A Modified NM-PSO Method for Parameter Estimation Problems of Models

Table 4

Results of Case 2 (A second-order system).

Method	𝑃1	𝑃2	𝑃3	𝑃4	Population size	Iterations	SSE
GA [5]	43.2233	30.8774	0.6170	−0.2812	—	100	0.4396
GA [5]	40.8112	33.3234	0.6400	−0.2464	—	200	0.3859
GA [5]	37.7414	36.3533	0.6753	−0.2123	—	500	0.3347
RGA [7]	42.5032	31.5469	0.6265	−0.2749	80	100	0.4315; (0.3204)*
RGA [7]	41.4371	32.6713	0.6346	−0.2563	80	200	0.3969; (0.2827)*
DE [9]	36.0250	38.1356	0.6933	−0.1895	—	100	0.3260
DE [9]	34.1450	39.9841	0.7155	−0.1702	—	300	0.2963
DE [9]	34.1266	40.0000	0.7157	−0.1699	—	500	0.2960
MDE [9]	35.4350	38.6848	0.6987	−0.1823	—	100	0.3142
MDE [9]	34.1266	40.0000	0.7157	−0.1699	—	300	0.2960
MDE [9]	34.1266	40.0000	0.7157	−0.1699	—	500	0.2960
PSO [6]	30.0761	44.0683	0.7680	−0.1279	20	100	0.2851
PSO [6]	30.7589	43.3814	0.7587	−0.1348	20	200	0.2847
NM-PSO [6]	30.5386	43.6025	0.7617	−0.1326	21	60	0.2847
M-NM-PSO	30.8616	43.2783	0.7573	−0.1358	21	53	0.2847

*Given the estimated values of 𝑃₁, 𝑃₂, 𝑃₃, and 𝑃₄, the SSE values of the RGA [7] should be 0.4315 and 0.3969, rather than 0.3204 and 0.2827, respectively.