## 4 The Algorithms
### Transportation Role
#### 4.3.1 Transport of an Agent  
Let there be a set of agents \(A\) that contains all types of agents needed to explore all types of environments \(S_{real}=\{s_{\{1,2\}},s_{\{2,1\}},...,s_{\{n,i\}}\}\). This set is located at the main entrance \(e_{S_{real}}\) to the space \(S_{real}\). The agents wait at the entrance \(e_{S_{real}}\), \(e_{S_{real}}=e_{x_{m}}\subset s_{\{x,k\}}\)\(x\in<1,n>,k\in<1,i>\) and check the pheromone marks \(Pena_{\{y,m,j\}}(t),y\in<1,n>,j\in<1,i>\) at the entrance \(e_{S_{real}}\). In the case that there is a pheromone mark placed at the entrance that informs of a needed addition of an agent from the agent group \(A_{j}\) into the environment \(s_{\{y,j\}}\), agent \(a_{\{j,y,v\}}\) then accepts the request and goes to the given entrance \(e_{S_{real}}\) (the pheromone mark \(Pena_{\{y,m,j\}}\) is then reset to zero). If the agent \(a_{\{j,y,v\}}\) is not capable of traversing the given type of environment \(s_{\{x,k\}}\), \(k\sim j\lor k\), \(j\in<1,i>\) it waits then at the entrance and requests transport. If, during the process of space exploration, an agent \(a_{\{k,x,v\}}\) comes to the vicinity of the agent \(a_{\{j,y,x\}}\), then the agent \(a_{\{k,x,v\}}\) automatically transports the agent \(a_{\{j,y,v\}}\) to the entrance \(e_{y_{m}}\) of the subspace \(s_{\{y,j\}}\). Both agents resume the space exploration task upon the arrival at the target location. The pheromone mark encodes in itself the individual entrances it has been transported through. 3.2 Creating a Request for Adding an Agent into a Subspace with an Environment Where the Request Creating Agent is Not Capable of Operation  
If the agent \(a_{\{k,x,v\}}\) exploring a subspace \(s_{\{x,k\}}\) finds the entrance \(e_{y_{m}}\subset s_{\{y,j\}}\) to the subspace \(s_{\{y,j\}}\), \(x\sim y\lor x,y\in<1,n>\), and it is not capable of exploring the subspace \(s_{\{y,j\}}\) (its abilities, construction, etc. prohibit it), and the entrance \(e_{y_{m}}\) was not marked by the pheromone mark of the agent \(a_{\{j,y,v\}}\), then the agent \(a_{\{k,x,v\}}\) goes to the entrance \(e_{x_{m}}\subset s_{\{x,k\}}\) it used to enter the subspace \(s_{\{x,k\}}\) and leaves there a pheromone mark requesting the addition of a corresponding agent from the set \(A_{y}\) (\(Pena_{\{y,m,j\}}\) from \(e_{y_{m}}\) is transported to the \(e_{S_{real}}\)). If the entrance \(e_{y_{m}}\) was already marked by the pheromone mark of the agent \(a_{\{j,y,v\}}\), the agent \(a_{\{k,x,v\}}\) continues to explore the subspace \(s_{\{x,k\}}\). 3.3 Transfer of the Addition Request Related to the Addition of an Agent into a Group that Is Different than the Group of the Transferring Agent  
Sometimes an agent that is needed elsewhere must transit several environments until it reaches the environment where it is capable of operating in. In that case, the problem of transferring the addition requests must be resolved. Let us assume that the subspace \(S=\{s_{\{1,f\}},s_{\{2,d\}}\},f,d,\in<1,i>\) must be explored. Let \(s_{\{1,f\}},s_{\{2,d\}}\) have entrances \(E_{1}=\{e_{1_{1}}\},e_{S_{real}}=e_{1_{2}}\subset s_{\{1,f\}}\) and \(E_{2}=\{e_{2_{m}}\},e_{2_{m}}\subset s_{\{2,d\}}\), respectively. Let us assume that \(s_{\{2,d\}}\) is enveloped by \(s_{\{1,f\}}\). There are agents \(a_{\{f,1,v\}}\) operating in the subspace \(s_{\{1,f\}}\) and \(a_{\{d,2,x\}}\) operating in the subspace \(s_{\{2,d\}}\) (the agent \(a_{\{d,2,x\}}\) reached the subspace \(s_{\{2,d\}}\), based on the previous two rules described in Section 4.1). If the agent \(a_{\{d,2,x\}}\) operating in the subspace \(s_{\{2,d\}}\) establishes that another agent is needed, agent \(a_{\{d,2,x\}}\) goes to the entrance \(e_{2_{m}}\) to the subspace \(s_{\{2,d\}}\) to place the pheromone mark \(Pa_{\{d,2,x\}}\). The value of the pheromone mark requesting the addition of an agent \(Pena_{\{2,m,d\}}(t)\) changes based on Equation (7) as the pheromone mark evaporates over time.