## 3 Heuristics Method to Calculate the Global Fitness of a Solution
### Computation of Global Fitness Value  
Based on the proposed Algorithms CNV and CST, we can calculate the partial fitness \(F(\mathbf{a}_{s})\) as well as the global fitness Y(**a**) by Algorithm 3 which is called _compute global fitness_ (CGF).  
In Algorithm CGF, for each AEOS \(s\), we use \(\Gamma_{s}\)to collect all observable targets in \(\mathbf{a}_{s}\) and initially set \(\Gamma_{s}=\{g_{1}\}\) and \(t_{g1}=\min_{k\in R}\{st_{g_{s},\ g1}^{k}\}\). Then, a loop (Lines 7-19) is executed to compute the start time for the observation of remaining targets in \(\mathbf{a}_{s}\), where \(g_{l}\in\Gamma_{s}\) is the current target and \(g^{\prime}\) is the target to be analyzed. In particular, each iteration can be divided into the following steps:  
Step 1: We use Algorithm CNV to obtain the non-conflict VTW set \(\mathbf{V}_{sg^{\prime}}(\Gamma_{s})\) of \(g^{\prime}\) under the known observations of targets in \(\Gamma_{s}\).  
Step 2: Let \(\mathbf{V}_{1}=\{[\varpi,\ \varphi]\in\mathbf{V}_{sg^{\prime}}(\Gamma_{s})\, \varpi\geq t_{gl}+d_{gl}\}\) be the feasible VTWs in \(\mathbf{V}_{sg^{\prime}}(\Gamma_{s})\) which begins after the observation of \(g_{l}\), and we further use Algorithm CST to obtain the start-observing time \(t_{g^{\prime}}\) of \(g^{\prime}\).  
Step 3: If \(t_{g^{\prime}}>0\), we add \(g^{\prime}\) into \(\Gamma_{s}\) and update \(g_{l}=g^{\prime}\), otherwise if \(t_{g^{\prime}}=0\), it indicates that \(g^{\prime}\) cannot be observed by \(s\) and we continue analyzing the next target.  
After all targets in \(\mathbf{a}_{s}\) have been analyzed, we compute the partial fitness \(F(\mathbf{a}_{s})\) according to (6), and the global fitness value \(\mathrm{Y}(\mathbf{a})=\Sigma_{s\in S}F(\mathbf{a}_{s})\) is finally outputted.  
```
Input: A candidate solution \(\mathbf{a}=[\mathbf{a}_{1},\,\mathbf{a}_{2},\,\ldots,\,\mathbf{a}_{m}]\); Output: the global fitness value \(Y(\mathbf{a})\);
1. for each\(s\in S\)
2. Denote \(\mathbf{a}_{s}=cg_{1},g_{2},\,\ldots,\,g\,|_{\mathbf{a}\in S}\,\);
3.\(t_{g1}=\min\{st_{s},g1^{k},k\in R\}\);
4. Set \(\Gamma_{s}=\{g_{1}\}\);
5. Set \(g_{l}=g_{1}\);
6. Set \(i=2\);
7. \(\mathbf{while}(i\leq|\mathbf{a}_{s}\,|\,)\)
8.\(g^{\prime}=g_{i}\);
9. According to Algorithm CNV, obtain non-conflict VTW set \(\mathbf{V}_{sg^{\prime}}(\Gamma_{s})\);
10. Let \(\mathbf{V}_{1}=[\lfloor\varpi,\,\varphi\rfloor\in\mathbf{V}_{sg^{\prime}}( \Gamma_{s})\,\rceil\,\alpha\geq t_{gl}+d_{gl}]\);
11. Let \(s,g_{l},g^{\prime}\), and \(\mathbf{V}_{1}\) be the inputs of Algorithm CST, obtain \(t_{g^{\prime}}\);
12. if\(t_{g^{\prime}}>0\)
13.\(\Gamma_{s}:=\Gamma_{s}\cup\{g^{\prime}\}\);
14.\(g_{l}=g^{\prime}\);
15. end if
16.\(i=i+1\);
17. end for
18.\(F(\mathbf{a}_{s})=\Sigma_{g\in\Gamma_{s}}\phi_{g}-1/e^{\tau}-(\Sigma_{g\in \Gamma_{s}}d_{g})/\text{Ave}(s)\), where \(\tau=1/(\,\lfloor\Gamma_{s}\,\rceil\,+\,1)\);
19. End
20. Output \(Y(\mathbf{a})=\Sigma_{g\in S}F(\mathbf{a}_{s})\);
21.\(F(\mathbf{a}_{s})=\Sigma_{g\in\Gamma_{s}}\phi_{g}-1/e^{\tau}-(\Sigma_{g\in \Gamma_{s}}d_{g})/\text{Ave}(s)\), where \(\tau=1/(\,\lfloor\Gamma_{s}\,\rceil\,+\,1)\);
22. End
23. Output \(Y(\mathbf{a})=\Sigma_{g\in S}F(\mathbf{a}_{s})\);
```  
**Algorithm 3**Compute global fitness (CGF).