Table 5 shows ten random results for different algorithms and the following can be seen:

• 1.

The average result for the bat algorithm was less than that for the genetic algorithm and particle swarm algorithm for the base and future periods.

• 2.

The average solution for the genetic algorithm was worse than for the particle swarm algorithm and the bat algorithm for the base and future periods.

• 3.

The coefficient of variation for the bat algorithm was smaller than for the genetic algorithm and particle swarm algorithm for the base and future periods.

• 4.

Results for the base period for all algorithms were less than for the future period.

Table 5

Ten random results for evolutionary algorithms

RunBat algorithmParticle swarm algorithmGenetic algorithm
Base period
1 1.54 2.99 3.95
2 1.55 2.98 3.89
3 1.54 2.99 3.95
4 1.54 2.98 3.89
5 1.55 2.98 3.89
6 1.54 3.05 3.89
7 1.54 2.98 3.89
8 1.54 2.98 3.89
9 1.54 2.98 3.89
10 1.54 2.98 3.89
Average 1.54 2.98 3.89
Variation coefficient 0.002 0.005 0.008
Future period
1 2.77 4.83 5.45
2 2.76 4.77 5.11
3 2.76 4.80 5.45
4 2.76 4.77 5.45
5 2.76 4.77 5.45
6 2.76 4.77 5.45
7 2.76 4.77 5.45
8 2.76 4.77 5.45
9 2.76 4.77 5.45
10 2.76 4.77 5.45
Average 2.76 4.77 5.45
Variation coefficient 0.002 0.003 0.019
RunBat algorithmParticle swarm algorithmGenetic algorithm
Base period
1 1.54 2.99 3.95
2 1.55 2.98 3.89
3 1.54 2.99 3.95
4 1.54 2.98 3.89
5 1.55 2.98 3.89
6 1.54 3.05 3.89
7 1.54 2.98 3.89
8 1.54 2.98 3.89
9 1.54 2.98 3.89
10 1.54 2.98 3.89
Average 1.54 2.98 3.89
Variation coefficient 0.002 0.005 0.008
Future period
1 2.77 4.83 5.45
2 2.76 4.77 5.11
3 2.76 4.80 5.45
4 2.76 4.77 5.45
5 2.76 4.77 5.45
6 2.76 4.77 5.45
7 2.76 4.77 5.45
8 2.76 4.77 5.45
9 2.76 4.77 5.45
10 2.76 4.77 5.45
Average 2.76 4.77 5.45
Variation coefficient 0.002 0.003 0.019
Figure 11 shows the convergence for different algorithms. It can be seen that the bat algorithm converged in a fewer number of iterations than the particle swarm and genetic algorithms for the base period and future periods. The main indicator that the algorithm achieved the global solution is that the convergence curve becomes stable.

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