Optimization of Collocated/Noncollocated Sensors and Actuators along with Feedback Gain Using Hybrid Multiobjective Genetic Algorithm-Artificial Neural Network

Table 3

Optimal solutions of MOGA considering PIc, PIo, and closed loop average damping ratio as objective functions.

S. number	𝛼1	𝛽1	𝛾1	Actuator’s location								Sensor’s location								PIc	PIo	Damping ratio
1	40.76800024	198.4794357	1.181020809	50	31	33	7	22	51	2	36	44	3	17	6	35	47	52	60	−4.24𝐸−11	−9.86𝐸+20	0.090787642
2	182.3526343	187.8703766	1.305345973	8	28	2	3	55	53	13	0	23	21	41	28	18	55	0	0	−3.59𝐸−12	−2.07𝐸+20	0.08550091
3	57.31960912	189.2998006	1.743118415	34	2	6	4	16	13	39	44	38	42	15	50	5	22	45	0	−2.31𝐸−12	−7.72𝐸+20	0.079966706
4	142.5709478	154.6021081	1.488729247	20	43	36	5	64	14	25	0	4	33	5	2	29	43	28	0	5.15𝐸−12	−1.93𝐸+20	0.068721487
5	25.50863504	101.1366512	1.350108138	8	23	24	3	2	51	22	29	36	22	30	6	15	56	18	4	−4.63𝐸−11	−3.73𝐸+20	0.066029584
6	58.7081194	147.8001474	1.872249679	5	40	13	18	7	0	0	0	12	40	1	22	59	61	7	28	1.44𝐸−12	−3.23𝐸+20	0.060240934
7	40.76800024	198.4794357	1.80226157	45	12	36	6	0	0	0	0	45	12	36	6	35	47	52	60	3.13𝐸−13	−9.82𝐸+20	0.056527615
8	69.23288235	138.9151384	1.346499753	63	19	15	34	12	51	2	0	27	33	1	59	60	48	14	9	−6.42𝐸−12	−5.72𝐸+20	0.05553932
9	77.3282777	113.9965065	1.07585429	32	8	61	1	0	0	0	0	36	30	57	5	45	0	0	0	−1.17𝐸−12	8.60𝐸+19	0.054674135
10	155.5703979	172.8726082	1.889472713	11	30	6	37	39	0	0	0	16	56	22	7	29	1	20	55	−1.60𝐸−11	−1.12𝐸+21	0.054636139
11	40.76800024	198.4794357	1.80226157	45	12	36	6	0	0	0	0	45	12	36	6	0	0	0	0	−4.09𝐸−15	−1.35𝐸+21	0.050992568
12	126.3484932	123.6175833	1.755905844	52	57	18	28	23	58	2	30	31	13	1	4	0	0	0	0	−1.79𝐸−11	−9.08𝐸+19	0.4937713
13	198.9672438	70.0810144	1.039405853	47	8	37	7	3	0	0	0	22	15	29	20	0	0	0	0	−6.68𝐸−12	−6.27𝐸+19	0.048958769
14	158.2865368	172.4029973	1.706346109	25	33	20	47	40	28	0	0	28	59	54	57	37	10	0	0	−1.02𝐸−12	7.51𝐸+17	0.048200649
15	12.90978247	48.30402703	1.041969641	37	9	4	2	0	0	0	0	26	5	2	18	27	7	0	0	6.40𝐸−12	−7.97𝐸+20	0.047898887
16	147.7508337	153.4513029	1.560336412	19	60	5	59	29	0	0	0	31	29	14	22	18	37	6	53	−1.07𝐸−11	−3.05𝐸+20	0.04562364
17	4.015136193	122.1554684	1.957975188	5	48	23	56	2	0	0	0	21	9	1	0	0	0	0	0	−1.15𝐸−11	9.16𝐸+18	0.044314222
18	119.5778657	57.26277573	1.155221621	1	38	23	5	55	0	0	0	1	38	23	5	55	27	46	35	−8.81𝐸−12	−1.67𝐸+21	0.041806579
19	17.958316	87.12059019	1.101537098	53	52	45	27	56	58	28	0	4	21	41	13	45	64	0	0	−6.95𝐸−12	4.41𝐸+19	0.041327241
20	27.84170219	63.8802927	1.58496986	56	42	21	6	20	13	44	0	18	14	19	22	10	46	54	29	4.93𝐸−14	−1.07𝐸+21	0.039753699
21	124.0239714	85.55609271	1.386161439	21	40	20	55	5	0	0	0	13	28	18	11	63	12	25	0	−1.11𝐸−12	−3.55𝐸+20	0.038435125
22	65.46154314	120.7143799	1.913152742	28	21	19	17	50	0	0	0	28	21	19	17	50	49	13	52	−8.10𝐸−12	−7.27𝐸+20	0.037552857
23	41.25598368	87.03513888	1.772081182	37	60	20	52	28	49	0	0	20	41	31	50	28	8	0	0	1.50𝐸−12	−2.47𝐸+20	0.035338397
24	196.4346696	103.1990576	1.992589818	23	39	28	32	14	53	0	0	23	39	28	32	14	53	56	29	−5.97𝐸−12	−2.45𝐸+20	0.034694696
25	8.670975038	85.42640081	1.489983673	38	46	4	0	0	0	0	0	38	46	4	2	59	12	30	31	−1.94𝐸−12	−3.91𝐸+20	0.034660397
26	15.13246991	49.84653431	1.34075215	53	62	8	24	34	10	0	0	8	60	30	19	20	45	55	0	−2.41𝐸−12	−2.82𝐸+20	0.034176387
27	161.6668255	39.85076999	1.182647036	25	63	3	1	45	20	15	64	3	24	32	8	22	60	35	0	−2.84𝐸−12	−6.17𝐸+20	0.033621678
28	99.24790026	94.58873349	1.613544711	25	48	24	56	28	44	63	0	21	40	4	39	20	22	0	0	−1.96𝐸−12	−7.01𝐸+19	0.032419707
29	31.03707493	92.78773648	1.717046802	28	43	5	0	0	0	0	0	4	57	14	35	24	12	21	0	−1.32𝐸−12	−5.56𝐸+19	0.031793377
30	18.941848	55.09096127	1.781590101	16	50	28	43	36	10	0	0	24	58	15	8	30	27	61	39	−5.10𝐸−12	−5.22𝐸+18	0.029935125
31	127.8782239	64.40887815	1.24556653	10	30	29	57	0	0	0	0	41	29	28	16	12	42	43	57	−4.31𝐸−13	−1.48𝐸+20	0.025886765