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

Table 2

Results of Case 1 (An enzyme effusion problem).

Method	𝑃 1	𝑃 2	𝑃 3	𝑃 4	𝑦 1 at 0.1	𝑦 2 at 0.1	Population size	Iterations	SSE
Ref. [4]	0.3180	2.6900	0.4188	0.1035	22	38	28	—	5301.2
Ref. [4]	0.3793	2.7211	0.4199	0.1030	22.9	40	68	—	5250.3
Ref. [4]	0.3190	2.7010	0.4190	0.1031	22	39	128	—	5076.6
GA [5]	0.3194	2.7010	0.3892	0.0782	21.00	38.75	—	100	5229.7
GA [5]	0.3050	2.6987	0.4005	0.1166	22.02	39.44	—	200	4547.3
GA [5]	0.2845	2.6717	0.3927	0.1614	23.99	40.14	—	500	4068.4
RGA [7]	0.2454	2.6092	0.3326	0.3217	22.005	38.608	60	100	4431.5
RGA [7]	0.2561	2.6269	0.3449	0.2696	22.043	38.403	60	200	4193.9
RGA [7]	0.2619	2.6336	0.3524	0.2575	21.986	38.704	60	300	4136.7
RCGA [8]	0.2624	2.6378	0.3599	0.2212	28.5443	0.2339		100	3068
RCGA [8]	0.2710	2.6442	0.3676	0.2429	28.5203	0.2566		500	3120
PSO [6]	0.2667	2.6437	0.3636	0.2282	28.5443	0.2339	20	100	3982.0
PSO [6]	0.2668	2.6440	0.3635	0.2280	28.5443	0.2339	20	200	3981.9
PSO [6]	0.2713	2.6513	0.3690	0.2079	28.5443	0.2339	20	300	3971.2
DE [9]	23.4543	37.3712	0.2726	2.6527	0.3643	0.2064		100	4048.7
DE [9]	23.2648	37.0019	0.2728	2.6535	0.3648	0.2095		300	4044.5
DE [9]	23.2548	37.0000	0.2728	2.6536	0.3649	0.2093		500	4044.5
MDE [9]	23.2437	37.0013	0.2729	2.6537	0.3650	0.2091		100	4044.5
MDE [9]	23.2543	37.0000	0.2728	2.6536	0.3649	0.2093		300	4044.5
MDE [9]	23.2543	37.0000	0.2728	2.6536	0.3649	0.2093		500	4044.5
NM-PSO [6]	0.2711	2.6504	0.3686	0.2098	28.5443	0.2339	21	149	3968.9
M-NM-PSO	0.2729	2.6539	0.3710	0.2004	27.8000	0.2339	21	150	3963.0