Genetic operators
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Genetic Operations - use of operators to probabilistically transform a set of schemata into a child population

Summary
Plans change in complex adaptive systems (
This page introduces the complex adaptive system (CAS) theory frame.  The theory provides an organizing framework that is used by 'life.'  It can illuminate and clarify complex situations and be applied flexibly.  It can be used to evaluate and rank models that claim to describe our perceived reality.  It catalogs the laws and strategies which underpin the operation of systems that are based on the interaction of emergent agents.  It highlights the constraints that shape CAS and so predicts their form.  A proposal that does not conform is wrong. 

John Holland's framework for representing complexity is outlined.  Links to other key aspects of CAS theory discussed at the site are presented. 
CAS
) due to the action of genetic operations such as mutation, splitting and recombination.  The nature of the operations is described. 
Introduction
Holland reviews biological adaptation in evolutionary biology is a trait that increased the number of surviving offspring in an organism's ancestral lineage.  Holland argues: complex adaptive systems (CAS) adapt due to the influence of schematic strings on agents.  Evolution indicates fitness when an organism survives and reproduces.  For his genetic algorithm, Holland separated the adaptive process into credit assignment and rule discovery.  He assigned a strength to each of the rules (alternate hypothesis) used by his artificial agents, by credit assignment - each accepted message being paid for by the recipient, increasing the sender agent's rule's strength (implicit modeling) and reducing the recipient's.  When an agent achieved an explicit goal they obtained a final reward.  Rule discovery used the genetic algorithm to select strong rule schemas from a pair of agents to be included in the next generation, with crossing over and mutation applied, and the resulting schematic strategies used to replace weaker schemas.  The crossing over genetic operator is unlikely to break up a short schematic sequence that provides a building block retained because of its 'fitness';  In Deacon's conception of evolution, an adaptation is the realization of a set of constraints on candidate mechanisms, and so long as these constraints are maintained, other features are arbitrary. 
through changes in genetic makeup.  Every
This page reviews the implications of reproduction initially generating a single initialized child cell.  For multi-cellular organisms this 'cell' must contain all the germ-line schematic structures including for organelles and multi-generational epi-genetic state.  Any microbiome is subsequently integrated during the innovative deployment of this creative event.  Organisms with skeletal infrastructure cannot complete the process of creation of an associated adult mind, until the proximate environment has been sampled during development.  The mechanism and resulting strategic options are discussed. 
organism
is an amalgam of characteristics based on the specific alleles, one of multiple alternative forms of a schematic sequence with the same address on a schematic string.   in its chromosomes are an aggregate of a very long DNA molecule with associated proteins including histones.  Human chromosomes are visible as 23 distinct pairs during cell division, prior to their refolding into chromatin structures. 
.  The enormous number of genotypes of a single vertebrate species is an indication of the complexity, M. Mitchell Waldrop describes a vision of complexity via:
  • Rich interactions that allow a system to undergo spontaneous self-organization and, for CAS, evolution
  • Systems that are adaptive
  • More predictability than chaotic systems by bringing order and chaos into
  • Balance at the edge of chaos
of such systems.  Holland notes how genes exert control over the processes operating in cells through building enzymes, a protein with a structure which allows it to operate as a chemical catalyst and a control switch. 
which have wide spread effects.  This adds to the complexity.  The effect of each allele depends strongly on what other alleles are present.  The phenotype is the system that results from the controlled expression of the genes.  It is typically represented by a prokaryotic cell or the body of a multi-cell animal or plant.  The point is that the genes provide the control surface and the abstract recipe that has been used to generate the cell.   depends on epistatic effects that hugely increase complexity. 

Because of pervasive epistasis adaptation becomes a search for co-adapted sets of alleles - schema - alleles on different genes which together significantly augment the performance of the phenotype in a particular environment.  This fitness is, according to Dawkins, a suitcase word with at least five meanings in biology:
  1. Darwin and Wallace thought in terms of the capacity to survive and reproduce, but they were considering discrete aspects such as chewing grass - where hard enamel would improve the relative fitness. 
  2. Population geneticists: Ronald Fisher, Sewall Wright, J.B.S. Haldane; consider selection at a locus where for a genotype: green eyes vs blue eyes; one with higher fitness can be identified from genotypic frequencies and gene frequencies, with all other variations averaged out. 
  3. Whole organism 'integrated' fitness.  Dawkins notes there is only ever one instance of a specific organism.  Being unique, comparing the relative success of its offspring makes little sense.  Over a huge number of generations the individual is likely to have provided a contribution to everyone in the pool or no one. 
  4. Inclusive fitness, where according to Hamilton, fitness depends on an organism's actions or effects on its children or its relative's children, a model where natural selection favors organs and behaviors that cause the individual's genes to be passed on.  It is easy to mistakenly count an offspring in multiple relative's fitness assessments. 
  5. Personal fitness represents the effects a person's relatives have on the individual's fitness [3].  When interpreted correctly fitness [4] and fitness [5] are the same. 
is analogous to the number of offspring that survive to reproduce.  Evolutionary selection can be seen as sampling.  Holland asks:
  • To what extent does the outcome of a sample influence or alter the kind of samples to be taken in the future? 
  • How does the history of the outcomes of previous samples influence the current sampling strategy?
In response Holland explains that reproductive plans, sampling strategies using reproduction in proportion to measured performance, are efficient over a broad range of conditions.  But analysis of the two questions identifies a dilemma: duplicate offspring have no provision for improvement, and random variation in the offspring removes the history of advances and is likely to be catastrophic.  The dilemma is resolved by the action of genetic operators, which redistribute alleles within the genetic population, but usually keep alleles together which are close together on the chromosome. 

He identified a process, the genetic algorithm that results in the iterative generation of a limited population of "fit"
Plans emerge in complex adaptive systems (CAS) to provide the instructions that agents use to perform actions.  The component architecture and structure of the plans is reviewed. 
schemata
from a current set and a current situation.  It's a simplified evolutionary algorithm

Holland's process "selects" schemata to be recombined into a subsequent generation.  Operators' probabilistically transform a selected pair of schemata.  Hence the process uses a sexual reproductive enforces the mixing of current germ-line DNA of a male and a female organism, with a recombination process, to ensure the generation of new schematic recipes and phenotypes in their shared offspring.  Matt Ridley argues that the cost of sexual reproduction is justified by the protection from parasites that long-lived organisms gain. 
The agents in complex adaptive systems (CAS) must model their environment to respond effectively to it.  Evolution's schematic operators and Samuel modeling together support the indirect recording of past successes and their strategic use by the current agent to learn how to succeed in the proximate environment. 
model
.  The genetic pooling and emergent adaptability of progressive generations is a significant benefit to
This page introduces the complex adaptive system (CAS) theory frame.  The theory provides an organizing framework that is used by 'life.'  It can illuminate and clarify complex situations and be applied flexibly.  It can be used to evaluate and rank models that claim to describe our perceived reality.  It catalogs the laws and strategies which underpin the operation of systems that are based on the interaction of emergent agents.  It highlights the constraints that shape CAS and so predicts their form.  A proposal that does not conform is wrong. 

John Holland's framework for representing complexity is outlined.  Links to other key aspects of CAS theory discussed at the site are presented. 
the complex adaptive system
(CAS). 

Holland's original operators included: Inversion, Recombination, Mutation and Dominance. 

Mutation introduces new aspects into a CAS.   Useful mutations typically create small changes in the
Plans are interpreted and implemented by agents.  This page discusses the properties of agents in a complex adaptive system (CAS). 
It then presents examples of agents in different CAS.  The examples include a computer program where modeling and actions are performed by software agents.  These software agents are aggregates. 
The participation of agents in flows is introduced and some implications of this are outlined. 
agents
This page reviews the implications of selection, variation and heredity in a complex adaptive system (CAS).  The mechanism and its emergence are discussed. 
Darwinian evolution
Richard Dawkin's explores how nature has created implementations of designs, without any need for planning or design, through the accumulation of small advantageous changes. 
creates statistically unlikely agents through cumulative small changes
.  As such any single large change is likely to drive the agent away from its currently useful structure. 

In DNA (DNA), a polymer composed of a chain of deoxy ribose sugars with purine or pyrimidine side chains.  DNA naturally forms into helical pairs with the side chains stacked in the center of the helix.  It is a natural form of schematic string.  The purines and pyrimidines couple so that AT and GC pairs make up the stackable items.  A code of triplets of base pairs (enabling 64 separate items to be named) has evolved which now redundantly represents each of the 20 amino-acids that are deployed into proteins, along with triplets representing the termination sequence.  Chemical modifications and histone binding (chromatin) allow cells to represent state directly on the DNA schema.  To cope with inconsistencies in the cell wide state second messenger and evolved amplification strategies are used.   based systems replacement mutations are substitutions of one base, a nucleotide base is the side chain purine (A or G) or pyrimidine (T or C).  A is a natural pair for T.  G pairs naturally with C.  These bases have multiple uses in cells including energy transfer, second messenger signalling as well as genetic data storage, transcription and translation.  Deacon argues that the multiple uses are significant to the emergence of evolution. 
pair for another.  With the requirement to transcribe is the process where DNA is converted into messenger m-RNA.  A complex of enzymes cooperates to bind to the DNA and generate the m-RNA copy.  There are a number of such transcription complexes which are based on RNA polymerase I, II or III. 
and translate is the process where messenger m-RNA is cross coded by Ribosomal agents and t-RNA into an amino-acid polymer.   the DNA sequences into proteins, a relatively long chain (polymer) of peptides.  Shorter chains of peptides are termed polypeptides.   the encoding, the mapping of DNA base triplet sequences, such as AAA and AAT, to amino-acids (AAA maps to the amino-acid lysine for example) and transcription termination sequences (TGA maps to stop transcription for example) that has currently evolved.   constrains these mutations to be reflected as:

An important adjunct of mutation is replication of a part of a schematic string.  This allows a mutation to act on a 'copy' of an important facet of the schematic structure.  Such mutations will not be catastrophic when they alter required facets of the agent. 

In cellular systems certain structural domains, evolution conserves many useful structures including DNA base sequence (content) addressable binding regions, protein active sites and signal structures which can then be reused through the mutation genetic operator. 
are preserved by
This page reviews the implications of selection, variation and heredity in a complex adaptive system (CAS).  The mechanism and its emergence are discussed. 
evolutionary selection
and leveraged as
This page discusses the physical foundations of complex adaptive systems (CAS).  A small set of rules is obeyed.  New [epi]phenomena then emerge.  Examples are discussed. 
phenomenological motifs
.  Recombination can leverage these domains and enable oligomerization which brings together binding and control domains.  The effect of recombination on selectable effects is extended by the presence of epistatic sequences. 

Prokaryotic, a single cell system with two main types: (1) Archaea, and (2) Eubacteria.  Prokaryotes have their own DNA and infrastructure within a single enclosure.  They are biochemically very versatile: Photosynthesis -> Electron transport & phosphorylation, Enzymatic regulation and catalysis of chemical reactions, Catabolize -> phosphate bond energy, ATP cycle, glycolysis, TCA cycle, Electron transports, oxidative phosphorylation, oxidation of fatty acids, oxidative degradation of amino acids; Biosynthesis & utilization of phosphate bond energy -> carbohydrates, lipids, amino acids, nucleotides, muscle & motile structures; membrane barriers & active transports, hormones; Replication, Transcription, Translation, Regulation of gene expression; self-assembly; They utilize cell membrane receptors and signalling to support symbiotic cooperation with other cellular entities, including: in the microbiome, and as chloroplasts and mitochondria within eukaryotic cells. 
bacteria can augment the recombination operator with plasmids and R-factors provide bacteria with a way to transfer parts of their DNA complement with one another.  The effect is to ensure that useful mutations can become rapidly distributed within a population of bacteria.  Because the plasmid reproduces asexually beneficial mutations will result in competition between hosts containing different plasmid variants through clonal interference. 
which enable the sharing of schematic material (DNA) between bacteria.  The mixing can then be augmented by recombination across the schematic strings. 

Recombination provides
Lou Gerstner describes the challenges he faced and the strategies he used to successfully restructure the computer company IBM. 
compartmentalized systems
with great
To benefit from shifts in the environment agents must be flexible.  Being sensitive to environmental signals agents who adjust strategic priorities can constrain their competitors. 
flexibility
, since additional states can potentially be supported. 

Adolescence in humans supports the transition from a juvenile configuration, dependent on parents and structured to learn & logistically transform, to adult optimized to the proximate environment.  And it is staged, encouraging male adolescents to escape the hierarchy they grew up in and enter other groups where they may bring in: fresh ideas, risk taking; and alter the existing hierarchy: Steve Jobs & Steve Wozniak, Bill Gates & Paul Allen; while females become highly focused on friendships and communications.  It marks the beginning of Piaget's formal operational stage of cognitive development.  The limbic, autonomic and hormone networks are already deployed and functioning effectively.  The frontal cortex has to be pruned: winning neurons move to their final highly connected positions, and are myelinated over time.  The rest dissolve.  So the frontal lobe does not obtain its adult configuration and networked integration until the mid-twenties when prefrontal cortex control becomes optimal.  The evolutionarily oldest areas of the frontal cortex mature first.  The PFC must be iteratively customized by experience to do the right thing as an adult.  Adolescents:
  • Don't detect irony effectively.  They depend on the DMPFC to do this, unlike adults who leverage the fusiform face area.  
  • Regulate emotions with the ventral striatum while the prefrontal cortex is still being setup.  Dopamine projection density and signalling increase from the ventral tegmentum catalyzing increased interest in dopamine based rewards.  Novelty seeking allows for creative exploration which was necessary to move beyond the familial pack.  Criticisms do not get incorporated into learning models by adolescents leaving their risk assessments very poor.  The target of the dopamine networks, the adolescent accumbens, responds to rewards like a gyrating top - hugely to large rewards, and negatively to small rewards.  Eventually as the frontal regions increase in contribution there are steady improvements in: working memory, flexible rule use, executive organization and task shifting.  And adolescents start to see other people's perspective. 
  • Drive the cellular transformations with post-pubescent high levels of testosterone in males, and high but fluctuating estrogen & progesterone levels in females.  Blood flow to the frontal cortex is also diverted on occasion to the groin.  
  • Peer pressure is exceptionally influential in adolescents.  Admired peer comments reduce vmPFC activity and enhance ventral striatal activity.  Adults modulate the mental impact of socially mean treatment: the initial activation of the PAG, anterior cingulate, amygdala, insula cortex; which generate feelings of pain, anger, and disgust, with the VLPFC but that does not occur in adolescents.  
  • Feel empathy intensely, supported by their rampant emotions, interest in novelty, ego.  But feeling the pain of others can induce self-oriented avoidance of the situations. 
, with its risk, is an assessment of the likelihood of an independent problem occurring.  It can be assigned an accurate probability since it is independent of other variables in the system.  As such it is different from uncertainty. 
taking encouraging transfer of a small team of youth from one band of humans to another, supports genetic mixing and memetic recombination and potential dominance changes. 

Holland stresses that adaptations do not proceed by substitution of advantageous mutant genes under
This page reviews the implications of selection, variation and heredity in a complex adaptive system (CAS).  The mechanism and its emergence are discussed. 
natural selection
.  And alleles are not typically replaced independently.  The adaptive in evolutionary biology is a trait that increased the number of surviving offspring in an organism's ancestral lineage.  Holland argues: complex adaptive systems (CAS) adapt due to the influence of schematic strings on agents.  Evolution indicates fitness when an organism survives and reproduces.  For his genetic algorithm, Holland separated the adaptive process into credit assignment and rule discovery.  He assigned a strength to each of the rules (alternate hypothesis) used by his artificial agents, by credit assignment - each accepted message being paid for by the recipient, increasing the sender agent's rule's strength (implicit modeling) and reducing the recipient's.  When an agent achieved an explicit goal they obtained a final reward.  Rule discovery used the genetic algorithm to select strong rule schemas from a pair of agents to be included in the next generation, with crossing over and mutation applied, and the resulting schematic strategies used to replace weaker schemas.  The crossing over genetic operator is unlikely to break up a short schematic sequence that provides a building block retained because of its 'fitness';  In Deacon's conception of evolution, an adaptation is the realization of a set of constraints on candidate mechanisms, and so long as these constraints are maintained, other features are arbitrary. 
process operates on pools of schemata with fitness is, according to Dawkins, a suitcase word with at least five meanings in biology:
  1. Darwin and Wallace thought in terms of the capacity to survive and reproduce, but they were considering discrete aspects such as chewing grass - where hard enamel would improve the relative fitness. 
  2. Population geneticists: Ronald Fisher, Sewall Wright, J.B.S. Haldane; consider selection at a locus where for a genotype: green eyes vs blue eyes; one with higher fitness can be identified from genotypic frequencies and gene frequencies, with all other variations averaged out. 
  3. Whole organism 'integrated' fitness.  Dawkins notes there is only ever one instance of a specific organism.  Being unique, comparing the relative success of its offspring makes little sense.  Over a huge number of generations the individual is likely to have provided a contribution to everyone in the pool or no one. 
  4. Inclusive fitness, where according to Hamilton, fitness depends on an organism's actions or effects on its children or its relative's children, a model where natural selection favors organs and behaviors that cause the individual's genes to be passed on.  It is easy to mistakenly count an offspring in multiple relative's fitness assessments. 
  5. Personal fitness represents the effects a person's relatives have on the individual's fitness [3].  When interpreted correctly fitness [4] and fitness [5] are the same. 
of individual schemas representing espistatic leverage and driving coadaptation.  Particular instances will grow rapidly reflecting excess performance over the average.  Schemata of above-average performance are combined and tested in new contexts by crossing-over outside their defining locations.  Because schemata increase or decrease exponentially in terms of observed performance the overall average performance is close to the best observed ensuring robustness. 

Using John Holland's theory of adaptation in complex systems Baldwin and Clark propose an evolutionary theory of design.  They show how this can limit the interdependencies that generate complexity within systems.  They do this through a focus on modularity. 
Baldwin & Clark
applied Holland's ideas to
This page discusses the strategy of modularity in a complex adaptive system (CAS).  The benefits, mechanism and its emergence are discussed. 
modularity
in design.  They concluded that the effect of modular design is to create new modular operators:
  • Splitting - of a system in to multiple modules.  Substituting - one module design for another.  Allowing improvement. 
  • Augmenting - adding a new module to a system.
  • Excluding - a module from the system.
  • Inverting to create new design rules.  Allowing redundant activities to be consolidated into single modules. 
  • Porting a module to another system.  Allowing systems to be linked by common modules.
Complex adaptive
Plans are interpreted and implemented by agents.  This page discusses the properties of agents in a complex adaptive system (CAS). 
It then presents examples of agents in different CAS.  The examples include a computer program where modeling and actions are performed by software agents.  These software agents are aggregates. 
The participation of agents in flows is introduced and some implications of this are outlined. 
agents
can generally use genetic operators expressed through reproduction as new
This page reviews the implications of reproduction initially generating a single initialized child cell.  For multi-cellular organisms this 'cell' must contain all the germ-line schematic structures including for organelles and multi-generational epi-genetic state.  Any microbiome is subsequently integrated during the innovative deployment of this creative event.  Organisms with skeletal infrastructure cannot complete the process of creation of an associated adult mind, until the proximate environment has been sampled during development.  The mechanism and resulting strategic options are discussed. 
organisms
where modular components
This page discusses the mechanisms and effects of emergence underpinning any complex adaptive system (CAS).  Physical forces and constraints follow the rules of complexity.  They generate phenomena and support the indirect emergence of epiphenomena.  Flows of epiphenomena interact in events which support the emergence of equilibrium and autonomous entities.  Autonomous entities enable evolution to operate broadening the adjacent possible.  Key research is reviewed. 
emerge


The creation of these modular systems hugely increases the
To benefit from shifts in the environment agents must be flexible.  Being sensitive to environmental signals agents who adjust strategic priorities can constrain their competitors. 
flexibility
and adaptability of the development process enabling the emergence of an eco-network. 

Holland's genetic algorithm enables an abstraction of the evolutionary process which can be applied directly by design to situations where the environment is fixed and corresponds to a series of situations that each provide
Agents use sensors to detect events in their environment.  This page reviews how these events become signals associated with beneficial responses in a complex adaptive system (CAS).  CAS signals emerge from the Darwinian information model.  Signals can indicate decision summaries and level of uncertainty. 
signals
and are associated with defined actions of an agent.  The genetic algorithms schemata become simple arrays of actions indexed by signalled situation.  In such a situation the operation of an action can also be associated with a value of a fitness function. 

Evolutionary algorithms
To generate truly
This page discusses the mechanisms and effects of emergence underpinning any complex adaptive system (CAS).  Physical forces and constraints follow the rules of complexity.  They generate phenomena and support the indirect emergence of epiphenomena.  Flows of epiphenomena interact in events which support the emergence of equilibrium and autonomous entities.  Autonomous entities enable evolution to operate broadening the adjacent possible.  Key research is reviewed. 
emergent
systems the assumption that the states, actions, and signals, can be pre-assigned must be abandoned.  New environmental niches, information, constraints, structures and dynamics must emerge.  Typically the agent must
The agents in complex adaptive systems (CAS) must model their environment to respond effectively to it.  Evolution's schematic operators and Samuel modeling together support the indirect recording of past successes and their strategic use by the current agent to learn how to succeed in the proximate environment. 
model
its previous successes, current signals, environment as well as other agents' likely actions to represent its situation.  In the struggle to survive a current agent may utilize schematically recombined mechanisms during its operation which allow it to enter a new environmental niche (implying additional emergent states).  The
Plans emerge in complex adaptive systems (CAS) to provide the instructions that agents use to perform actions.  The component architecture and structure of the plans is reviewed. 
schematic strings
are consequently more feature rich than the simple genetic algorithm's situation addressed action arrays. 
































































































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This page looks at schematic structures and their uses.  It discusses a number of examples:
  • Schematic ideas are recombined in creativity. 
  • Similarly designers take ideas and rules about materials and components and combine them. 
  • Schematic Recipes help to standardize operations. 
  • Modular components are combined into strategies for use in business plans and business models. 

As a working example it presents part of the contents and schematic details from the Adaptive Web Framework (AWF)'s operational plan. 

Finally it includes a section presenting our formal representation of schematic goals. 
Each goal has a series of associated complex adaptive system (CAS) strategy strings. 
These goals plus strings are detailed for various chess and business examples. 
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  • A business can gain focus from targeting key customers,
  • Business planning activities performed by the whole organization can build awareness, empowerment and coherence. 
  • A program approach can ensure strategic alignment. 
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