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

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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