Proceso transaccional

In the previous two experiments we have only considered cases in which Team A and Team B both have the same number of units. In general, this is not the case. In Experiment III we measured the performance of the ULTRA algorithm as the number of units on each team varies independently. Here we assumed that ULTRA used the either the zero or the unit greedy initial target assignment strategy. As in the previous two experiments, the model was simulated 25,000 times for each scenario considered, each instance having randomly generated probability of kill values such that Pi^B = ∀ ∈^{1 1, 2,}i

{

…^,NB

}

.

First, we examined two cases. The first, in which the number of units on Team A varies from one to 6 while the number of units on Team B remains constant at four and the second in which the number of units on Team B varies from one to 6 while the number of units on Team A remains constant. We evaluated each of these scenarios using both the unit greedy assignment and the zero assignment as the initial strategy using four metrics. In the first metric, we measured how the average accuracy was affected by non-uniformly varying the number of units per team.

The resulting data can be seen in Figure 3.23.

95 95.5 96 96.5 97 97.5 98 98.5 99 99.5 100

1 2 3 4 5

Number of Units on Varying Team

Average Accuracy (%)

6 Zero Initial Strategy - Constant #Units on Team A

Zero Initial Strategy - Constant #Units on Team B

Unit Greedy Initial Strategy - Constant #Units on Team A Unit Greedy Initial Strategy - Constant #Units on Team A

Figure 3.23 – Average Accuracy of ULTRA with Dissimilar Teams

Several interesting concepts are illustrated in Figure 3.23. On one hand, the lowest average accuracy occurred when Teams A and B had an equal number of units, the case when both were composed of four units. ULTRA appears to generate better strategies for situations involving teams of dissimilar numbers of units than for more balance situations. On the other, when using the unit greedy target assignment strategy, the average accuracy of the strategy ULTRA calculates for Team A is approximately the same when there are many units on Team A and few on Team B as in the case when there are few units on Team A and many on Team B. This symmetry is not found when the zero target assignment strategy is used as the initial strategy.

For example, the when the zero initial strategy is employed, on average ULTRA generates a better Strategy for Team A when N_A = and 6 N_B = then when 4 N_A = and 4 N_B =6.

In the second metric we explored the manner in which having teams of dissimilar size effects the threshold performance of ULTRA. In particular we examined the probability that ULTRA returns an optimal strategy. These measurements are shown in Figure 3.24. From Figure 3.24 we can conclude that ULTRA often yields an optimal target assignment strategy when there are few units on Team A and many units on Team B. In contrast, ULTRA almost never yields an optimal target assignment strategy when there are many units on Team A and few units on Team B. This makes sense as when there are few units on Team A and many on Team B each unit on Team A will often be assigned to the Unit on Team B it is most suited to attack. On the other, when there are many units on Team A and few units on Team B it can be very difficult to coordinate an optimal attack.

0 10 20 30 40 50 60 70 80 90 100

1 2 3 4 5 6

Number of Units on Varying T eam

100% Accuracy (%)

Zero Initial Strategy

-Constant #Units on Team A Zero Initial Strategy

-Constant #Units on Team B Unit Greedy Initial Strategy -Constant #Units on Team A Unit Greedy Initial Strategy -Constant #Units on Team B

Figure 3.24 – Chance of ULTRA obtaining Optimal Strategy with Dissimilar Teams

The third metric used to examine the effects of teams of dissimilar numbers of units is the run time requirements of ULTRA. In particular, we examined the average number of objective function evaluations required for ULTRA to converge. This is shown in Figure 3.25. Here we see that the number of units on Team A has a larger effect on the time required for ULTRA to calculate a target assignment strategy for Team A than the number of units on Team B.

1 10 100 1000

1 2 3 4 5 6

Number of Units on Varying Team

Avg Number of Obj. Fn. Evaluations

Zero Initial Strategy - Constant #Units on Team A Zero Initial Strategy - Constant #Units on Team B

Unit Greedy Initial Strategy - Constant #Units on Team A Unit Greedy Initial Strategy - Constant #Units on Team B

Figure 3.25 – Avg. Number of Objective Function Evaluations Assuming Dissimilar Teams

In the second part of Experiment III, instead of fixing the number of units on one team and varying the number of units on the other we examined all combination of number of units per team when N_A∈

{

1, 2,3, 4, 5, 6

}

and N_B∈

{

1, 2,3, 4, 5, 6

}

. Every scenario we measured the average accuracy of the ULTRA algorithm for each of the three initial target assignment strategies presented earlier over 25,000 iterations. Figure 3.26 illustrates the result of this simulation. From these plots, we can conclude that the conclusions drawn previously in

Experiment III are applicable in a more general sense. These conclusions seem to apply to all combinations of units on each side rather that the specific case when one team has four units.

Figure 3.26 – Surface Plots of Avg Accuracy versus # of Units on Team A and B

In document Estilos de liderazgo y sus efectos en el desempeño de la administración pública mexicana (página 106-111)