Brazilian Firms
2008
2007
2006
2005
2004
% Cash Available (Mean)
9.10%
11.39%
9.22%
7.49%
6.75%
Standard Deviation
15.81%
17.35%
16.27%
14.72%
13.87%
Number of Firms
567
369
366
350
353
Table 1 – Share of total assets in cash - Brazilian companies (elaborated by the
authors, Source: Economática).
Random Number Generation
Mean
Standard Deviation
Class 1
1,000
500
Class 2
1,000
5,000
Class 3
1,000
50,000
Class 4
20,000
500
Class 5
20,000
5,000
Class 6
20,000
50,000
Class 7
100,000
500
Class 8
100,000
5,000
Class 9
100,000
50,000
Table 2 – General diagram of the life cycle of genetic algorithm ( Rezende, 2005 ).
Class of Problem
Optimal Algorithm Miller-Orr
GA Algorithm
PSO Algorithm
Cost
Time
Cost
Iteration
Time
Cost
Iteration
Time
1
4,638.63
196.04
3,932.32
18.88
2.88
3,839.03
131.44
23.54
2
5,346.83
196.25
5,294.23
4.20
3.03
4,568.75
123.24
23.46
3
20,740.28
196.51
19,170.62
48.55
2.93
18,315.77
150.22
23.34
4
18,895.27
189.63
15,079.21
13.07
2.89
14,997.96
70.78
23.24
5
19,694.68
196.09
14,992.53
8.33
2.88
14,880.98
118.48
23.52
6
24,517.72
200.66
20,166.89
13.80
2.97
19,444.35
164.92
23.60
7
36,110.19
178.35
29,800.56
3.10
2.84
29,817.45
17.06
23.28
8
37,227.33
182.92
29,813.75
13.41
2.92
29,812.04
41.68
23.36
9
40,346.49
194.90
28,990.28
13.61
3.02
28,829.36
92.06
23.91
Table 3 – Comparative results between groups by Optimal Algorithm, GA and PSO
Class of Problem
GA Algorithm
PSO Algorithm
Cost Reduction
% Var
Cost Reduction
% Var
1
706.30
18.60%
799.60
21.28%
2
52.60
1.28%
778.07
17.08%
3
1,569.66
8.24%
2,424.52
13.28%
4
3,816.06
25.33%
3,897.31
26.00%
5
4,702.15
31.38%
4,813.70
32.36%
6
4,350.83
21.65%
5,073.37
26.15%
7
6,309.63
21.17%
6,292.74
21.11%
8
7,413.58
24.87%
7,415.29
24.87%
9
11,356.21
39.18%
11,517.13
39.96%
General
21.30%
24.68%
Table 4– Comparative results of cost reduction in GA and PSO in relation to
Miller-Orr model
Class of Problem
ARD
ARD
ADR
Best Solution
Optimal Algorithm Miller-Orr
GA Algorithm
PSO Algorithm
GA
PSO
1
24.74%
5.54%
3.04%
42.00%
58.00%
2
17.09%
15.94%
0.00%
0.00%
100.00%
3
13.28%
4.68%
0.00%
0.00%
100.00%
4
26.47%
0.93%
0.38%
43.00%
57.00%
5
32.68%
0.99%
0.24%
31.00%
69.00%
6
26.15%
3.73%
0.00%
0.00%
100.00%
7
21.37%
0.16%
0.22%
55.00%
45.00%
8
25.11%
0.20%
0.19%
54.00%
46.00%
9
40.09%
0.66%
0.09%
25.00%
75.00%
General
25.22%
3.65%
0.46%
27.78%
72.22%
Table 5 – Comparative results between groups by Optimal Algorithm, GA and PSO
t-Test: two sample assuming equal variances
GA
PSO
Mean
18,582.27
23,060.51
Variance
86,859,400.32
151,313,595.00
Observations
900
900
Stat t
-8.705272018
P(T<=t) bi-caudal
7.03163e-18
t critical bi-caudal
1.961284203
Table 6 – Comparative results of cost reduction in GA and PSO in relation to
Miller-Orr model