N.J.Radcliffe. Equivalence class analysis of genetic algorithms. In Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... in conventional genetic search (for example, single parameter optimisation) and it has been strongly argued elsewhere the problem is highly detrimental to the effectiveness of the search process both in the specific context of neural networks [Radcliffe 1990] Belew 1990] and more generally [Radcliffe 1991a] Radcliffe 1991c] Radcliffe develops the notion of formae (in their original conception formae were introduced as equivalence classes induced by arbitrary equivalence relations over the search space) to deal with this problem. The counting arguement used to suggest that binary ....

N. J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems. 5(2):183- 205, 1991.

.... of solutions (but see [99] for an alternative view, and [100] for a transfer of schema theory to S expression representations used in genetic programming) Practical experience, as well as some theoretical hints regarding the binary encoding of continuous object variables [101] 102] 103] [104], 105] however, indicate that the binary representation has some disadvantages. The coding function might introduce an additional multimodality, thus making the combined objective function f = f ffi h (where f : M IR) more complex than the original problem f was. In fact, the ....

N. J. Radcliffe, "Equivalence class analysis of genetic algorithms, " Complex Systems, vol. 5, no. 2, pp. 183--206, 1991.

....There have been some debates on the cardinality of the genotype alphabet. Some have argued that the minimal cardinality, i.e. the binary representation, might not be the best [48] 114] Formal analysis of nonstandard representations and operators based on the concept of equivalent classes [115], 116] has given representations other than ary strings a more solid theoretical foundation. Real numbers have been proposed to represent connection weights directly, i.e. one real number per connection weight [27] 29] 30] 48] 63] 65] 74] 95] 96] 102] 110] 111] 117] ....

N. J. Radcliffe, "Equivalence class analysis of genetic algorithms, " Complex Syst., vol. 5, no. 2, pp. 183--205, 1991.

....sections to characterise the working of the genetic algorithm from a formal point of view. There are many formal versions based on other characterisations, e.g. overviews and set based in [Gol89, HB92, Hol92a] as well as algebra based, notably by Radcliffe and Surry [Rad91, Rad93, Rad94a, Rad94b] In a way similar to Hoffmeister and Bck in [HB92] a genetic algorithm GA can be modelled as a 5 tuple GA = INT (Z) # (4.44) using the symbols introduced in the preceding section. However, this model is static in nature, and does not take into account the more interesting dynamic ....

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. In Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1994.

....introduced in the preceding sections to characterise the working of the genetic algorithm from a formal point of view. There are many formal versions based on other characterisations, e.g. overviews and set based in [Gol89, HB92, Hol92a] as well as algebra based, notably by Radcliffe and Surry [Rad91, Rad93, Rad94a, Rad94b] In a way similar to Hoffmeister and Bck in [HB92] a genetic algorithm GA can be modelled as a 5 tuple GA = INT (Z) # (4.44) using the symbols introduced in the preceding section. However, this model is static in nature, and does not take into account the ....

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, pages 183--205, Vol. 5, No. 2, 1991.

....Mills, Graham, 21, 22] Mitchell, Melanie, 35, 36, 37, 53, 54, 60, 61] Montana, David J. 68] Moriarty, David, 67] Muntean, Traian, 86, 87] Naillon, Martine, 24] Napliotis, Nicholas, 56] Ostermeier, Andreas, 69] Perkins, Sonya, 21] Petridis, V. 8, 18] Radcliffe, Nicholas J. [9, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81] Romaniuk, Steve G. 82] Santib a nez Koref, Ivan, 29, 30] Saravanan, N. 4] Schwefel, Hans Paul, 83] Silva, A. De, 22] Surry, Patrick, 9] Tackett, Walter Alden, 84] Talbi, El Ghazali, 85, 86, 87, 88, 89, 90] Tarroux, Philippe, 10] Thornton, Chris, 15] Voigt, Hans Michael, ....

....subject keywords of the papers given by the editor of this bibliography are shown next. The keywords neural networks , optimization , and evolution strategies have been omitted in this list because of their high occurrence rate. aerospace, 22] ALECSYS, 31, 34] algebra, 79] analyzing GA, [70, 71, 72, 74, 37] artificial life, 36] automata network, 10] bibliography evolutionary computing, 4] parallel GA, 7] Boltzmann tournament, 62] building blocks hypothesis, 35] CAD, 9] cell regulation proteins, 10] cellular automata, 60, 61] chaos, 60] classifiers, 31] comparison branch and ....

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Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5(2):183--205, 1991. (also as

....list contains references to all papers published as technical reports. The list is arranged in alphabetical order by the name of the institute. Aristotle University of Thessaloniki, 7] Bolt Beranek and Newman, 68] California Institute of Technology, 23] Edinburgh Parallel Computing Centre, [9, 70, 72, 73, 75, 78, 79] Florida Atlantic University, 4] International Computer Science Institute, 33, 34] International Computer Science Institute (ICSI) 31] Iowa State University, 55] Mitsubishi Electric Research Laboratories, 26] National University of Singapore, 82] Santa Fe Institute, 36, 60, 61] ....

....Mills, Graham, 21, 22] Mitchell, Melanie, 35, 36, 37, 53, 54, 60, 61] Montana, David J. 68] Moriarty, David, 67] Muntean, Traian, 86, 87] Naillon, Martine, 24] Napliotis, Nicholas, 56] Ostermeier, Andreas, 69] Perkins, Sonya, 21] Petridis, V. 8, 18] Radcliffe, Nicholas J. [9, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81] Romaniuk, Steve G. 82] Santib a nez Koref, Ivan, 29, 30] Saravanan, N. 4] Schwefel, Hans Paul, 83] Silva, A. De, 22] Surry, Patrick, 9] Tackett, Walter Alden, 84] Talbi, El Ghazali, 85, 86, 87, 88, 89, 90] Tarroux, Philippe, 10] Thornton, Chris, 15] Voigt, Hans Michael, ....

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Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Technical Report TR-90-03, Edinburgh Parallel Computing Centre, 1990. (also as [74]; available via anonymous ftp cite ftp.epcc.ed.ac.uk directory /pub/tr/90 file tr9003.ps.Z) ga:Radcliffe90a.

..... Since length is variable, the chromosomes defined here are very different from those used with classic genetic algorithms. For this reason we needed to define new genetic operators to match their structure. The crossover operators need to have a property defined by Radcliff and termed respect ([10]) This prop 412 erty says that all children must inherit all the common genes of their parents. Figure 2 shows the way a crossover verifying this property for variable length chromosomes works : the common genes (here R1) are first copied in the children; then, a site is randomly chosen on ....

N. J. Radcliffe, "Equivalence class analysis of genetic algorithms ", in Complex Systems, vol. 5, pp. 183--205. 1991.

....do not necessarily capture relationships among meaningful properties that determine fitness [Altenberg, 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 ....

....and complexity penalty ffl Alternative approaches for imposing parsimony pressure The rooted tree schema property Generalized schemata can be defined by partitioning the space of structures with other relations. Such attempts have been presented in the GA literature [Vose and Liepins, 1991; Radcliffe, 1991] Next we propose a simple structural property that defines a different type of partitioning of the space of programs. The space of programs will be partitioned based on the topmost structure of trees. We will call the relation induced by this property a rooted tree schema or tree schema. The ....

Nicholas J. Radcliffe, "Equivalence Class Analysis of Genetic Algorithms, " Complex Systems 5, (2):183--205, 1991.

....ES, and as possibly harmful for EP. The modern tendencies are more pragmatic, and put the discussions back to the representation issue: GAs users have turned to real number representations when dealing with real numbers, following experimental results by [JM91] and heuristic demonstrations by [Rad91]. ESs researchers have included recombination as a standard operator, as in [Sch81] and are designing specific operators for non real valued problems (e.g. in [BS95] And EP is being used on any representation, as for instance by [Ang93, FS95] But the whole EC community now takes for granted ....

N. J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5:183--20, 1991.

....and Artificial Intelligence, 134] Artificial Intell. Eng. 234] Artificial Intelligence, 398, 424] Assem Autom, 350] Atmospheric Environment Part A General Topics, 488] Automotive Engineer, 616] Br. Telecommun. Eng. UK) 15] CC AI, 531] CIRP Ann. 46] Complex Systems, [677] Comput Control Eng. J. 333] Comput. Econ. Netherlands) 307] Comput. Geosci. UK) 41] Comput. Graph. UK) 337] Comput. Methods Appl. Mech. Eng. 188] Computer, 150] Computers Industrial Engineering, 324] Computers Operations Research, 264, 300, 345] Computing (UK) 710] ....

....344, 359, 364, 369, 370, 372, 373, 665, 666] Prager, Richard, 16] Probert, Penelope, 58, 331] Prosser, P. 185] Prugel Bennett, A. 51] Purchase, G. 427] Purvis, A. 645, 646] Pye, C. J. 266] Quick, R. J. 423] Quinn, L. 353, 668] Rabelo, L. C. 324] Radcliffe, Nicholas J. [18, 80, 93, 134, 148, 11, 437, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684] Rafiq, Y. 413] Rakowski, Tomasz, 295] Rana, A. S. 268] Rastogi, M. 318] Rattray, M. 51] Rayne, C. M. 79] Raywardsmith, V. J. 310] Rayward Smith, V. J. 329, 423] Rayward Smith, Vic J. 105, 54, 81, 233, 541, 542] Redmill, D. W. 286] Reeves, Colin R. 82, 135, 149, ....

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Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5(2):183--205, 1991. (also as [672]; available via anonymous ftp cite ftp.epcc.ed.ac.uk directory /pub/tr/90 file tr9003.ps.Z ) ga:Radcliffe91c.

....Wales, 618] total 8 thesis in 8 schools 4.4 Report series The following list contains references to all papers published as technical reports. The list is arranged in alphabetical order by the name of the institute. Coventry University, 222] EPRI, 160] Edinburgh Parallel Computing Centre, [18, 672, 675, 676, 678, 681, 682, 707, 708] IBM, 698] Loughborough University of Technology, 667] Patents 11 Plymouth Engineering Design Centre, 502, 503] The University of Sheffield, 515] University College London, 601] University of Cambridge, 472] University of Durham, 639] University of East Anglia, 138, 539] ....

....344, 359, 364, 369, 370, 372, 373, 665, 666] Prager, Richard, 16] Probert, Penelope, 58, 331] Prosser, P. 185] Prugel Bennett, A. 51] Purchase, G. 427] Purvis, A. 645, 646] Pye, C. J. 266] Quick, R. J. 423] Quinn, L. 353, 668] Rabelo, L. C. 324] Radcliffe, Nicholas J. [18, 80, 93, 134, 148, 11, 437, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684] Rafiq, Y. 413] Rakowski, Tomasz, 295] Rana, A. S. 268] Rastogi, M. 318] Rattray, M. 51] Rayne, C. M. 79] Raywardsmith, V. J. 310] Rayward Smith, V. J. 329, 423] Rayward Smith, Vic J. 105, 54, 81, 233, 541, 542] Redmill, D. W. 286] Reeves, Colin R. 82, 135, 149, ....

[Article contains additional citation context not shown here]

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Technical Report TR-90-03, Edinburgh Parallel Computing Centre, 1990. (also as [677]; available via anonymous ftp cite ftp.epcc.ed.ac.uk directory /pub/tr/90 file tr9003.ps.Z ) ga:Radcliffe90a.

....344, 359, 364, 369, 370, 372, 373, 665, 666] Prager, Richard, 16] Probert, Penelope, 58, 331] Prosser, P. 185] Prugel Bennett, A. 51] Purchase, G. 427] Purvis, A. 645, 646] Pye, C. J. 266] Quick, R. J. 423] Quinn, L. 353, 668] Rabelo, L. C. 324] Radcliffe, Nicholas J. [18, 80, 93, 134, 148, 11, 437, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684] Rafiq, Y. 413] Rakowski, Tomasz, 295] Rana, A. S. 268] Rastogi, M. 318] Rattray, M. 51] Rayne, C. M. 79] Raywardsmith, V. J. 310] Rayward Smith, V. J. 329, 423] Rayward Smith, Vic J. 105, 54, 81, 233, 541, 542] Redmill, D. W. 286] Reeves, Colin R. 82, 135, 149, ....

....keywords neural networks , optimization , and evolution strategies have been omitted in this list because of their high occurrence rate. A , 421] acoustics, 705] adaptation, 555] directed, 26] adaptive filters, 174] adaptive plan, 645, 646] AI, 525] algebra, 682] analysing GA, [672, 674, 675, 677, 502, 640, 80, 82, 134, 270, 297, 394, 404, 424, 463] analysing GA crossover, 503, 44] deception, 87, 276] hardness, 276] long path problems, 468] reproduction, 259] Royal Road functions, 423] selection, 216] statistical mechanics formulation, 51] analysis of GA, 271] animation, 605] ant colony search, 385] antennas, 190] ....

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Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. In ? [731], page ? y(ssq) ga94aRadcliffe.

....[32] total 12 books 4.2 Journal articles The following list contains the references to every journal article included in this bibliography. The list is arranged in alphabetical order by the name of the journal. Archives of Control Sciences, 245] Artificial Intelligence, 311] Complex Systems, [358] DIMACS, 155] Evolutionary Computation, 66, 67, 73, 78, 89, 92, 367] Fuzzy Systems Artificial Intelligence Reports and Letters, 135] IEE Proceedings C: Generation, Transmission and Distribution, 109] IEE Proceedings, Vision, Image, Signal Processing, 47] IEEE Transactions on Power ....

....[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, ....

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Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5(2):183--205, 1991. (also as [354]; ftp.epcc.ed.ac.uk: /pub/tr/90/ tr9003.ps.Z) Key: ga:Radcliffe91c.

....by the name of the institute. Akademie der Wissenschaft der DDR, 306] Argonne National Laboratory, 136] Aristotle University of Thessaloniki, 107] Bolt Beranek and Newman, 350] California Institute of Technology, 299] Carnegie Mellon University, 11, 44] Edinburgh Parallel Computing Centre, [111, 354, 356, 357, 359, 362, 363] Florida Atlantic University, 4] International Computer Science Institute (ICSI) 310, 312, 313] Iowa State University, 337] Leiden University, 194] Michigan State University, 48] Mitsubishi Electric Corp. 303] Mitsubishi Electric Research Laboratories, 302] National University of ....

....[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, ....

[Article contains additional citation context not shown here]

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Technical Report TR-90-03, Edinburgh Parallel Computing Centre, 1990. (also as [358]; ftp.epcc.ed.ac.uk: /pub/tr/90/ tr9003.ps.Z) Key: ga:Radcliffe90a. Bibliography 61

....9 schools 4.4 Report series The following list contains references to all papers published as technical reports. The list is arranged in alphabetical order by the name of the institute. Army Strategic Defense Command, 106] Carnegie Mellon University, 176] Edinburgh Parallel Computing Centre, [243] General Motors Research Laboratories, 53] IBM, 256] Indian Institute of Technology, 245] Institute of Psychology CNR, 211] Los Alamos National Laboratory, 108] NASA Ames Research Center, 55] Naval Ocean Systems Center, 105] Navy Research Laboratory, 49] Oregon Graduate Center, ....

....Carsten, 230] Petry, Frederick E. 16, 17, 44] Pettey, Chrisila Cheri Baxter, 231] Pichler, E. E. 232] Pitney, Gilbert, 233] Poon, P. W. 234] Porto, Vincent W. 98, 104, 235] Powell, David J. 236, 237] Preis, K. 205, 302] Quinlan, J. R. 238] Radcliffe, Nicholas J. [242, 243, 244] Raedt, L. De, 72] Rajeev, S. 245] Ralston, Patricia A. S. 293] Ramsey, Connie Loggia, 132] Rao, Vasant B. 258] Rasmussen, Steen, 246] Ray, Thomas S. 247] Reynolds, Robert G. 248] Rice, James P. 187, 188] Rich, S. S. 249] Richards, Dana S. 50] Richards, G. G. 241] ....

[Article contains additional citation context not shown here]

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Technical Report TR-90-03, Edinburgh Parallel Computing Centre, 1990. (also as [?]; available via anonymous ftp cite ftp.epcc.ed.ac.uk directory /pub/tr/90 file tr9003.ps.Z ) ga:Radcliffe90a.

....theorem relies on the static building block hypothesis which does not take the dynamic of the process into account. Though extensions of the schema theorem have been performed either for non binary encoded chromosomes (e.g. see [1] or for other structures than schemata (predicates [39] formae [30, 31], interval for real coded individuals [13] Other works on the behavior of GAs focus on giving a proof of convergence of the algorithm, either by enhancing the schema theorem [43] 41, 26, 40] or by modeling the behavior of the GA with Markov s chain [11] 29] 8] A very interesting review of ....

Nicholas J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5:183--205, 1991.

....the sequence of departments, bay by bay, read from top to bottom, left to right. The second chromosome contains an encoding of the number of bays, and where in the sequence the breaks between bays occur. The encoding is shown in Fig. 1. For breeding, we used a variant of uniform crossover [15]. Each location in the offspring s sequence is occupied by the department in the corresponding location from one or the other parent with equal probability, so that all common locations in the parents are carried over to the child. Conflicts are then resolved to ensure that each department occurs ....

Radcliffe, N. J., "Equivalence Class Analysis of Genetic Algorithms, Complex Systems 5, 183-205 (1991).

....(no search strategy can given access only to such a representation) but rather that the Schema Theorem still holds in this case. The careless interpretation that this suggests that a genetic algorithm will out perform a random enumeration is incorrect in these circumstances. Radcliffe [16] also showed that the Fundamental Theorem can be applied to arbitrary subsets of the search space. An extreme example of Radcliffe s observation was given by Liepins and Vose [13] who showed how to convert a fully deceptive GA problem to a fully easy problem by changing the representation. 4.2.4: ....

Radcliffe, N. J., "Equivalence Class Analysis of Genetic Algorithms," Complex Systems, 5, 2, 1991, pp. 183-205.

....of this is the choice of network topology. Secondly, the failure modes of the genetic algorithm seen in neural network applications are common to a broader class of problems, and their study can yield more general insights. This paper is a study in the application of forma analysis (Radcliffe [22, 23]) to this and related problems. It begins in section 2 witha brief review and a discussion of the difficulties with previous genetic approaches to problems in neural networks. This is followed, in section 3, by a short review of schema and forma analysis and a discussion of the permutation ....

.... genetic search (for example, simple parameter optimisation) and it has been strongly argued elsewhere the problem is highly detrimental to the effectiveness of the search process both in the specific context of neural networks (Radcliffe [20, 21] Belew et al. 1] and more generally (Radcliffe [22, 23]) 3 Schema and Forma Analysis 3.1 Formulation and Principles In order to understand the motivations for the ideas put forward in this paper it is necessary briefly to review some of the theory of genetic algorithms. Holland s ground breaking formulation and analysis of genetic algorithms ....

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Nicholas J. Radcliffe. Equivalence Class Analysis of Genetic Algorithms. Complex Systems, 5(2):183--205, 1991.

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:183--205, 1991.

....of solutions over the space C of chromosomes. These considerations and others (including Goldberg s principles of minimal alphabets and meaningful building blocks, 4] led to the proposal of six design principles for constructing useful representations, formae and genetic operators (Radcliffe [10]) In the following, the number of formae induced by an equivalence relation will be referred to as the precision of both the relation and the formae it induces. 3 The set of equivalence relations which induce the formae (equivalence classes) under consideration will be written Psi and the set ....

....random edges in such a way as to complete a legal tour. The lack of separability simply ensures that R 3 does not properly assort the formae. 10 Locality Formae All of the formae discussed thus far have been fairly similar to traditional schemata. We now introduce locality formae, Radcliffe [10]) which are rather different in character. Locality formae relate chromosomes on the basis of their closeness to each other. Suppose our function is defined over a real interval [a; b) We then define formae which divide the interval up into strips of arbitrary width. Thus, a forma is a half open ....

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N. J. Radcliffe, Equivalence Class Analysis of Genetic Algorithms, to appear in Complex Systems.

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N.J.Radcliffe. Equivalence class analysis of genetic algorithms. In Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1994.

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N.J.Radcliffe. Equivalence class analysis of genetic algorithms. In Foundations of Genetic Algorithms 3. Morgan Kaufmann, 1994.

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N. J. Radcliffe. Equivalence Class Analysis of Genetic Algorithms. Complex Systems, 5:183--205, 1991.

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