*4.2. Battlefield Scenario Experiment*

In this experiment, scheduling optimization was performed assuming a situation in which 100 enemy ballistic missiles of four different types from four different launch sites flocked toward five friendly radar sites distributed appropriately. This is a much worse situation than that of local-scale model problem. Through this experiment, we verified the effectiveness and practical applicability of the optimal scheduling technique that employs the seamless handover method proposed in this study. Table 6 and Figure 11 show the parameters and conceptual diagram for this experiment, respectively. Compared to the local-scale model, the optimization planning horizon was increased to 1000 s and the number of targets and radars increased to 100 and 5, respectively. The most important

parameter—the simultaneous tracking capability—was increased to 20 so that five radars could cover all the 100 targets.

**Figure 11.** Conceptual diagram for the battlefield scenario.


**Table 6.** Parameter set for battlefield scenario experiment.

One of the most different aspects compared to the local-scale model is the importance of target, which is the first term of Equation (4). It is reflected in the objective function for this scenario unlike the previous experiment. The problem was solved with the assumption that the importance of target is uniform in the previous experiment. However, in this scenario, the target distance from radar and the response time available for the target were taken into consideration, as written in Equation (1), as in a real situation. Another difference related to the time window creation. In the local-scale model, a random function was used to generate a time window between arbitrary times selected by the user. However, in this experiment, it was assumed that the early warning radar provides the trajectory information of the ballistic missiles, so that the time windows could be created for radars located in various regions.

4.2.1. Weights of Objective Function Sensitivity Analysis

The objective function used in Equation (2) can be said to have some form of weighted sum. To check the dominance of each term of the objective function, the optimum value of individual objective was checked, as shown in Table 7.

**Table 7.** Solution ranges of each term of objective function and proposed coefficient setting.


As shown in Table 7, the first term, the priority of the target, was the dominant term that had the greatest influence on the objective function value. The third, the maximization number of tracked target, was found to have very little effect compared to the others. The fourth term, the minimization of the number of handover, is not included in this table because it acted as a penalty term. To analyze properly, the objective function needed to be normalized. In this study, considering the penalty terms, instead of dividing the objective by those optimum values, the most influential objective's coefficient (*c*1) was set to 1 and the remaining coefficients were normalized accordingly.

Based on the coefficients determined above, a sensitivity analysis was conducted according to the penalty term, the minimization of the number of handover, as shown in Figure 12. It is trivial that the objective function value decreased with increasing *c*4. One interesting point is that the number of handover decreased step-wise. These results indicate that, if *c*<sup>4</sup> is smaller than necessary, the overall objective function value can be high, but there are many unnecessary handovers. Therefore, choosing *c*<sup>4</sup> at which it starts to no longer decrease is the best decision to maximize the objective function value and reduce the number of handovers. Thus, *c*<sup>4</sup> of 35 was chosen for this case.

**Figure 12.** Sensitivity with respect to the penalty term.
