## 3 Statement and Formulation of the Problem
By construction, it is obvious that \(\widetilde{\Omega}_{\bar{p},\bar{b}}\subseteq\Phi^{n}\). \(\bar{p}\) is an initial location and an assignment of boats \(\bar{b}\). For each possible route \(\tilde{\omega}_{\bar{p},\bar{b}}\in\widetilde{\Omega}_{\bar{p},\bar{b}}\), the function is  
\[T:\widetilde{\Omega}_{\bar{p},\bar{b}}\rightarrow\mathbb{R}^{n},\,T(\tilde{ \omega}_{\bar{p},\bar{b}})=(T_{1},\,T_{2},\,\ldots,\,T_{n}), \tag{3}\]  
where \(T_{i}(\tilde{\omega}_{\bar{p},\bar{b}})\) reports the time it takes for crew member \(i\) to get from his/her initial position to the lifeboat from the instant the abandon ship order is given. Due to the dynamics of the problem under study, it should be emphasized that  
\[T_{i}(\tilde{\omega}_{\bar{p},\bar{b}})=T_{i}(\phi_{1}(\bar{p}_{1},\bar{b}_{1} ),\,\phi_{2}(\bar{p}_{2},\bar{b}_{2}),\,\ldots,\,\phi_{n}(\bar{p}_{n},\bar{b} _{n})), \tag{4}\]  
because this time depends not only on the route taken by crew member \(i\) but also the routes assigned to the rest of the embarked population because blockages may occur in different areas of the ship. For an initial configuration \(\bar{p}\), \(\bar{b}\), and a route \(\tilde{\omega}_{\bar{p},\bar{b}}\), the evacuation time is defined as the first instant that the entire embarked population is in the lifeboats; that is  
\[t^{\varepsilon p}(\tilde{\omega}_{\bar{p},\bar{b}})=\max\Bigl{\{}T_{i}(\tilde{ \omega}_{\bar{p},\bar{b}}),i=1,\,\ldots,\,n\Bigr{\}}. \tag{5}\]  
In general, the ship is in state \(k\), where the location of the members is known \(\bar{p}^{k}=(\bar{p}^{k}_{1},\,\bar{p}^{k}_{2},\,\ldots,\,\bar{p}^{k}_{n})\). In addition, each embarked member is assigned a fixed lifeboat \(\bar{b}^{f}=(\bar{b}^{f}_{1},\,\bar{b}^{f}_{2},\,\ldots,\,\bar{b}^{f}_{n})\). The objective of this work is to establish an initial position \(\hat{p}^{k}\) and a boat assignment \(\tilde{b}^{f}\) for the embarked members to minimize the ship's evacuation time,  
\[t^{op}=\min t^{ev}(\tilde{\omega}_{\tilde{p},\tilde{b}})=\min\max\Bigl{\{}T_{i} (\tilde{\omega}_{\tilde{p},\tilde{b}}),i=1,\,\ldots,\,n\Bigr{\}}; \tag{6}\]  
that is, we seek the optimal route set \(\tilde{\omega}_{\hat{p}^{k},\hat{p}^{f}}^{op}\) such that  
\[\tilde{\omega}_{\hat{p}^{k},\hat{p}^{f}}^{op}=\arg\min\Bigl{\{}t^{ev}(\tilde{ \omega}_{\tilde{p},\tilde{b}}),\,\tilde{\omega}_{\hat{p}^{k},\hat{p}^{f}}\in \widehat{\Omega}_{\hat{p}^{k},\hat{p}^{f}}\Bigr{\}}. \tag{7}\]  
The ship evacuation dynamic monitoring system (SIMONE) is a prototype software, developed within the framework of a doctoral dissertation at the Universidad Politecnica de Cartagena (UPCT) in Spain, implementing this optimization problem. SIMONE simulates complex process system integration, as described above. Its main contribution is that it provides an optimal evacuation engine for a contingent embarked on a military ship. Thus, this engine recalculates a network of alternative escape routes in the event of an indefinite breakdown occurring in real time, monitoring the movement of the contingent at all times by using decision support techniques to achieve evacuation in the shortest possible time. SIMONE is thus a simulator modeling a dynamic structure emulating the general layout of a worship that has suffered an unforeseen breakdown. An optimal evacuation process is determined for the members of the crew (agents) in the shortest possible time. To automate the configuration of a scenario (fire, structural damage, smoke, heat, etc.) and control and monitor the people on board, it is essential to integrate the fundamental information provided by the different systems through a communications gateway. To emulate the automation of the environment, run the simulation of the evacuation, track the results, and make decisions; that is, to implement the functionality of the developed system, the following sequence of steps must be carried out. * Loading the scenario model, consisting of a file containing the features of the ship scenario or environment (graph).