Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming

Table 3

Execution time and speedup of parallel version of the genetic algorithm when varying the problem size. The average and standard deviation of the values of DMUs are shown. In each case, 𝑝 is the number of processors used, time is the execution time in seconds, and sp is the speedup.

𝑚	𝑛	𝑠	𝑝	Time	sp
2	15	1	1	0.210.30	—
			2	0.140.19	1.241.24
			4	0.090.12	1.850.59
			8	0.080.10	2.031.23
			16	0.120.17	1.530.50
3	25	2	1	0.300.27	—
			2	0.180.15	1.550.22
			4	0.110.09	2.460.67
			8	0.080.07	3.221.37
			16	0.100.09	2.590.86
4	30	2	1	0.170.17	—
			2	0.100.10	1.650.19
			4	0.060.05	2.590.46
			8	0.050.05	3.170.85
			16	0.060.05	2.620.87
5	40	4	1	0.810.55	—
			2	0.460.30	1.720.21
			4	0.250.17	3.040.44
			8	0.190.12	4.190.93
			16	0.170.12	4.711.44
6	60	4	1	2.111.14	—
			2	1.130.60	1.850.10
			4	0.610.32	3.360.33
			8	0.380.20	5.380.96
			16	0.290.16	7.111.84
10	100	10	1	0.660.08	—
			2	4.371.68	1.940.13
			4	2.320.83	3.590.37
			8	1.310.46	6.330.70
			16	0.800.27	10.271.55