Radcliffe N J (1992) Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259-268. Morgan Kaufmann.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the expectation of the number of schema representatives can be replaced by its actual value in (4) one obviously conclude that schemata with above average fitness ( f(H; n) f( n ) tend to colonize the population. The usefulness of the Schema Theory has been seriously questioned [52, 93, 71, 63, 19, 97, 36, 22]. One of the main limitations of the Schema theory is that it is only valid for one generation prediction and cannot be iterated more than once (as it maps a schemata into the next expected one only) hence cannot be used for studying the long term behavior. Recent work [17, 84, 85, 96] prove a ....

N. J. Radcliffe. Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259--268. Morgan Kaufmann, 1992.

....might ask what advantages a formulation based on schemata, as presented here, has over other existing formulations such as the Vose Markov chain model. Indeed, the value of schemata and the Schema theorem in understanding GA evolution has been seriously questioned (Grefenstette, 1989; Vose, 1991; Radcliffe, 1992; M uhlenbein, 1991) There are many possible answers to this question: first a pragmatic one that all things are made out of building blocks, whether they be tables, giraffes or computer programs. Having an exact, amenable description of complex systems from the microscopic point of view is a ....

Radcliffe, N. J. (1992). Non-Linear Genetic Representations. In M anner, R. and Manderick, B., editors, Parallel Problem Solving from Nature 2, pages 259--268, North Holland, Amsterdam, Netherlands.

....[270] Phon Amnuaisuk, Somnuk, 95] Postaire, Jack G erard, 279] Potter, Mitchell A. 82] Preux, Philippe, 167] Probert, Penelope, 124, 188] Proenca, Luis Miguel, 21, 24, 26] Punch, William F. 55, 84] Punch, III, William F. 49, 79] Pyylampi, Tero, 101, 294] Radcliffe, Nicholas J. [111, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365] Ranito, J. V. 21] Rasanen, Petri, 121] Raymer, Michael L. 55, 84] Reeves, Colin R. 126, 138, 215] Romaniuk, Steve G. 366] Rooij, A. J. F. Van, 64] Rosca, Justinian, 281] Rost, Ursula, 272] Rowe, Jon, 169, 229] Ryan, Conor, 287] Ryynanen, Matti, 127, 230, 240, 291] Saarinen, ....

.... [102] protection relays, 292] protein folding, 220, 75] lattice model, 53, 96] proteins docking, 36] interaction, 55] ligands, 208, 84] psychology motivation, 67] rapid prototyping, 265] recombination, 355, 359, 321, 360, 365] redundancy GP, 110] REM, 96] representations, [361, 362] review, 315, 115] applications, 69] designing neural networks, 179] fundamentals, 304] GA research volume, 251] GA SA hybrids, 319] image processing, 259] optimization, 367] parallel GA, 150, 187] research topics, 305] training neural networks, 179] robotics, 310, 326, 327, ....

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Nicholas J. Radcliffe. Non-linear genetic representations. In Manner and Manderick [430], pages 259--268. (also as [362]; ftp.epcc.ed.ac.uk: /pub/tr/92/ tr9204.ps.Z) Key: ga:Radcliffe92a.

....[393] Poon, P. W. 554] Porter, B. 37] Porto, Vincent W. 555] Potter, M. A. 452] Potter, Walter D. 685, 686] Prabhu, Obili S. 631] Prados, D. L. 556] Preis, K. 268] Pryor, R. J. 557, 558] Qi, Xiaofeng, 559, 560, 561] Rabitz, Herschel, 363] Radcliffe, Nicholas J. [572, 573, 574, 575] Rahmani, Adel Torkaman, 533] Rajeev, S. 576] Ranjithan, S. 569] Rasmussen, Steen, 577] Ravichandran, B. 17] Rawlins, Gregory J. E. 444] Ray, Lawrence A. 98] Ray, Thomas S. 578, 579, 580] Reed, R. 570] Reeves, Colin R. 581, 582] Renders, Jean Michel, 10] Reynolds, ....

.... 507, 508, 620, 621, 15] psychology decision making models, 383] QAP, 213, 463, 528, 707] quality, 157] quality control, 308] random number generators, 32, 84] real coding, 245] recombination, 103, 299, 300, 572] discontinuous, 527] report of activities, 219] representations, [573, 574] response surface changing, 271] review, 19, 22, 70, 72, 74, 159, 178, 239, 1, 322, 323, 327, 335, 385, 395, 420, 461, 615, 695, 9] review artificial life, 431] Davidor, 25] GA and neural networks, 582, 697, 704] GA SA hybrids, 250] in Italian, 171] optimization, 624] process ....

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Nicholas J. Radcliffe. Non-linear genetic representations. In Manner and Manderick [539], pages 259--268. (also as [574]; available via anonymous ftp cite ftp.epcc.ed.ac.uk directory /pub/tr/92 file tr9204.ps.Z ) ga:Radcliffe92a. Bibliography 55

....2 g strings in the search space. Hence, there are 2 g possible representations of the search space corresponding to the different invertible mappings from the search space to the set of all length g binary strings. Since the Fundamental Theorem applies to any such representation, Radcliffe [17] argues that selecting one randomly cannot preserve information and that, hence, the genetic algorithm cannot be expected to perform better than random search. Radcliffe concludes: The critical point to note from this discussion is not that the genetic search can do no better than random search ....

Radcliffe, N. J., "Non-linear Genetic Representations," Parallel Problem Solving from Nature, eds. R. Mnner and B. Manderick, 2, 1992, North Holland, pp. 259268.

....p. 106] 7] which have been contradicted with empirical evidence in [3] 4] 8] 10] and many others) 2) the idea that the schema theorem suggests that genetic algorithms offer a near optimal procedure for searching among alternative solutions (e.g. 6, p. 38] which was discounted in [11] (also see [12] where it was shown that the schema theorem holds even when the schemata defined by a representation may not capture the properties that determine fitness, and moreover the theorem does not apply to schemata not included in the current population (i.e. it does not address the ....

N.J. Radcliffe, "Non-Linear Genetic Representations," Parallel Problem Solving from Nature 2, R. Mnner and B. Manderick (eds.), North-Holland, The Netherlands, pp. 259268, 1992.

....solutions of related fitness is mean forma variance. By generating random formae of a particular size and measuring the fitness variance within them, we can estimate the mean variance for formae of a given size. This was shown to be a good qualitative indicator of relative algorithmic performance (Radcliffe Surry, 1994b) 120 For Dedekind representation, all formae are convex simplices R m in bounded by hyper planes perpendicular to the coordinate axes, while for the Isodedekind representation formae are convex simplices bounded by arbitrary hyper planes. In order to investigate analytically the forma variance ....

N. J. Radcliffe, 1992b. Non-linear genetic representations. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam).

....recombination operators on genotypic encodings (see for example [11] 40] and [5] visualizing the landscapes for genotypic EAs is very difficult. Thus we use a phenotypic representation as it is easier to identify the features of the landscape and tailor the recombination operator to them (both [38] and [27] also find the phenotypic space easier to work with) On a phenotypic landscape there are at least three ways in which a recombination operator can be tuned to a landscape: directionality, using knowledge about the landscape to limit the directions in which offspring are located from the ....

....No Free Lunch theorems for search which provide theoretical limitations on any operator. Even though the majority of work in EAs has used a binary encoding and operators there are those who have used non binary representations with non traditional operators and found them to work better. In [38], Radcliffe argues that the conventional binary operators and encoding are ill suited to many problems. Comparisons between EAs on real valued functions have generally shown the algorithm using the real valued encoding gives better results (see [27] 50] and [12] Graph problems, such as the ....

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Nicholas J. Radcliffe. Non-linear genetic representations. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature, 2, pages 259--268. North-Holland, 1992.

....These difficulties would seem to rule out the use of a traditional GA; at any rate no promising results using such an approach have been reported. 3.2 q ary coding Early work on GAs had emphasized binary coding, virtually to the exclusion of any other representation. However, recently Radcliffe [23] and others [24, 25] have made a strong case for the appropriate use of non binary codings. Certainly, in many problems binary coding would not appear to be a sensible procedure, and a q ary coding i.e. using an alphabet of q( 2) characters is more appropriate. However, in COPs, the same type ....

N.J.Radcliffe (1992) Non-linear genetic representations. In R.Manner and B.Manderick (Eds.) (1992) Parallel problem-Solving from Nature 2. Elsevier Science Publishers, Amsterdam.

....concept of a schema to include sets of individuals whose alleles belong to particular subsets of allele values for each gene. This dramatically increases the number of schemata represented by any individual. As part of more generalised characterisations of GA processing, Vose [52] and Radcliffe [40,41,42,43,44,45] independently stretched schemata even further by adopting completely generalised views under which any arbitrary subset of individuals may be viewed as constituting a schema. Although these two developments represent an alternative approach to Holland s, it is certainly true that these ....

....failed in his attempt to show that such an algorithm could consistently outperform classical optimisation procedures. As our last illustration of the weaknesses in schema processing arguments, consider the GA s processing on a problem where the individuals have been assigned random fitnesses [34,43,47]. Now, clearly no algorithm can solve this problem efficiently, irrespective of the degree of schema processing or intrinsic parallelism employed by the algorithm. 9 Focus on Exploration If progress is to be made in our understanding of the GA it is essential that the focus of research move away ....

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Radcliffe, N.J., "Non-Linear Genetic Representations," in [31] (1992)

....promising results using such an approach have been reported. 4. 2 q ary coding Early work on GAs had emphasized binary coding, virtually to the exclusion of any other representation (the permutation coding for the TSP and similar problems was very much a special case) However, recently Radcliffe [24] and others [25, 26] have made a strong case for using non binary codings in many problems. Using a q ary (q 2) alphabet to encode a bin packing problem seems a natural approach, but as we pointed out above (section 3.1) it is in fact full of pitfalls. The example given there used 1 point ....

N.J.Radcliffe (1992) Non-linear genetic representations. In R.M¨anner and B.Manderick (Eds.) (1992) Parallel problem-Solving from Nature 2. Elsevier Science Publishers, Amsterdam.

....even here it would also be useful if one could identify particular varieties of epistasis. If one could detect problems of a deceptive nature, for instance, one might suggest using an approach such as the messy GA of [9, 10] There is another aspect to this too: it is well known (see e.g. [7, 11]) that the coding used for a GA may be of critical importance in how easy it is to solve. In fact (as we shall also demonstrate later) a particular choice of coding may render a simple linear function epistatic. Conversely, by choosing a different coding, it may be possible to reduce the degree of ....

....him Goldberg [15] stressed the advantage of a binary alphabet, in that it allows the sampling of the maximum number of schemata per individual in the population. More recently, Antonisse has put forward a counter argument in [17] by redefining the concept of a schema, while Radcliffe s work [11] makes a very similar point. On the other hand, Reeves [18] has recently argued that there are certain theoretical advantages in using binary coding in cases where GAs need to be limited to a small number of function evaluations. An ED approach throws a further interesting sidelight on the ....

N.J.Radcliffe (1992) Non-linear genetic representations. In R.Manner and B.Manderick (Eds.) (1992) Parallel problem-Solving from Nature 2. Elsevier Science Publishers, Amsterdam.

....1995] Generalized schemata can be defined by partitioning the space of structures with many other relations. Such attempts have been presented in the GA literature [Vose and Liepins, 1991; Radcliffe, 1991] Relations analogous to the schema theorem will hold for other representations as well [Radcliffe, 1992]. Indeed, schema theory explains the proliferation of substructures through selection but this fact is indicative more of when a schema hypothesis can be refuted. An argument for this remark is the intended use of Price s covariance and selection theorem [Price, 1970] Price s theorem states that ....

Nicholas J. Radcliffe, "Non-linear Genetics Representations," In R. M fagnner and B. Manderick, editors, Parallel Problem Solving from Nature, 2. Elsevier Science Publishers, 1992.

....are being used in a genetic search. 3 GA Neighbourhoods In what follows, we shall assume that x is binary vector of length n. The i th bit of x will be denoted by x i . The set X is thus a subset of the n dimensional hypercube f0; 1g n . We recognize that there is a continuing debate see [21, 22] for example as to the desirability or otherwise of using binary coding. However, binary encoding is still commonly used in applications of GAs, and it makes the exposition of the concepts we shall develop somewhat easier. Nevertheless, the ideas discussed below are clearly capable of being ....

N.J.Radcliffe (1992) Non-linear genetic representations. In [43].

....tested for an instance of a real problem with 525 events and results show that the selfish and co operative mutation operators are useful to increase the quality of the algorithm presented. A recombination operator based on the Forma Theory of memetic algorithm introduced by Radcliffe et al. in [Radcliffe 92] called respect amd assortment produces what Paechter calls an ancestral memory. The idea is to produce a suggestion list for each child which keeps an ancestral tree (from parents, grandparents, etc) of suggestions. The intention then is to keep and use the information gained by the ancestors ....

Nicholas J. Radcliffe. Non-linear genetic representations. In Manner and Manderick, editors, Proceedings of Parallel Problem Solving from Nature, pages 259--268. Elsevier, 1992.

....for the representation solution have dominated GA research since there are theoretical results that show them to be the most appropriate ones (Goldberg, 1991a) and as they are amenable to simple implementation. But the GA s good properties do not stem from the use of bit strings (Antonisse, 1989; Radcliffe, 1992). For this reason, the path has been lain toward the use of non binary representations more adequate for each particular application problem. One of the most important ones is the real number representations, which would seem particularly natural when optimization problems with variables in ....

....for the representation solution have dominated GA research since there are theoretical results that show them to be the most effective ones (Goldberg, 1991a) and as they are amenable to simple implementation. But the GA s good properties do not stem from the use of bit strings (Antonisse, 1989; Radcliffe, 1992). This reason motived in many cases that GA practitioners devised non binary representations, accompanied of genetic operators, more natural for the specific application problems. Examples of such cases are the following: Gamma vectors of floating point numbers, for chemometric problems ....

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Radcliffe N.J. (1992). Non-Linear Genetic Representations. Parallel Problem Solving from Nature 2, R. Manner and B. Manderick (Ed.), (Elsevier Science Publichers, Amsterdam), 259-268.

....in Foundations of Genetic Algorithms III , Ed: L.D. Whitley, M.D. Vose, Morgan Kaufmann (San Mateo) pp51 72, 1994. Fitness Variance of Formae and Performance Prediction Nicholas J. Radcliffe njr epcc.ed.ac.uk Edinburgh Parallel Computing Centre University of Edinburgh King s Buildings EH9 3JZ Scotland Patrick D. Surry pds epcc.ed.ac.uk Edinburgh Parallel Computing Centre University of Edinburgh King s Buildings EH9 3JZ Scotland Abstract Representation is widely ....

Nicholas J. Radcliffe, 1992. Non-linear genetic representations. In R. M anner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam).

....attracted much interest. Although some theoretical progress has been made in the study of stochastic search techniques, most attention has focused on the artificial situation of arbitrary ( blackbox ) search problems. Despite occasional warnings from various researchers (Vose Liepins, 1991; Radcliffe, 1992, 1994; Wolpert Macready, 1995) a great deal of research seems oblivious to the fact that in such a situation there is no scope for distinguishing any of these biased sampling methods from enumeration random or fixed as we demonstrate below. There are exceptions to this, for example the ....

....stochastic search algorithms, particularly evolutionary algorithms, and emphasizes that there are many possible improvements that are not strongly limited by the theorems. A more accessible and general form of the No Free Lunch Theorem is first presented, based on arguments put forward previously (Radcliffe, 1992, 1994) Strictly, this result shows that over the ensemble of all representations of one space with another, all algorithms (in a rather broad class) perform identically on any reasonable measure of performance. This has as an immediate corollary the No Free Lunch Theorem, and provides an ....

N. J. Radcliffe, 1992. Non-linear genetic representations. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers /North Holland (Amsterdam).

....re states the features of schema analysis that have motivated the development of forma analysis and connects the necessarily rather formal content of the body of this paper to practical problems encountered when using genetic algorithms. Its content is similar to but less detailed than that of Radcliffe (1992b) Section 3 formally introduces equivalence relations, which are central to forma analysis, together with a certain amount of associated notation. Readers already familiar with equivalence relations and forma analysis may wish to proceed directly to definition 1 in section 3 after this ....

....section 3) that partition the search space into appropriate equivalence classes which play the role of formae. Having achieved this, the task addressed is the construction of a genetic representation and operators for searching the given space effectively. 3 Background on Equivalence Relations Radcliffe (1990,1992b) has shown that domain specific knowledge must be utilised if a genetic algorithm is to have any opportunity to exceed the performance of an enumerative search. In schema analysis, this knowledge is used implicitly in the construction of an appropriate genetic representation. The way in which ....

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Radcliffe, 1992b. Nicholas J. Radcliffe. Non-linear genetic representations. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam), 1992.

....in the subset and apply appropriate genetic operators directly. In this case the elements themselves can form alleles, and approaches as simple as choosing the desired number of elements from those available between the parents can be effective. This method happens to equate to use of RAR 0 (Radcliffe, 1992b) Forma analysis for set problems is covered extensively in Radcliffe (1992a) General Representations It has been argued in the preceding sections that there are theoretical, practical and empirical motivations for moving away from the very simple binary string representations that have ....

....case the elements themselves can form alleles, and approaches as simple as choosing the desired number of elements from those available between the parents can be effective. This method happens to equate to use of RAR 0 (Radcliffe, 1992b) Forma analysis for set problems is covered extensively in Radcliffe (1992a) General Representations It has been argued in the preceding sections that there are theoretical, practical and empirical motivations for moving away from the very simple binary string representations that have dominated genetic algorithms for so long. Combined with the successes shown by ....

Radcliffe, 1992b. Nicholas J. Radcliffe. Non-linear genetic representations. In R. M anner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam), 1992.

.... immune system (Smith et al. 1992) The niching techniques range from the explicit crowding schemes suggested by DeJong (1975) and 1 We will not revisit the arguments over the alleged superiority of binary representations here but refer the interested or sceptical reader to Radcliffe (1994) and Radcliffe (1992b) for respectively more and less technical theoretical discussions of this issue and Davis (1991) for empirical evidence that complex non binary representations work at least as well as their binary counterparts. fitness sharing mechanisms introduced by Goldberg Richardson (1987) Goldberg et ....

.... even for strict optimisation problems (Muehlenbein, 1989) A higher level genetic algorithm will then take rules generated by the lower level algorithms and use them as basic genetic material from which to form sets of rules using techniques for genetic set based optimisation developed by Radcliffe (1992a) More precisely, rules will be taken from each of the low level populations to form a universal set of rules from which it will be the task of the high level genetic algorithm to find the best set of some given size for example, the best set of twenty rules. Notice that this is not to say ....

[Article contains additional citation context not shown here]

Radcliffe, 1992b. Nicholas J. Radcliffe. Nonlinear genetic representations. In R. M anner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam), 1992.

.... Variance of Formae and Performance Prediction Nicholas J. Radcliffe njr epcc.ed.ac.uk Edinburgh Parallel Computing Centre University of Edinburgh King s Buildings EH9 3JZ Scotland Patrick D Surry pds epcc.ed.ac.uk Edinburgh Parallel Computing Centre University of Edinburgh King s Buildings EH9 3JZ Scotland Abstract Representation is a widely recognised key ....

Nicholas J. Radcliffe, 1992. Non-linear genetic representations. In R. M anner and B. Manderick, editors, Parallel Problem Solving from Nature 2, pages 259--268. Elsevier Science Publishers/North Holland (Amsterdam).

No context found.

Radcliffe N J (1992) Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259-268. Morgan Kaufmann.

No context found.

Radcliffe N J (1992) Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259-268. Morgan Kaufmann.

No context found.

N. J. Radcliffe. Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259-268. Morgan Kaufmann, 1992.

No context found.

N. J. Radcliffe. Nonlinear genetic representations. In R. Manner and B. Manderick, editors, Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pages 259-268. Morgan Kaufmann, 1992.

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