# A Novel Genetic Algorithm for the Synthetical Sensor-Weapon-Target Assignment Problem
## 4 Experimental Studies
### Experiments on Initialization  
In order to verify the performance of the proposed initialization method, the random initialization method is used for comparison. Using the random initialization method means that the encoding of an individual is generated randomly without any prior knowledge. Since many of the evolutionary mechanisms used in ds-GA differ from the proposed algorithm, it is difficult to rule out the influence of different evolutionary mechanisms on algorithm performance. As a result, in order to ensure the fairness of the comparison, the proposed initialization method in GA-SWTA is replaced by the random initialization method. Meanwhile, the other mechanisms and parameters remain unchanged. The variant is called GA-SWTA-r1. We performed 30 independent runs on each algorithm for each instance. Figure 12 shows the results of the two algorithms.  
Figure 11: Comparison results of MRBCH, Swt-opt, ds-GA and GA-SWTA with respect to the objective value.  
From Figure 12, it can be found that the difference in the performance of the given indexes between GA-SWTA and GA-SWTA-r1 are very small. It means that the proposed initialization method does not affect the convergence of the algorithm. This is because the convergence of the proposed algorithm is mainly affected by the evolutionary operators. As the initialization method is designed to improve the quality of the initial population, its main function is to improve the efficiency of the convergence. In this paper, the evolution of the mean value of the objective value versus number of iterations is used to demonstrate the efficiency of the proposed initialization method. As we stop both of the algorithms until the best solutions found so far remain unchanged in 500 generations, the convergent generation of each run of the algorithm is different. Therefore, we calculate the maximum number of iterations of all the runs, then extend the number of iterations of all the runs to the same size as the maximum number. In this paper, the best objective value of each run is used as the value of the extended iteration. The results are shown in Figure 13.  
As presented in Figure 13, the proposed initialization method can obtain a better initial value for almost all the instances. This means the proposed initialization method can generate a superior population at the beginning of the algorithm. In addition, for many instances, such as instances 2, 5, 9, 16, and 19, the maximum number of iterations of the proposed initialization method is remarkably less than the random method. This indicates our proposed method can effectively improve the convergence speed of the algorithm. Furthermore, for the very small-scale instances, instances No. 1 and No. 2, and the very large-scale instances, instances No. 21 to No. 25, our proposed initialization method is remarkably better than the random method. According to these experimental results, it can be concluded that the proposed initialization method can effectively improve the convergence efficiency of the algorithm, especially for the very small-scale and very large-scale S-WTA problems. This method cannot only improve the quality of the initial population, but also improve the convergence speed of the algorithm.  
Figure 12: Comparison results of GA-SWTA-r1 and GA-SWTA with respect to the objective value.