New Enhanced Artificial Bee Colony (JA-ABC5) Algorithm with Application for Reactive Power Optimization

Table 2

Statistical Results of Optimization Algorithms.

1	MIN	Average	STD DEV	15	MIN	Average	STD DEV
ABC	1.22  − 14	1.47  − 13	1.65  − 13	ABC	3.56  − 07	9.44  − 01	8.38  − 01
BABC1	4.44  − 16	6.22  − 16	1.50  − 16	BABC1	0.00 + 00	2.00  − 01	4.84  − 01
IABC	4.44  − 16	6.40  − 16	4.82  − 16	IABC	0.00 + 00	7.01  − 14	6.95  − 14
EABC	4.44  − 16	6.31  − 16	1.58  − 16	EABC	0.00 + 00	6.72  − 12	2.10  − 11
JA-ABC5	3.33  − 16	5.48  − 16	8.71  − 17	JA-ABC5	0.00 + 00	1.00  − 01	3.05  − 01
2	MIN	Average	STD DEV	16	MIN	Average	STD DEV
ABC	2.29  − 08	3.77  − 01	5.87  − 01	ABC	−2.92 + 01	−2.90 + 01	1.40  − 01
BABC1	0.00 + 00	2.98  − 01	4.64  − 01	BABC1	−2.96 + 01	−2.94 + 01	1.08  − 01
IABC	0.00 + 00	0.00 + 00	0.00 + 00	IABC	−2.96 + 01	−2.96 + 01	1.58  − 02
EABC	0.00 + 00	8.02  − 14	3.02  − 13	EABC	−2.96 + 01	−2.95 + 01	9.68  − 02
JA-ABC5	0.00 + 00	2.32  − 01	5.01  − 01	JA-ABC5	−2.96 + 01	−2.90 + 01	1.29  − 02
3	MIN	Average	STD DEV	17	MIN	Average	STD DEV
ABC	2.23  − 02	9.03 + 00	2.11 + 00	ABC	7.85  − 03	4.09  − 02	1.81  − 01
BABC1	2.32  − 02	3.04 + 01	3.30 + 01	BABC1	7.85  − 03	5.69  − 01	5.62  − 01
IABC	9.66  − 02	5.63 + 00	5.85 + 00	IABC	7.85  − 03	4.08  − 02	1.81  − 01
EABC	1.48  − 02	4.42 + 00	7.16 + 00	EABC	7.85  − 03	7.85  − 03	1.75  − 16
JA-ABC5	1.31  − 02	4.97 + 00	1.44 + 01	JA-ABC5	3.03  − 03	6.55  − 03	1.37  − 01
4	MIN	Average	STD DEV	18	MIN	Average	STD DEV
ABC	2.48  − 06	1.82  − 05	1.12  − 05	ABC	1.59  − 14	3.29  − 13	2.53  − 13
BABC1	3.46  − 14	4.86  − 14	7.52  − 15	BABC1	4.42  − 16	6.29  − 16	1.05  − 16
IABC	8.98  − 12	1.97  − 11	6.75  − 12	IABC	4.44  − 16	5.72  − 16	8.91  − 17
EABC	1.66  − 12	4.15  − 12	1.56  − 12	EABC	4.92  − 16	6.62  − 16	1.23  − 16
JA-ABC5	2.75  − 14	3.12  − 14	3.16  − 15	JA-ABC5	4.19  − 16	5.32  − 16	7.03  − 17
5	MIN	Average	STD DEV	19	MIN	Average	STD DEV
ABC	1.07  − 01	2.96 + 02	1.20 + 02	ABC	2.80 + 01	3.13 + 01	6.05 + 00
BABC1	3.82  − 04	1.54 + 02	1.33 + 02	BABC1	2.78 + 01	6.29 + 01	3.13 + 01
IABC	3.82  − 04	6.71 + 01	8.62 + 01	IABC	2.80 + 01	4.20 + 01	1.87 + 01
EABC	3.82  − 04	9.28 + 01	1.06 + 02	EABC	2.76 + 01	4.76 + 01	2.68 + 01
JA-ABC5	3.82  − 04	1.03 + 02	1.23 + 02	JA-ABC5	2.74 + 01	4.18 + 01	1.30 + 01
6	MIN	Average	STD DEV	20	MIN	Average	STD DEV
ABC	−7.83 + 01	−7.83 + 01	1.55  − 07	ABC	3.20  − 08	6.65  − 02	3.64  − 01
BABC1	−7.83 + 01	−7.82 + 01	4.09  − 01	BABC1	0.00 + 00	5.98  − 01	9.30  − 01
IABC	−7.83 + 01	−7.83 + 01	1.21  − 14	IABC	0.00 + 00	0.00 + 00	0.00 + 00
EABC	−7.83 + 01	−7.83 + 01	2.28  − 01	EABC	0.00 + 00	1.67  − 16	5.18  − 16
JA-ABC5	−7.83 + 01	−7.83 + 01	2.39  − 01	JA-ABC5	0.00 + 00	1.33  − 01	5.06  − 01
7	MIN	Average	STD DEV	21	MIN	Average	STD DEV
ABC	4.60  − 11	4.53  − 10	3.99  − 10	ABC	1.66  − 10	2.30  − 09	3.28  − 09
BABC1	4.55  − 16	6.66  − 16	1.10  − 16	BABC1	1.11  − 16	3.89  − 16	1.66  − 16
IABC	4.09  − 16	5.89  − 16	9.03  − 16	IABC	5.55  − 17	3.11  − 16	1.85  − 16
EABC	4.72  − 16	6.57  − 16	1.24  − 16	EABC	1.11  − 16	4.86  − 16	1.32  − 16
JA-ABC5	3.29  − 16	5.62  − 16	1.08  − 16	JA-ABC5	5.55  − 17	3.05  − 16	1.21  − 16
8	MIN	Average	STD DEV	22	MIN	Average	STD DEV
ABC	4.27  − 11	4.82  − 10	5.12  − 10	ABC	1.80  − 10	2.89  − 09	3.60  − 09
BABC1	4.54  − 16	6.37  − 16	1.02  − 16	BABC1	0.00 + 00	3.94  − 16	1.45  − 16
IABC	2.87  − 16	5.38  − 16	9.62  − 17	IABC	0.00 + 00	2.55  − 16	1.30  − 16
EABC	4.69  − 16	6.65  − 16	8.62  − 17	EABC	2.22  − 16	4.37  − 16	1.33  − 16
JA-ABC5	4.21  − 16	4.66  − 16	7.66  − 17	JA-ABC5	0.00 + 00	2.46  − 16	1.28  − 16
9	MIN	Average	STD DEV	23	MIN	Average	STD DEV
ABC	9.72  − 10	3.85  − 08	4.32  − 08	ABC	7.05  − 12	1.60  − 10	1.70  − 10
BABC1	1.11  − 16	4.57  − 16	1.36  − 16	BABC1	4.32  − 16	6.20  − 16	1.07  − 16
IABC	1.11  − 16	4.09  − 16	1.42  − 16	IABC	3.23  − 16	5.57  − 16	8.87  − 17
EABC	2.22  − 16	5.41  − 16	1.76  − 16	EABC	4.80  − 16	6.78  − 16	9.50  − 17
JA-ABC5	1.11  − 16	3.81  − 16	1.27  − 16	JA-ABC5	3.22  − 16	5.57  − 16	8.72  − 17
10	MIN	Average	STD DEV	24	MIN	Average	STD DEV
ABC	1.96  − 06	1.07  − 05	5.44  − 06	ABC	7.50  − 01	7.50  − 01	2.20  − 04
BABC1	5.55  − 17	2.44  − 15	1.79  − 15	BABC1	7.50  − 01	7.50  − 01	3.23  − 16
IABC	6.93  − 12	2.64  − 11	9.63  − 12	IABC	7.50  − 01	7.50  − 01	3.44  − 16
EABC	2.95  − 12	8.20  − 12	4.41  − 12	EABC	7.50  − 01	7.50  − 01	1.78  − 16
JA-ABC5	0.00 + 00	1.85  − 18	1.01  − 17	JA-ABC5	7.50  − 01	7.50  − 01	1.36  − 16
11	MIN	Average	STD DEV	25	MIN	Average	STD DEV
ABC	1.85  − 10	2.62  − 09	2.40  − 09	ABC	0.00 + 00	0.00 + 00	0.00 + 00
BABC1	3.93  − 16	6.42  − 16	1.11  − 16	BABC1	0.00 + 00	0.00 + 00	0.00 + 00
IABC	3.95  − 16	5.77  − 16	9.15  − 17	IABC	0.00 + 00	0.00 + 00	0.00 + 00
EABC	4.39  − 16	6.54  − 16	1.04  − 16	EABC	0.00 + 00	0.00 + 00	0.00 + 00
JA-ABC5	3.31  − 16	5.76  − 16	1.06  − 17	JA-ABC5	0.00 + 00	0.00 + 00	0.00 + 00
12	MIN	Average	STD DEV	26	MIN	Average	STD DEV
ABC	3.33  − 03	8.34  − 03	3.92  − 03	ABC	1.79 + 01	1.97 + 01	4.65  − 01
BABC1	4.60  − 13	1.77  − 12	1.30  − 12	BABC1	1.70 + 01	1.82 + 01	6.89  − 01
IABC	5.65  − 09	1.82  − 08	1.15  − 08	IABC	1.66 + 01	1.85 + 01	7.64  − 01
EABC	2.50  − 10	8.02  − 10	5.34  − 10	EABC	1.80 + 01	1.92 + 01	5.92  − 01
JA-ABC5	5.24  − 16	8.08  − 16	1.71  − 16	JA-ABC5	1.60 + 01	1.73 + 01	3.86  − 01
13	MIN	Average	STD DEV	27	MIN	Average	STD DEV
ABC	1.63  − 10	7.50  − 09	1.60  − 08	ABC	2.98 + 02	3.25 + 02	1.36 + 01
BABC1	4.49  − 16	6.38  − 16	1.06  − 16	BABC1	2.12 + 02	2.88 + 02	2.01 + 01
IABC	4.21  − 16	5.41  − 16	9.08  − 17	IABC	2.59 + 02	2.99 + 02	1.97 + 01
EABC	4.64  − 16	6.34  − 16	1.06  − 16	EABC	2.50 + 02	2.93 + 02	2.32 + 01
JA-ABC5	2.67  − 16	5.30  − 16	8.66  − 17	JA-ABC5	2.08 + 02	2.85 + 02	1.26 + 01
14	MIN	Average	STD DEV
ABC	3.32  − 08	4.03  − 04	1.31  − 03
BABC1	4.08  − 16	7.40  − 03	2.82  − 02
IABC	2.72  − 16	1.06  − 15	2.41  − 15
EABC	3.03  − 16	1.43  − 11	4.70  − 11
JA-ABC5	2.57  − 16	3.70  − 03	2.03  − 02