## 5 Performance Evaluation
The greedy algorithm achieves 6% to 35% higher target coverage rates than do the other three evolutionary algorithms as the number of targets increases. However, Figure 5b reveals that the active sensor rate of the greedy algorithm is 4-41% higher than the other three algorithms. Therefore, the quality of the solutions of the evolutionary algorithms is higher than that of greedy algorithm for larger numbers of targets (Figure 5c). Moreover, among the proposed metaheuristic algorithms, the DPSO_GA algorithm outperforms the GA and DPSO algorithms in terms of the target coverage rate and the fitness values despite requiring the most active sensors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Meaning** \\ \hline \(N\) & 50, 75, 100, 125, 150, 175, 200 & Number of directional sensors \\ \(M\) & 50, 100, 150, 200 & Number of targets \\ \(R\) & 60, 80, 100, 120 & Sensing radius (m) \\ \(\theta\) & 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\) & Field of view \\ \(w\) & 0.5 & Weight of fitness function \\ \(P\) & 100 & Population size \\ \(P_{c}\) & 0.8 & Probability of GA crossover operator \\ \(P_{m}\) & 0.1 & Probability of GA mutation operator \\ \(\omega\) & 0.1 & Probability of DPSO mutation \((F_{1})\) \\ \(c_{1}\) & 0.5 & Probability of DPSO crossover \((F_{2})\) \\ \(c_{2}\) & 0.5 & Probability of DPSO crossover \((F_{3})\) \\ \(l_{c}\) & 1000 & Number of generations or iterations \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. The fitness of the DPSO_GA algorithm is 0.17-1.23% higher than that of the GA and DPSO algorithm. Figure 5d plots the fitness values versus the number of generations for the GA, DPSO, and DPSO_GA schemes with \(N=100\), \(M=150\), \(R=80\), \(\theta=60^{\circ}\), \(w=0.5\), and \(Ic=1000\). The fitness values of the DPSO_GA and DPSO approaches were greater than that of the GA approach after the first three generations, that of the DPSO_GA approach was greater than the DPSO approach after 110 generations, and DPSO_GA obtained solutions that were 0.58% and 1.23% better than those of DPSO and GA, respectively, after 1000 generations. As a result, the hybrid scheme was more likely to achieve the global optimum solutions for the MCMRS problem in terms of the number of targets. Figure 6 shows how the field of view has an impact on the target coverage rate, active sensor rate, and fitness values in the GA, DPSO, and DPSO_GA algorithms compared with the solutions obtained by the greedy algorithm. In this experiment, \(N=200\) targets and \(M=100\) sensors were randomly generated in the specified region. The sensors' coverage radius \(R=80\) m and the weight of fitness function \(w=0.5\). The field of view varied from \(30^{\circ}\) to \(120^{\circ}\) in increments of \(30^{\circ}\). Figure 6a,b reveals that, as in the other experiments, the greedy algorithm achieves a \(>20\%\) higher target coverage rate but requires a \(>25\%\) higher active sensor rate and thus is outperformed by the evolutionary algorithms by 2.53-45.61% (Figure 6c). The DPSO_GA algorithm again outperforms the GA and DPSO algorithms by 4.73% to 8.89% but requires more active sensors. Figure 6d plots the fitness values versus the number of generations for GA, DPSO, and DPSO_GA with \(N=100\), \(M=200\), \(R=80\), \(\theta=90^{\circ}\), \(w=0.5\), and \(Ic=1000\). DPSO_GA and DPSO outperformed the GA approach after 12 generations, and DPSO_GA ultimately obtained solutions that were 3% and 5% better than those of DPSO and GA, respectively. As a result, the hybrid scheme was more likely to achieve the global optimum solutions for the MCMRS problem in terms of the field of view. Figure 4: Effect of the number of sensors on the target coverage rate, active sensor rate, and fitness values for the greedy, GA, DPSO, and DPSO_GA algorithms. (**a**) Target coverage rate, (**b**) active sensor rate, (**c**) fitness values, and (**d**) fitness values versus the number of generations for GA, DPSO, and DPSO_GA.