## 3 The Proposed Model
### Design of the CSRO Algorithm
When the sum of the cost function in a given scenario, \(X^{\prime}_{i}\big{(}f\big{(}X^{\prime}_{i}\big{)}\big{)}\), is superior to the existing one, \((f(X_{i}))\), then the preceding location (\(X\)) would be saved in an accidental position in the memory matrix (\(M\)), and would be described as novel situation. If not, then the situation would be left, and the memory would not be upgraded. \[M_{n}=\left\{ \begin{array}{l}X_{j}\;if\;f\big{(}X^{\prime}_{i}\big{)}>f(X_{i })\\ M_{n}\;otherwise\end{array} \right. \tag{16}\]  
\[X_{i}=\left\{ \begin{array}{l}X^{\prime}_{i}\;if\;f\big{(}X^{\prime}_{i} \big{)}>f(X_{i})\\ X_{i}\;otherwise\end{array} \right. \tag{17}\]  
where \(n\) determines a random integer among \(1\) and \(N\), and \(M_{n}\) defines the location of clue number, \(n\), in the memory matrix. Time is critical in locating lost individuals due to threat of injury, and any delay that occurs at the time of searching could lead to death [69; 70; 71; 72]. Hence, when a person does not discover a notable clue during their search, it leaves the next person with the existing position. \[usn_{i}=\left\{ \begin{array}{l}usn_{i}+1\;if\;f\big{(}X^{\prime}_{i}\big{)}< f(X_{i})\\ 0\;otherwise\end{array} \right. \tag{18}\]  
where \(usn\) determines the unproductive searching number. When \(usn\) is superior to \(MU\) for a person, it moves towards the other location in the space solution. Figure 2 portrays the flow chart of SRO method. Figure 2: Flowchart of SRO. Search and rescue optimization (SRO), when searching for people, typically takes place in two distinct phases: social and individual. Collection followers search for clues founded in their location, and focus on areas that are more likely to yield clues in the social phase. There is no regard for where or how many clues have been found by others during the individual search phase. In general, clues fall into two categories, as follows:  
* Remember to save a clue: A member of the exploration group is present and searching the surrounding area. * Forgotten clue: Members of the group discovered the clue, but no one is in the location to solve it. To put it another way, the person who discovered the hint has abandoned it in search of further potentially relevant information. Members of the group, on the other hand, have access to the information about that clue. To increase exploration competence and ensure that the ideal answer is reached, the chaotic approach is combined with the krill head algorithm (KHA). Because Chebyshev maps are the most utilized chaotic behavioral maps, chaotic sequences are likely to be created efficiently and fast. Furthermore, longer sequences are not necessary  
Therefore, the existing solution has been switched to an accidental resolution in the solution space, according to Equation (7) for a possible solution, when \(usn>MU\) (\(Multi-User\)). In addition, for an unfeasible solution, \(usn\) is superior to \(MU\), the memory matrix solution using the minimum number of limitation violations is selected, and the current solution is switched through the solution, so that the current solution substitutes the memory matrix. \[X_{ij}=X_{j}^{\text{min}}\ +r_{4}\times\left(X_{j}^{\text{max}}\ -X_{j}^{\text{ min}}\ \right)\ j=1,2,\ d \tag{19}\]  
where \(r_{4}\) shows a frequently distributed random number within the range of 0-1. Under instruction to recover the worldwide optimization capability of an SRO algorithm, the chaotic concept is integrated into it. The chaotic state is an unstable state, which is extremely sensitive to initial conditions, which can be utilized for avoiding the local optimum problem and improving the quality of the solution. It is applied for achieving improved exploration and exploitation in every searching region, thereby enhancing the outcome in determining optimum global solutions [46; 47; 48]. The chaotic map was used in this study to indicate human searches around their current location in the individual phase, and the concept of linking different hints is used in the communal stage for exploration.