D. Whitley, K. Mathias, and P. Fitzhorn. Delta-Coding: An iterative search strategy for genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 77-84, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....results of L i , and evaluate it in T i 1 together with a network selected from the second population, which is learning L i 1 from scratch. The resulting score is shared by both networks. 2.2. 2 Delta Coding To seed a population from the results of L i , we use a technique called delta coding [21]. When delta coding, we take the result of a given layer, h i , and use it to create a new population, each member of which is a perturbation of h i . The network that will perform task L i optimally in T i 1 is likely to be near h i but occasionally may be radically di erent. Hence, we base the ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta-Coding: An iterative search strategy for genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 77-84, 1991.

....within the interval and 99:9 within the interval 318:3 . This technique of recharging the subpopulations keeps diversity in the population so that ESP can continue to make progress toward a solution even in prolonged evolution. Burst mutation is similar to the Delta Coding technique of [9] which was developed to improve the precision of genetic algorithms for numerical optimization problems. Because our goal is to maintain diversity, we do not reduce the range of the noise on successive applications of burst mutation and we use Cauchy rather that uniformly distributed noise. roll ....

Whitley, D., Mathias, K., Fitzhorn, P.: Delta-Coding: An iterative search strategy for genetic algorithms. In Belew, R.K., Booker, L.B., eds.: Proceedings of the Fourth International Conference on Genetic Algorithms, San Francisco, CA: Morgan Kaufmann (1991) 77-84

....Then, in (d) the nest moves to the best generated point so far. Hunting sites are then created again as in (b) and so on. API s strategy has the following main properties: It centers the search around a given point. This is similar to what happens in the delta coding technique introduced in [23]. In delta coding, the binary representation used in the GA is not the direct representation of a solution but rather the representation of a small displacement (called #) from a central point (called partial solution) This representation can thus periodically change as the central point moves. ....

D. Whitley, K. Mathias, P. Fitzhorn, Delta coding: an iterative search strategy for genetic algorithms, in: R.K. Belew, L.B. Booker (Eds.), Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, San Francisco, CA, 1991, pp. 77--84.

.... is the self adaptation of strategy parameter, e.g. the global frequency of operator applications [6] or adaptation of the mutation variance in ES [22] EP [10] or GA [3] In addition there are approaches which dynamically adjust the global interpretation of the representation based on heuristics [15, 23, 26]. There are also methods which allow adaptation of crossover operators by adjusting the probability that a position is chosen as a crossover point [20, 21] This approach has also been successfully applied to GP [2, 11] In GP, there is also an implicit adaptation of variation by neutral ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms,. In Rick Belew and Lashon Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 77--84, San Mateo, CA, 1991. Morgan Kaufman.

....distribution of hunting sites may be di erent from the initial one (see for instance illustrations (b) and (c) in Figure 4) API s strategy has the following main properties: It centers the search around a given point. This is similar to what happens in the delta coding technique introduced in [23]. In delta coding, the binary representation used in the GA is not the direct representation of a solution but rather the representation of a small displacement (called ) from a central point (called partial solution) This representation can thus periodically 6 (1) Choose randomly the initial ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: an iterative search strategy for genetic algorithms. In R.K. Belew and L.B. Booker, editors, Fourth International Conference on Genetic Algorithms, pages 77-84. Morgan Kaufmann, San Francisco, California, 1991.

....for instance, moving the nest is similar to a restart operator as used in GA [12] because, as it will be seen in the next section, ants will forget everything once the nest has been moved. In the same way, centering searches on a given point is similar to the delta coding technique introduced in [13]. 3.3 Local behavior of ants Initially and as soon as the nest has been moved, each ant a i is going to leave the nest to create p hunting sites in its memory according to a uniform distribution, centered around the nest. To create these initial sites, a i makes use of O explo with an amplitude ....

Whitley D., Mathias K., Fitzhorn P. (1991) Delta Coding:an iterative search strategy for Genetic Algorithms. Proceedings of the Fourth International Conference on Genetic Algorithms, Belew R.K. and Booker L.B.(Eds.), Morgan Kaufmann publishers, pp. 77-84. 16

....prune the search space) although they are performed in a different order and in a totally different way. More elaborated descendants of the basic GA have emerged lately (mGA messy genetic algorithms ( Goldberg et al. 1989] Goldberg et al. 1990] Goldberg et al. 1991] delta coding [Whitley et al. 1991]) in order to cope with some of the already recognized difficulties of GAs. In GAs individuals are traditionally represented as fixed length binary strings. Individuals are genetically bred using three main genetic operations: reproduction, mutation, and crossover (characterized by probabilities ....

D. Whitley, K. Mathias, and P. Fizhorn, "Delta Coding: An Iterative Search Strategy for Genetic Algorithms," Proceedings of the International Conference on Genetic Algorithms, pages 77--84, 1991.

....Recognition, 2nd ed. San Diego, CA: Academic, 1990. 12] C. C. Lai, Outdoor autonomous land vehicle guidance by road information using computer vision and fuzzy wheel adjustment techniques, M.S. thesis, Inst. Comput. Inf. Sci. National Chiao Tung Univ. Hsinchu, Taiwan, R.O.C. June 1993. [13] S. D. Cheng and W. H. Tsai, Model based guidance of autonomous land vehicles in indoor environments by structured light using vertical line information, J. Elect. Eng. vol. 34, pp. 441 452, Dec. 1991. 14] A. Ohya, A. Kosaka, and A. Kak, Vision based navigation of mobile robot with obstacle ....

....algorithm is warranted. However, experience indicates that many problems can be solved to a satisfactory accuracy using the faster convergence of genetic algorithms and specifically by the fuzzy GAP coding methodology proposed in this paper. C. Delta Coding The delta coding algorithm proposed in [13] also motivates components of the fuzzy GAP coding algorithm. The delta coding algorithm begins by performing a standard genetic search until the population of strings has converged. After convergence, the best solution found by the genetic algorithm is saved. The genetic algorithm is restarted ....

[Article contains additional citation context not shown here]

D. Whitley, K. Mathias, and P. Fitzhorn, "Delta coding: An iterative search strategy for genetic algorithms," in Proc. 4th Int. Conf. Genetic Algorithms, L. Booker and R. Belew, Eds. San Mateo, CA: Morgan Kauffman, 1991, pp. 77--84.

....problems with continuous objective functions over R n . Traditionally, researchers have used GAs with binary coded genes that are decoded into real values to solve this problem [5] However, special manipulation of this encoding is often necessary to increase the efficiency of the algorithm [26, 33]. Recent research on real coded GAs suggests that they can be more efficient, provide increased precision, and allow for genetic operators that are more appropriate for a continuous domain [7, 15, 34] Convergence analyses of real coded GAs have naturally focused on the role of crossover, since ....

D. Whitley, K. Mathias, and P. Fitzhorn, Delta coding: An iterative search strategy for genetic algorithms, in Proceedings of the Fourth Intl. Conf. on Genetic Algorithms, R. K. Belew and L. B. Booker, eds., San Mateo, CA, 1991, MorganKaufmann, pp. 77--84. 25

....within each evaluation task, because the sub populations may prematurely converge before the evaluation task has been optimized. To accomplish task transfer despite convergence, ESP is combined with an iterative search technique known as Delta Coding. 4. 2 Delta Coding The idea of Delta Coding (Whitley et al. 1991) is to search for optimal modifications of the current best solution. In a conventional single population GA, when the population of candidate solutions has converged, Delta Coding is invoked by first saving the best solution and then initializing a population of new individuals called ....

Whitley, D., Mathias, K., and Fitzhorn, P. (1991). Delta-coding: An iterative search strategy for genetic algortihms. In Proceedings of the Fourth International Conference on Genetic Algorithms. Los Altos, CA: Morgan Kaufmann.

....Emanuel, 118] Fan, Alex, 751] Fang, Hsiao Lan, 627] Authors 17 Farrell, Patrick G. 27] Faulkner, T. R. 734] Feddersen, S. 797] Fersht, Alan R. 705, 821] Ficek, Rhonda Janes, 246] Field, P. 14] Filho, J. R. 534] Finch, J. W. 402] Finck, I. 636] Fitzhorn, P. [136] Fleming, Peter J. 357, 390] Fogarty, Terence C. 22, 285, 659, 315, 535, 687, 756, 536, 537, 538, 539] Fogel, David B. 164, 801, 44, 670] Fonlupt, C. 314] Fontain, Eric, 757] Foo, Han Yang, 481] Forrest, Stephanie, 323, 327] Foster, James A. 64] Fox, Robert O. 704] ....

....J. 66] Marland, C. 572] Marques, R. M. Lopes, 770] Martin, Martin C. 368] Martin, Ralph R. 24, 59] Martin, Worthy N. 521] Maslov, S. Yu. 692, 693, 694] Mason, Andrew J. 110] Mason, Andrew, 172] Mason, J. S. 248] Masters, Timothy, 575] Masuda, T. 38] Mathias, Keith E. [21, 26, 128, 136, 337] Matou sek, Radek, 316] Mattfeld, Dirk C. 196, 807] Maturana, F. 487] Mauri, G. 91] May, Alex C. W. 375] Mayne, Howard R. 102] Mayoh, Brian, 443] Mazumder, Pinaki, 147, 406] McClurkin, G. D. 529] McGarrah, D. B. 767] Medsker, C. 576] Megson, G. M. 470, 351, 488] Mehrotra, ....

[Article contains additional citation context not shown here]

Darrell L. Whitley, Keith E. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Belew and Booker [836], pages 77-84. ga:Whitley91b.

....[49, 50] Dickinson, John, 41] Doi, Hirofumi, 96] Dontas, Kejitan, 36] Eaton, Malachy, 130, 54] El Hawary, M. E. 141] Eshelman, Larry J. 59, 149] Falkenauer, Emanuel, 142] Fanelli, A. 20] Farrell, Patrick G. 14] Feltus, M. A. 13] Field, P. 89] Fiorito, N. 21] Fitzhorn, P. [87] Flores, Benjamin C. 10] Fogarty, Terence C. 98] Fogel, David B. 115] Foster, James A. 41, 43] Franich, R. E. H. 153] Franti, Pasi, 24, 32] Furuhashi, Takeshi, 73, 77, 78] Furusawa, Mitsuru, 96] Garg, S. 69] Gero, John S. 104, 108] Gerrits, Marleen, 82] Gerth, R. 109] ....

....129] Lucas, S. M. 125] Maekawa, Keiji, 62] Maeshiro, Tetsuya, 34] Maini, Harpal Singh, 100] Makki, R. Z. 61] Malgeri, M. 21] Marchette, David J. 126] Martin, Ralph R. 66, 81] Masand, Brij, 45] Mason, Andrew J. 79] Masuda, T. 106] Mathias, Keith E. 97, 101] Mathias, Keith, [84, 87] Mattfeld, Dirk C. 119] McInnes, F. R. 16, 26, 51, 30] Mehrotra, Kishan, 100] Meng, Qing chun, 17] Michalewicz, Zbigniew, 61, 148] Michielssen, Eric, 40] Mill, Frank, 122] Miller, J. A. 11, 47] Mittra, Raj, 40] Mohan, Chilukuri K. 100] Mora, Jorge Luis, 10] Muddappa, S. 61] ....

[Article contains additional citation context not shown here]

Darrell Whitley, Keith Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Belew and Booker [168], pages 77--84. ga:Whitley91b.

....experiments. GAs have traditionally used binary encodings of real numbers to perform optimization on R n [16] While binary encodings have been used to successfully solve optimization problems, special manipulation of this encoding is often necessary to increase the efficiency of the algorithm [83, 100]. There is evidence that optimization on R n can and should be performed with real parameters. Goldberg [27] provides formal arguments that floating point GAs manipulate virtual alphabets, a type of schema that is appropriate in R n . Wright [103] and Janikow and Michalewicz [46] suggests that ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Richard K. Belew and Lashon B. Booker, editors, Proceedings of the Fourth Intl. Conf. on Genetic Algorithms, pages 77-- 84. Morgan-Kaufmann, 1991.

....by the delta2 value. The rate of change of the weight and delta1 (their gradient ) is changeable due to the delta2 value. This is used to provide a heuristic second order change mechanism to the weight modification rule. This use of deltavalues is somewhat like the delta coding described in [ 11 ] Note that length of the chromosome, which becomes of the order of hundreds or thousands of bits using mechanisms such as dynamic parameter encoding (Schraudolph [ 8 ] will be shorter using this representation. By manipulating shorter chromosomes, we hope to solve larger problems using ....

D. Whitley, K.Mathias, and P.Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Proceedings of the Fourth International Conference on Genetic Algorithms, pages 77--84, San Mateo, 1991. Morgan Kaufman.

....regardless of the fitness values of either string. Incremental or one at a time reproduction guarantees that the best solutions found so far will be held undisturbed in the population until a better solution is located. This strategy has been found to perform well in a variety of applications [5, 6, 7]. However, one common drawback which often affects the incremental GA in particular is premature convergence. Generally, the parameters ( genes ) are encoded by a string (usually binary as in this paper) whose length determines not only the number of alleles over which the GA searches and the ....

....section of the gene. In this situation one strategy to obtain a highprecision result might be to use a very crude precision at first and allow the GA to converge, then reduce the search range of the parameters. This type of strategy has been used successfully by Shaefer [8] Whitley et al. [6] and Schraudolph and Belew [9] Here, a somewhat simpler approach than these was employed. An obvious possibility is to search in stages; when convergence has occurred the range of each parameter is simply halved, and a new stage commences. However, in univariate search it is wellknown that a ....

D.Whitley, K.Mathias and P.Fitzhorn (1991) Delta coding: an iterative search strategy for genetic algorithms, In Richard K. Belew and Lashon B. Booker, editors, Proc. 4th Intl. Conf. Genetic Algorithms, 77-84, Morgan Kaufmann, San Mateo, CA.

....kind of approach is effective but can be extremely slow due to the limitations of the underlying evolutionary search method many generations are required to recover from minute changes to the environment. Using an incremental approach in conjunction with a local search technique (Delta Coding; Whitley et al. 1991) to sustain diversity, we demonstrate that ESP can cope with more significant changes to the environment. Instead of evolving on the goal task directly, ESP evolves on a sequence of increasingly difficult tasks. The paper is organized as follows. Section 2 describes the ESP and Delta Coding ....

....This is a problem, especially in incremental evolution, because a converged population cannot easily adapt to a new task. To accomplish task transfer despite convergence, ESP is combined with an iterative search technique known as Delta Coding. 2. 3 Delta Coding The idea of Delta Coding [Whitley et al. 1991] is to search for optimal modifications of the current best solution. In a conventional single population GA, when the population of candidate solutions has converged, Delta Coding is invoked by first saving the best solution and then initializing a population of new individuals called ....

[Article contains additional citation context not shown here]

D. Whitley, K. Mathias, and P. Fitzhorn. Delta-coding: An iterative search strategy for genetic algortihms. In Proceedings of the Fourth International Conference on Genetic Algorithms, Los Altos, CA, 1991. Morgan Kaufmann.

.... the GA issues that are adapted throughout the GA run: adaptive parameter settings ( 32, 41, 7, 63, 11, 20, 14, 59, 60, 12, 3, 5, 38, 53, 1, 55, 34] adaptive genetic operators ( 42, 30, 31, 44] adaptive genetic operator selection ( 48, 54, 52, 62, 51] adaptive representation ([46, 61, 50]) and adaptive fitness function ( 22, 42, 35, 45] The other one, suggested by Spears ( 54] concerns the interaction between the adaptive method and the evolutive process: Tightly Coupled. The adaptation is driven by the internal forces of evolution itself. There are three levels where ....

....an interval is assumed. 4.1.3 GDMs Based on Hamming Distance Other approaches for measuring the diversity of BCGAs are based on the Hamming distance. Louis et al. 39] calculated the Hamming distance between all non redundant combinations of two strings and take an average. Whitley et al. [61]) proposed measuring the Hamming distance between the worst and the best chromosomes in the population for monitoring population diversity. 4.1.4 GDMs Based on Euclidean Distance For real coded GAs, it seems interesting to dispose of GDMs based on the Euclidean distance between chromosomes. We ....

D. Whitley, K. Mathias, P. Fitzhorn, Delta coding: an iterative search strategy for genetic algorithms, in: R. Belew, L.B. Booker, Ed., Proc. of the Fourth Int. Conf. on Genetic Algorithms (Morgan Kaufmmann, San Mateo, 1991) 77-84.

....over R n . Traditionally, researchers have used GAs with binary coded genes that are decoded into real values to solve this problem [De Jong, 1975] However, special manipulation of this encoding is often necessary to increase the efficiency of the algorithm [Schraudolph and Belew, 1992, Whitley et al. 1991] Recent research on real coded GAs suggests that they can be more efficient, provide increased precision, and allow for genetic operators that are more appropriate for a continuous domain [Eshelman and Schaffer, 1993, Janikow and Michalewicz, 1991, Wright, 1991] Two different types of ....

Whitley, D., Mathias, K., and Fitzhorn, P. (1991). Delta coding: An iterative search strategy for genetic algorithms. In Belew, R. K. and Booker, L. B., editors, Proc. of the Fourth Intl. Conf. on Genetic Algorithms, pages 77--84, San Mateo, CA. Morgan-Kaufmann.

....function changes rapidly, a longer string would be desirable. But this would be a waste where it is not needed, increasing the search space unnecessarily. Related work on the use of special encoding schemes for function optimisation includes Dynamic Parameter Encoding by [SB92] Delta Coding by [WM91]. Both pieces of work try to address the aforementioned problem using fixed length binary strings. The method presented in this paper suggests an alternative way of doing it. Dynamic Parameter Encoding Dynamic Parameter Encoding (DPE) successively reduces the search domain under consideration ....

....which it is not possible to recover. Delta coding Delta coding (DC) is a simple search strategy based on the idea that the encoding used by genetic algorithms can express a distance away from some previous partial solution. DC values are added to a partial solution before evaluating the fitness. [WM91] The information used in Delta coding represent distances from the current reference point. To produce some value, the encoding is added to the current solution, which is like probing a region near to the current point. As Delta values are small the resulting solution can have high precision ....

D. Whitley and K. Mathias. Delta coding: An iterative search strategy for genetic algorithms. In Richard K. Belew and Lashon B. Booker, editors, Proceedings of the fourth international conference on Genetic Algorithms, pages 77--84, Univ. of California, San Diego, 1991. Morgan Kaufmann Publichers.

....chosen R. An obvious and common example is object spaces that involve real numbers. The computational process is restricted to dealing with that part of O that is representable with the choice of R. There is of course nothing to stop the process from adopting a new R at any point, for example see [25, 31, 34, 39]. The objects in O are of interest for some reason or reasons, and we will suppose that the degree to which an object is interesting or desirable can be expressed as a single real value. This is commonly called the fitness of the object in question. We will denote the fitness of an object a 2 R by ....

Whitley, D., Mathias, K. and Fitzhorn, P. [1991], "Delta Coding: An Iterative Search Strategy for Genetic Algorithms" In Richard K. Belew and Lashon B. Booker (Eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, pp. 77--84.

....the representation of a genetic algorithm based on levels of allele convergence and variance. 15] s dynamic parameter encoding (DPE) adaptively adds precision to the representation as their genetic algorithm converges on a single value for any l bit gene. Similarly, the delta encoding method of [16] uses the Hamming distance between the best and worst strings in the population to determine when to adjust the interpretation of a genetic algorithm s representation. When this value falls below one, the representation is modified to search an appropriately smaller region of the search space. All ....

D. Whitley, K. Mathias, and P. Fitzhorn, "Delta coding: an iterative search strategy for genetic algorithms", Proc. of the Fourth International Conference on Genetic Algorithms, R. K. Belew and L. B. Booker (eds.), San Mateo, CA: Morgan Kaufmann, pp 77-84, 1991.

....parameters, often with heuristics computed over the current or past populations. Such methods include updating the global frequency of operator application [Rechenberg 1973; Davis 1989] and dynamically adjusting the interpretation of the representation [Shaefer 1987; Schraudolph and Belew 1992; Whitley, Mathias and Fitzhorn 1991]. Individuallevel adaptations associate parameters with each individual that determine how the algorithm manipulates the individual. Examples include evolving crossover positions in genetic algorithms [Rosenberg 1967; Schaffer and Morishima 1987] and adapting the relative probability of ....

Whitley, D., Mathias, K. and Fitzhorn, P. (1991) Delta coding: an iterative search strategy for genetic algorithms.

....there is no indicator for the presence of a global optimum outside the search space. Two more approaches closely related to ARGOT and DPE have recently come to our attention: the Adaptive Search Space Scaling algorithm applied to medical image registration [8] and the technique of Delta Coding [12]. Like ARGOT, these methods employ a form of inverse zoom that makes implicit assumptions (such as piecewise monotonicity) about the function being searched, thus sacrificing generality for performance. By contrast, the heuristic DPE employs for deciding when to trigger a zoom operation is based ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Richard K. Belew and Lashon B. Booker, editors, Proc. 4th Intl. Conf. Genetic Algorithms, pages 77--84, San Mateo, CA, 1991. Morgan Kaufmann.

....for dealing with this difficulty if to use matrices instead of vectors. There are matrix genetic operators [6] but generalizing them to n dimensions is not practical. An alternative approach is to learn the second attribute function on top of the first, e.g. a delta coding genetic algorithm [21]. We learn the second attribute function in a manner similar to the first attribute, except that performance is evaluated using a linear combination of the two functions. The learning is repeated in search of the best combining coefficient, keeping the first attribute function constant. ....

D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In Proc. of the Fourth International Conference on Genetic Algorithms, pages 77--85, San Diego, CA, 1991.

....what it means to have a good representation. Also, very little has been done in the way of adaptive representations, with the exception of messy GAs (Goldberg, 1991) Argot (Shaefer, 1987) the dynamic parameter encoding (DPE) scheme of Schraudolph and Belew (1992) and the Delta coding of Whitley et al. 1991). Messy GAs, Argot, DPE, and Delta coding all attempt to manipulate the granularity of the representation, thus focusing search at the appropriate level. Despite some initial success in this area, it is clear that much more work needs to be done. 3.5 Adaptive EAs Despite some work on adapting ....

Whitley, D., Mathias, K., & Fitzhorn, P. (1991) Delta coding: an iterative search strategy for genetic algorithms. Proceedings of the Fourth International Conference on Genetic Algorithms, 77-84. La Jolla, CA: Morgan Kaufmann.

....diversity. This is a problem, especially in incremental evolution, because a converged population cannot easily adapt to a new task. To accomplish task transfer despite convergence, ESP is combined with an iterative search technique known as Delta Coding. 4. 3 Delta Coding The idea of Delta Coding (Whitley et al. 1991) is to search for optimal modifications of the current best solution. In a conventional single population GA, when the population of candidate solutions has converged, Delta Coding is invoked by first saving the best solution and then initializing a population of new individuals called ....

....distribution for ff = 0:5. Most of the Delta values represent small modifications to the best solution, but large values are also possible. Delta chromosomes are added to the best solution to form the new best solution for the next iteration of the Delta phase. Delta Coding was developed by Whitley et al. 1991) to enhance the fine local tuning capability of Genetic Algorithms for numerical optimization. However, its potential for adaptive behavior lies in the facilitation of task transfer. Delta Coding provides a mechanism for transitioning the evolution into each progressively more demanding task: t 1 ....

Whitley, D., Mathias, K., and Fitzhorn, P. (1991). Delta-coding: An iterative search strategy for genetic algortihms. In Proceedings of the Fourth International Conference on Genetic Algorithms. Los Altos, CA: Morgan Kaufmann.

....global optimum. Since during each run the action interval of the parameters is limited, the precision shall be more refined. Two techniques based on this idea for refining precision have been proposed: ARGOT (Shaefer, 1987) dynamic parameter encoding (Schraudolph et al. 1992) and delta coding (Whitley et al. 1991). An effect that appears using the binary alphabet for representing elements in continuous domains is the so called Hamming cliff. It is produced when the binary coding of two adjacent values differs in each one of their bits, for example, the strings 01111 and 10000 represent the values 31 and ....

Whitley, D., Mathias, K. & Fitzhorn, P. (1991). Delta Coding: An Iterative Search Strategy for Genetic Algorithms. Proc. of the Fourth Int. Conf. on Genetic Algorithms, R. Belew and L.B. Booker (Ed.) (Morgan Kaufmmann, San Mateo), 77-84.

No context found.

Whitley, D., Mathias, K., Fitzhorn, P. (1991) "Delta Coding: An Iterative Search Strategy for Genetic Algorithms." Proc. of the 4 th Int'l. Conf. on Genetic Algorithms. Washington, D.C., Morgan Kaufmann.

No context found.

Whitley, D., Mathias, K. and P. Fitzhorn, 1991. "Delta Coding: An Iterative Search Strategy for Genetic Algorithms" - In Proceedings of the Fourth International Conference on Genetic Algorithms - Belew, R. and Booker, L.B. (eds.) - pp.77-84.

No context found.

D. Whitley, K. Mathias, and P. Fitzhorn, 1991a. Delta coding: An iterative search strategy for genetic algorithms. In Proceedings of the Fourth International Conference on Genetic Algorithms. Morgan Kaufmann (San Mateo).

No context found.

L. D. Whitley, K. Mathias, and P. Fitzhorn. Delta coding: An iterative search strategy for genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 77--84, San Mateo, CA, 1991. Morgan Kaufmann.

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