Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Even in simple fixed representation GAs this remains disputed, although there is a growing body of theory about building blocks in GAs. From the empirical studies of GP it has been known for some time that programs within GP populations tend to rapidly increase in size as the population evolves [13, 1, 33, 4, 26, 16, 32, 24]. If unchecked, this consumes excessive machine resources and so is usually addressed either by enforcing a size or depth limit on the programs or by an explicit size component in the GP fitness [13, 12, 34, 29] although other techniques have been proposed [30, 6, 32, 31, 18] Depth or size limits ....

....(i.e. addition of ineffective code, code that has no impact on the behaviour of the program) can sometimes be helpful. Therefore it is still interesting to explore why such bloat happens, and the factors influencing its speed and its limits. 3 Bloating Tackett [33, page 112] and Altenberg [1] both suggest the common intron explanation for bloat is due to Singleton (however James Rice and Peter Angeline may also have contributed) Briefly this says program size tends to increase over time because programs which are bigger contain more ineffective code ( junk code, code that has no ....

Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....Even in simple fixed representation GAs this remains disputed, although there is a growing body of theory about building blocks in GAs. From the empirical studies of GP it has been known for some time that programs within GP populations tend to rapidly increase in size as the population evolves [13, 1, 33, 4, 26, 16, 32, 24]. If unchecked, this consumes excessive machine resources and so is usually addressed either by enforcing a size or depth limit on the programs or by an explicit size component in the GP fitness [13, 12, 34, 29] although other techniques have been proposed [30, 6, 32, 31, 18] Depth or size limits ....

....(i.e. addition of ineffective code, code that has no impact on the behaviour of the program) can sometimes be helpful. Therefore it is still interesting to explore why such bloat happens, and the factors influencing its speed and its limits. 3 Bloating Tackett [33, page 112] and Altenberg [1] both suggest the common intron explanation for bloat is due to Singleton (however James Rice and Peter Angeline may also have contributed) Briefly this says program size tends to increase over time because programs which are bigger contain more ineffective code ( junk code, code that has no ....

Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....is given in Section 6. In Section 7 conclusions are given. The paper concludes with a brief discussion of further work in section 8. 2 RELATED WORK The problem of the rapid growth of programs produced by Genetic Programming is very well known and is generally referred to as program bloat [1][2] 4] 8] 10] 11] 17] 18] 27] 28] 29] Unfortunately this growth in program size is almost always due to the growth of pieces of sub code that have little or no semantic effect. Various ideas have been proposed to explain this phenomenon. Originally it was viewed as hitchhiking [29] which viewed ....

L. Altenberg (1994). Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel (eds.), Evolutionary Programming: Proceedings of the Third Annual Conference, 233-241. World Scientific Publishing.

....faster than program functionality. In standard GP, program size growth is near quadratic [19] yet the exact causes of bloat are not known. Nevertheless, a number of theories have been proposed. These include 35 hitchhiking [39] protection from disruptive operators [7] operator biases [1], removal biases [38] and search space bias [21] Enzyme GP, on the other hand, does not su#er from bloat [25, 24] This is true both when solution length is bounded, which is the case for uniform crossover, and when length is unbounded, in the case of TR crossover. Genome size evolution for both ....

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming -- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....a size penalty into the fitness function. However, both of these approaches modify or constrain the behaviour of search. The exact causes of bloat are not known, though a number of theories have been proposed. These include hitchhiking [3] protection from disruptive operators [4] operator biases [5], removal biases [6] and search space bias [7] Enzyme genetic programming is an approach to genetic programming that uses a biomimetic representation for defining programs. This paper explains how this representation can be adapted to maintain local context during crossover and presents an ....

L. Altenberg, "Emergent phenomena in genetic programming," in Evolutionary Programming -- Proceedings of the Third Annual Conference, A. V. Sebald and L. J. Fogel, Eds. 1994, pp. 233--241, World Scientific Publishing.

....the purely macroscopic ones. This distinction is important because the latter are simpler and easier to analyse than the former. The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems [6, 1, 11, 24, 17, 21], only very recently exact schema theories have become available [14, 12] which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation. These exact theories are applicable to GP with one point crossover [16, 17, 18] No exact ....

....schema theories normally provide a lower bound for or, equivalently, for . Obtaining theoretical results for GP using the idea of schema is much less straightforward than for GAs. A few alternative definitions of schema have been proposed in the literature [6, 1, 11, 24, 17, 21], but for brevity here we will describe only the definition introduced in [17, 18] This is used in the rest of this paper. We will refer to this kind of schemata as fixed size and shape schemata. Syntactically a GP fixed size and shape schema is a tree composed of functions from the set ....

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....like in [2] In the case of GP theory the space of models is signi cantly less densely populated than the space of GA models. Before the present work only approximate schema theorems [15, 24, 58, 33, 44] which we will review in the next section, and one exact 4 microscopic model presented in [1] (see Section 2.2) were available. These models are represented by the gray blobs in Figure 1. This paper presents the rst theoretical results on GP schemata which provide an exact macroscopic formulation (rather than a lower bound) for the expected number of instances of a schema in the next ....

....on GP using the idea of schema is that the de nition of schema is much less straightforward than for GAs and a few alternative de nitions have been proposed in the literature. Syntactically all of them de ne schemata as composed of one or multiple trees or fragments of trees. In some de nitions [15, 1, 24, 58, 59] schema components are non rooted and a schema is seen as a set of components (subtrees) that can be present multiple times within the same program. The focus in these theories is to predict how the number or the frequency of such components vary over time. However, the variability of the size and ....

[Article contains additional citation context not shown here]

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming | Proceedings of the Third Annual Conference, pages 233-241. World Scientic Publishing, 1994.

....and node reference systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory. 1 Introduction Genetic programming theory has had a difficult childhood. After some excellent early efforts leading to different approximate schema theorems [1, 2, 3, 4, 5, 6, 7], only very recently have schema theories become available which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation. These exact theories are applicable to GP with one point crossover [8, 9, 10] standard crossover and other ....

....equivalently, for # . One of the difficulties in obtaining theoretical results on GP using the idea of schema is that finding a workable definition of a schema is much less straightforward than for GAs. Several alternative definitions have been proposed in the literature [1, 2, 3, 4, 6, 7, 5]. For brevity here we will describe only the definition introduced in [6, 7] since this is what is used in the rest of this paper. We will refer to this kind of schemata as fixed size and shape schemata. Syntactically a GP fixed size and shape schema is a tree composed of functions from the set ....

L. Altenberg, "Emergent phenomena in genetic programming, " in Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, eds.), pp. 233--241, World Scientific Publishing, 1994.

....the purely macroscopic ones. This distinction is important because the latter are simpler and easier to analyse than the former. The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems [6, 1, 11, 24, 17, 21], only very recently exact schema theories have become available [14, 12] which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation. These exact theories are applicable to GP with one point crossover [16, 17, 18] No exact ....

....worst casescenario schema theories normally provide a lower bound for (H; t) or, equivalently, for E[m(H; t 1) Obtaining theoretical results for GP using the idea of schema is much less straightforward than for GAs. A few alternative definitions of schema have been proposed in the literature [6, 1, 11, 24, 17, 21], but for brevity here we will describe only the definition introduced in [17, 18] This is used in the rest of this paper. We will refer to this kind of schemata as fixed size and shape schemata. Syntactically a GP fixed size and shape schema is a tree composed of functions from the set F [ f=g ....

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....macroscopic ones. The paper gives examples which show how the theory can be specialised to specific operators. 1 Introduction The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems [1, 2, 3, 4, 5, 6, 7], exact schema theories have become available only very recently [8, 9, 10, 11] These new theories give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation, and are applicable to GP with various types of subtree crossover. No exact ....

....normally provide a lower bound for (H; t) or, equivalently, for E[m(H; t 1) One of the difficulties in obtaining theoretical results on GP using the idea of schema is that its definition is much less straightforward than for GAs. Various definitions have been proposed in the literature [1, 2, 3, 4, 5, 7], but for brevity here we will describe only the definition of fixed size and shape schema introduced in [5, 6] which is what is used in this paper and in other recent work [8, 9, 10, 11, 16] 2.1 GP Schemata Syntactically a GP fixed size and shape schema (or just schema for simplicity) is a ....

L. Altenberg. Emergent phenomena in genetic programming. In Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....macroscopic ones. The paper gives examples which show how the theory can be specialised to specific operators. 1 Introduction The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems [1, 2, 3, 4, 5, 6, 7], exact schema theories have become available only very recently [8, 9, 10, 11] These new theories give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation, and are applicable to GP with various types of subtree crossover. No exact ....

....provide a lower bound for 4 or, equivalently, for 42050 . One of the difficulties in obtaining theoretical results on GP using the idea of schema is that its definition is much less straightforward than for GAs. Various definitions have been proposed in the literature [1, 2, 3, 4, 5, 7], but for brevity here we will describe only the definition of fixed size and shape schema introduced in [5, 6] which is what is used in this paper and in other recent work [8, 9, 10, 11, 16] 2.1 GP Schemata Syntactically a GP fixed size and shape schema (or just schema for simplicity) is a ....

L. Altenberg. Emergent phenomena in genetic programming. In Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

....and node reference systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory. 1 Introduction Genetic programming theory has had a difficult childhood. After some excellent early efforts leading to different approximate schema theorems [1, 2, 3, 4, 5, 6, 7], only very recently have schema theories become available which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation. These exact theories are applicable to GP with one point crossover [8, 9, 10] standard crossover and other ....

.... (H; t) or, equivalently, for E[m(H; t 1) One of the difficulties in obtaining theoretical results on GP using the idea of schema is that finding a workable definition of a schema is much less straightforward than for GAs. Several alternative definitions have been proposed in the literature [1, 2, 3, 4, 6, 7, 5]. For brevity here we will describe only the definition introduced in [6, 7] since this is what is used in the rest of this paper. We will refer to this kind of schemata as fixed size and shape schemata. Syntactically a GP fixed size and shape schema is a tree composed of functions from the set ....

L. Altenberg, "Emergent phenomena in genetic programming, " in Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, eds.), pp. 233--241, World Scientific Publishing, 1994.

....Rudolph 1997b, Rowe 1999, Spears 1999) 1 In the last year or so the theory of schemata has made considerable progress, both for GAs and GP. This includes several new schema theorems which give exact formulations (rather than the lower bounds previously presented in the literature (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997, Rosca 1997, Poli and Langdon 1998b) for the expected number of instances of a schema at the next generation. These exact theories are applicable to GP with one point crossover (Poli 2000a, Poli 2000b, Poli 2001a) standard and ....

Altenberg, Lee (1994). Emergent phenomena in genetic programming. In: Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, Eds.). World Scientific Publishing. pp. 233--241.

....systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory. 1 Introduction The theory for genetic programming has had a difficult childhood. After some excellent early efforts leading to different approximate schema theorems (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997, Poli and Langdon 1998b, Rosca 1997) only very recently have schema theories become available which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next generation. These ....

....equivalently, for E[m(H; t 1) One of the difficulties in obtaining theoretical results on GP using the idea of schema is that finding a workable definition of a schema is much less straightforward than for GAs. Several alternative definitions have been proposed in the literature (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997, Poli and Langdon 1998b, Rosca 1997) For brevity here we will describe only the definition introduced in (Poli and Langdon 1997, Poli and Langdon 1998b) since this is what is used in the rest of this paper. We will refer to this ....

Altenberg, Lee (1994). Emergent phenomena in genetic programming. In: Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, Eds.). World Scientific Publishing. pp. 233--241.

....as shown by recent work (Stephens and Waelbroeck 1997, Stephens and Waelbroeck 1999) then don t have to be so. 1 The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997b, Rosca 1997) only very recently exact schema theories have become available (Poli 2000a, Poli 2000b) which give exact formulations (rather than lower bounds) for the expected number of instances of a schema at the next ....

.... we denote with (H; t) the success probability of each trial (i.e. the probability that a newly created individual samples H) which we term the total transmission probability of H , an exact schema theorem is simply E[m(H; t 1) M (H; t) 1) 1 To be precise, one of the models proposed in (Altenberg 1994) is an exact model. However, this is a microscopic model of the propagation of program components (subtrees) in GP with standard crossover, rather than a theorem about schemata as sets. This model allows one to compute the exact proportion of subtrees of a given type in an infinite population in ....

[Article contains additional citation context not shown here]

Altenberg, Lee (1994). Emergent phenomena in genetic programming. In: Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, Eds.). World Scientific Publishing. pp. 233--241.

....work (Stephens and Waelbroeck 1997, Stephens and Waelbroeck 1999) however has shown that they don t have to be so. The theory of schemata in genetic programming has had a difficult childhood. After some excellent early efforts leading to different worst case scenario schema theorems (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997b, Rosca 1997) exact schema theories have become available only very recently (Poli 2000a, Poli 2000b, Poli and McPhee 2000, Poli 2000c) These new theories give exact formulations (rather than lower bounds) for the expected number ....

....provide a lower bound for (H; t) or, equivalently, for E[m(H; t 1) One of the difficulties in obtaining theoretical results on GP using the idea of schema is that its definition is much less straightforward than for GAs. Various definitions have been proposed in the literature (Koza 1992, Altenberg 1994, O Reilly and Oppacher 1995, Whigham 1995, Poli and Langdon 1997b, Rosca 1997) but for brevity here we will describe only the definition of fixed size and shape schema introduced in (Poli and Langdon 1997b, Poli and Langdon 1998) which is what is used in the rest of this paper and in other ....

Altenberg, Lee (1994). Emergent phenomena in genetic programming. In: Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, Eds.). World Scientific Publishing. pp. 233--241.

....Depending upon implementation, we predict run time O(no. generations 2:0 Gamma3:0 ) and memory O(no. generations 1:0 Gamma2:0 ) 1 INTRODUCTION It has been known for some time that programs within GP populations tend to rapidly increase in size as the population evolves [ Koza, 1992, Altenberg, 1994, Tackett, 1994, Blickle and Thiele, 1994, Nordin and Banzhaf, 1995, Nordin, 1997, McPhee and Miller, 1995, Langdon, 1998b, Soule et al. 1996, Langdon et al. 1999 ] If unchecked this consumes excessive machine resources and so is usually addressed either by enforcing a size or depth limit on ....

....(corresponding to generation 12) Co incidentally this is also the point where the size limited population diverges from the unlimited population. Given the variability between runs, the agreement between the prediction and measurements is surprisingly good. 7 DISCUSSION [ Tackett, 1994 ] and [ Altenberg, 1994 ] both suggest Andy Singleton first proposed what is now often called the intron explanation for bloat. i.e. programs become longer not because longer programs are better but because they harbour more ineffective code (introns) than shorter ones. Since crossover chooses a point in the parent at ....

[Article contains additional citation context not shown here]

Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pp233-- 241. World Scientific Publishing, 1994.

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Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

No context found.

L. Altenberg. Emergent phenomena in genetic programming. In Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

No context found.

Altenberg, L. (1994). Emergent phenomena in genetic programming. In Sebald, A. V. and Fogel, L. J., editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241, San Diego, CA, USA. World Scientific Publishing.

No context found.

Lee Altenberg, "Emergent phenomena in genetic programming ", in Evolutionary Programming --- Proceedings of the Third Annual Conference, A. V. Sebald and L. J. Fogel, Eds. 1994, pp. 233--241, World Scientific Publishing.

No context found.

L. Altenberg, "Emergent phenomena in genetic programming, " in Evolutionary Programming --- Proceedings of the Third Annual Conference (A. V. Sebald and L. J. Fogel, eds.), pp. 233--241, World Scientific Publishing, 1994.

No context found.

Lee Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming --- Proceedings of the Third Annual Conference, pages 233--241. World Scientific Publishing, 1994.

No context found.

Altenberg, L. (1994). Emergent phenomena in genetic programming. In Sebald, A. and Fogel, L., editors, Proceedings of the Third Annual Conference on Evolutionary Programming, pages 233--241. World Scientific.

No context found.

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, editors, Evolutionary Programming | Proceedings of the Third Annual Conference, pages 233-241. World Scienti c Publishing, 1994.

No context found.

L. Altenberg. Emergent phenomena in genetic programming. In A. V. Sebald and L. J. Fogel, eds., Evolutionary Programming, pp 233-241, 1994. World Scienti c.

No context found.

Lee Altenberg. 1994. Emergent phenomena in genetic programming. In Anthony V. Sebald and Lawrence J. Fogel, editors, Proceedings of the Third Annual Conference on Evolutionary Programming, pages 233--241. World Scientific.

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