“At worst, it will disclose new sights and perspectives. At best, it will reveal the general principles we seek.”
Primer
Part one ( https://medium.com/@xorder/x-order-hidden-order-inside-complex-adaptive-systems-part-one-a67d840c176f) described the basic components to constructing a complex adaptive system model. Now let’s delve deeper into how to incorporate them into a model that has strong explanatory power.
The Echo Model
To build such a model, the first thing Holland did was creating a framework of desirable effects, and then built up the model incrementally, eventually giving birth to the Echo Model.
In the Echo Model, basic building blocks are a collection of resources, each of each is represented by a letter, which then can be arranged into strings, which can describe chromosomes of agents. Apart from resources, there is a world formed by geographical regions. Agents and resources are distributed in this world. There can be more than one agent in the same location.
Model One
In Model one, an agent is composed of two parts, one part is a storage for resources, the other is a chromosome that is represented by strings that represent resources. A chromosome has two tags, one offense tag and one defense tag. The chromosome not only decides the genetic substance of the agent, but also its abilities.
The agent in the Echo Model is illustrated below.
Agents can receive resources from special locations or by interacting with other agents. The key point is agents will reproduce after they have received an adequate amount of resources. The adaptive capabilities of an agent, in other words its ability to reproduce is implied in its ability to gather resources. We can compare the agent in the Echo Model to the rules described in Part One. Each of them is represented by a single chromosome, which contains information about its adaptive capabilities as well the ability to reproduce under certain circumstances. Exchanges between agents are facilitated through a matching algorithm. If the offense tag of an agent matches the defense tag of another agent, then a large portion of the resources (including resources in chromosome) stored in the agent with the defense tag will be transferred to the agent with the offense tag.
Here lies a caveat, although the book talks about the scenario where agents can potentially die from exchanges described above, it doesn’t give specifics to the circumstances in which an agent might die. There are two views that are worth discussing here: (1) An agent is deemed dead if it loses all its resources. (2) An agent is deemed dead if it loses all its resources and has not been able to improve the situation after a certain length of time. The author is more inclined towards the later view, which seems to adhere more to experiences in real life. For instance, a company does not go bankrupt the instance it has more debt than asset, but rather it would persist for a certain amount time hoping to get above water by making profits. Only has it been unable to create enough income to pay for expenses for some time would it go bankrupt.
With Model One as the basis, we can extend the single layer model into a complex multilayer model. The goal is to be able to simulate the process in which a single seed gradually evolves into a complex and self organized aggregate, akin to how a fertilized egg develops into an extremely complex organism such as a human being.
On top of this, Holland added five more mechanisms:
· One that allows selective exchange and interaction.
· One that allows resource conversion and transformation.
· One that determines adhesion between agents.
· One that allows selective mating.
· One that allows replications of conditions.
Next, let us find an instance of real life that adheres to each mechanism and attempt to offer justification of its existence.
Selective Interaction
According to economics, selective interaction is each one takes what one needs or desires. Agents in any kind of complex adaptive system can interact selectively. Herbivores do not eat meat, a factory that manufactures industrial machines would not collaborate with consumer product companies. If we let all agents to interact without selection, not only would it increase the amount of invalid interactions, it would also not reflect real life.
Resource Conversion and Transformation
The essence of resource conversion is that agents have the ability to transform resources that are abundant into resources that are scarce. This ability is ubiquitous in the development of organisms or economics. In biology, enzymes often catalyze molecular recombination to induce resource transformation. In economics, a corporation tends to be dealing resource shortage throughout its life. It must take initiatives to solve the shortage problems by converting available resources into needed scarce resources. Without the ability to transform resources, agents in CAS would lose a significant source of adaptive capabilities.
Adhesion
To a certain extent, this mechanism can be understood as selective cooperation. Our modern society has highly developed division of labour, each field has given birth to numerous distinctive niches. Therefore, by adding this mechanism into the model, agents will also develop effects similar to the real world. Some agents will have a stronger offense tag; others will have a stronger defense tag. If they adhere to each other then they could complement each other and, as an aggregate, be better able to gather and protect resources. Meanwhile, this mechanism can also serve as a block to be repeatedly employed, forming a layered effect. Here two agents adhere together to form an aggregate, which is treated also as an agent that can adhere to other agents or aggregates. Blow is a diagram that illustrates a complex aggregate with 8 simplest agents.
Adhesion brings another effect called boundary, which entails that agents that are surrounded by outer boundaries are unable to interact directly with other agents outside of the boundaries, but instead have to seek a “representative” to exchange with outside agents. This is similar to how in a company, departments such as treasury, human resources normally do not interact with stakeholders outside of a company. Instead the interaction is usually facilitated by sales and purchasing, who act as representatives for the company to interact with its external stakeholders. With boundaries, agents are restricted in a limited region for interaction, which is more fitting for the properties of agents of CAS observed in real life CAS.
Selective Mating
Similar to selective interaction, agents should also have the need to mate in order to preserve chromosomes that have stronger adaptive capabilities within the population. This is quite similar to CAS in the real world. The significance of selective mating in the model is identical to the significance of its counterpart in biological evolution.
Conditional Replication
Conditional replication is a quite complicated mechanism. It is designed to imitate the process whereby a single-cell organism develops into multi-cell organisms even though their chromosomes are exactly the same. This implies that there exists a certain mechanism that allows different parts of the same chromosomes to have various different effects. This is what conditional replication attempts to capture.
Previously we have mentioned an aggregate agent. Thanks to conditional replication, we can introduce another kind of aggregate, multi-agents. The difference between the two is that chromosomes in an aggregate can be selectively activated or deactivated due to conditional replication, whereas chromosomes within simple aggregates are only tandem strings that cannot control their own activation or deactivation.
So far, Holland’s methodology is to add successive layers incrementally to the initial Echo Model as a means to incorporate various mechanisms, eventually creating a complex mechanism that is constructed from simple rules, just like how real life complex adaptive systems look like in the real life.
The serialization and realization of the complete model using computer simulation can be seen below:
The diagram above illustrates two important procedures for CAS, the first is the process of free agents evolving into multiagents, the second process is how a single seed multiagents can become a special aggregate of multiagents.
We are also able to observe procedures that show credit assignment and rule discovery described in Part One. The exchange of adhesion scores represents credit assignment; the exchange of resources represents rule discovery.
This simulation model reflects all the properties of CAS and generalizes CAS to an Echo Model in a formal equivalence manner. In terms of application, Holland pointed to two directions, one is assist people in conducting thought experiments, the other is directing research in CAS and further adding more elements to better reflect reality. The Echo Model can help us grasp the possibilities lying in the future.
Two-Tiered Models
Holland also derived a more abstract model that has stronger explanatory power than the Echo Model called Two-Tiered Model, in which more emphasis is put on painting a real time picture of resource flow at the lower tier. The upper tier is more concerned with the changes of the final state due to evolution and network. Because the former is over a shorter time horizon, it gives a model of fast dynamics, whereas the latter gives that of slow dynamics of long term adaption and evolution. The combination of both help us understand the universe. Just like Holland said at the end of the book, “At worst, it will disclose new sights and perspectives. At best, it will reveal the general principles we seek.”
Professor Holland passed away in August, 2015, let us give our regards to the father of genetic algorithm.
Reference:
Hidden Order — John Holland
— — —
Check out our website at www.xtoken.org.
If you are interested in our research and ventures, join our Discord at https://discord.gg/tVMZyc
