## 3 Statement and Formulation of the Problem  
The development of an application (SIMONE) with the capacity to reconfigure an environment in the event of failure is proposed. This implies recalculating the network of alternate routes through which the embarked contingent will move. To do this, a powerful simulation engine undertakes real-time monitoring and optimal management of the crew to evacuate it in the reconfigured scenario in the shortest possible time. To provide the SIMONE simulator with the aforementioned capabilities, it must be integrated into the IPCS (see Figure 2) through a communications gateway. This is a system that automatically evaluates, identifies, and quantifies the damage the incident causes to the general layout of the ship. Thus, to monitor the contingent of reference, we implement a network of RFID nodes. This is widely deployed and validated technology that was applied in the study undertaken by the GIMO. It allows us to monitor the position of the members of an embarked population as they move throughout the naval platform. Following this functional model for the SIMONE simulator and the methodologies and techniques implemented [22], it is possible to develop and program the engines that emulate the supervening scenario and the optimal evacuation process to obtain the fastest possible evacuation. The proposed model seeks to minimize the evacuation times of each member of the embarked contingent, thereby minimizing the total time used for evacuation. The magnitude or reference value of the process will be determined by the time taken by the last agent  
Figure 2: Data flow diagram (DFD, level 0). Functionality of the proposed system. to leave the platform. Considering the premises, characteristics of the problem, and stated solution, its resolution is mathematically formulated as follows. \(n\in\mathbb{N}\) is the number of people making up the population on board a navy ship. \(P=\{p_{1},\,p_{2},\,\ldots,\,p_{m_{1}}\}\) is the set of different compartments/rooms into which we have divided the ship and that indicate the location of any member of the embarked population. \(B=\{b_{1},\,b_{2},\,\ldots,\,b_{m_{2}}\}\) is the set of available lifeboats on the ship. \(\bar{p}=(\bar{p}_{1},\,\bar{p}_{2},\,\ldots,\,\bar{p}_{n})\), where \(\bar{p}_{i}\in P\), \(i=1,\,\ldots,\,n\), denotes the location of each arbitrary member \(i\) of the crew. \(\bar{b}=(\bar{b}_{1},\,\bar{b}_{2},\,\ldots,\,\bar{b}_{n})\), where \(\bar{b}_{i}\in B\), \(i=1,\,\ldots,\,n\), denotes the assignment of a particular lifeboat to each member \(i\) of the embarked population. For each \(p\in P\) and for each \(b\in B\), the following holds. * \(\phi^{j}(p,b)\) is a possible route (without loops), leading us from starting point \(p\) to boat \(b\). * \(\Phi_{p,b}=\{\phi^{j}(p,b)\}_{j\in I_{p,b}}\) is the set of all possible routes (without loops) from starting point \(p\) to boat \(b\). Finally, we define  
\[\Phi=\bigcup_{ \begin{subarray}{c}p\in P\\ b\in B\end{subarray} }\Phi_{p,b} \tag{1}\]  
as the set of all possible paths (without loops) from any starting point to any destination boat. Given an initial location \(\bar{p}\) and an assignment of boats \(b\), the set of all available routes \(\widetilde{\Omega}_{\bar{p},\bar{b}}\) for the embarked population is defined as  
\[\widetilde{\Omega}_{\bar{p},\bar{b}}=\bigcup_{ \begin{subarray}{c}\phi_{1}(p_ {1},\bar{b}_{1})\in\Phi_{p_{1},\bar{b}_{1}}\\ \phi_{2}(p_{2},\bar{b}_{2})\in\Phi_{p_{2},\bar{b}_{2}}\\ \phi_{\bar{\alpha}}(p_{\alpha},\bar{b}_{\alpha}^{-})\in\Phi_{p_{\alpha},\bar{b }_{\alpha}}\end{subarray} }\{\phi_{1}(\bar{p}_{1},\bar{b}_{1}),\,\phi_{2}(\bar {p}_{2},\bar{b}_{2}),\,\ldots,\,\phi_{n}(\bar{p}_{n},\bar{b}_{n})\}, \tag{2}\]  
where \(\phi_{i}(\bar{p}_{i},\bar{b}_{i})\in\Phi_{\bar{p}_{i},\bar{b}_{i}}\). That is, each onboard member located at a certain location \(\bar{p}_{i}\) and with a lifeboat \(\bar{b}_{i}\) assigned obtains a possible route \(\phi_{i}(\bar{p}_{i},\bar{b}_{i})\) to reach it.