Goldberg 85] based on Holland s original context stated that the number of schemata processed should be proportional to the cube of the population size. This suggested a very large population for a long chromosome. However, in recent research, Goldberg 89b, Schaffer and Eshelman 89] investigated the ....

David E. Goldberg. Optimal Initial Population Size for Binary-Coded Genetic Algorithms. Technical Report TCGA 85001, University of Alabama, 1985. BIBLIOGRAPHY 49

.... contradict some other beliefs about the GA that it will routinely outperform hillclimbing and other gradient descent methods on hard problems such as those with nonlinear interactions (Holland, 1988) and that a population must be of a sufficient size to support effective schema processing (Goldberg, 1985; Goldberg, 1989d) In order to better understand the sources of Tanese s results, we performed a number of additional experiments, which are described in the following sections. 5. Experimental Setup The experiments we report in this paper were performed with a similar GA and identical parameter ....

....the two was measured only in terms of proximity to the optimum of the best fitness discovered. As Tanese points out, these results run against conventional wisdom about GAs: it has been thought that on difficult problems a large population is needed for processing a sufficient number of schemas (Goldberg, 1985). Tanese proposes three main reasons for this surprising result. 1. Tanese functions have a large number of local optima and the GA tends to converge on one. Each of the smaller subpopulations of the partitioned GA will converge earlier than a larger single population, but the subpopulations ....

Goldberg, D. E. (1985). Optimal initial population size for binary-coded genetic algorithms. Technical Report TCGA Report No. 85001, University of Alabama, Tuscaloosa, AL.

....on the number of effective schemata processed [1] where n is the number of structures processed and c 1 is a small integer. This result is usually interpreted to say that, despite the processing of only n structures, the GA processes at least n 3 schemata. This result has been analyzed in [2] [3], 4] 5] 6] 7] 8] In our paper, fixed k, e and a parameter b 0, we found a lower bound of the type n f(b) on the expected number of schemata processed by the genetic algorithm applied to a population of n = 2 bl individuals obtained by random extractions from 0,1 k with probability ....

Goldberg D.E. (1985). Optimal Initial Population Size for Binary-coded Genetic Algorithms. TCGA Report N.85001, The University of Alabama, Tuscaloosa, AL.

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Goldberg, D. E. (1985). Optimal initial population size for binary-coded genetic algorithms. TCGA Report No. 850001. The Clearinghouse for Genetic Algorithms. Tuscalossa: University of Alabama.

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