Modelling and Simulation in Engineering

Research Article

Performance Comparison of Mode Choice Optimization Algorithm with Simulated Discrete Choice Modeling

Table 16

The experimental results of four algorithms responding to a new way of calculating the initial Hessian matrix adopted from either BHHH or BHHH-2 algorithm (exp. 3) ().


Algorithms & performance measures	Step size ()
Algorithms & performance measures	1/32	1/16	1/8	1/4	1/2	1	2	4

DFP-(BHHH)
One iteration time	-	0:00:18	0:00:18	0:00:24	0:00:20	-	-	-
Number of iterations	-	74	37	19	11	-	-	-
Convergence time	-	0:22:27	0:11:05	0:07:20	0:03:31	-	-	-
DFP-(BHHH-2)
One iteration time	-	0:00:20	0:00:20	0:00:20	0:00:19	-	-	-
Number of iterations	-	74	37	19	10	-	-	-
Convergence time	-	0:24:10	0:12:07	0:06:13	0:03:00	-	-	-
BFGS-(BHHH)
One iteration time	0:00:18	0:00:17	0:00:18	0:00:18	0:00:20	0:00:17	-	-
Number of iterations	147	74	37	19	10	6	-	-
Convergence time	0:42:48	0:21:01	0:10:44	0:05:33	0:03:07	0:01:38	-	-
BFGS-(BHHH-2)
One iteration time	0:00:18	0:00:18	0:00:18	0:00:18	0:00:19	0:00:15	-	-
Number of iterations	147	73	37	19	10	6	-	-
Convergence time	0:44:29	0:22:12	0:11:11	0:05:42	0:03:03	0:01:40	-	-

Algorithms & performance measures	Interval of uncertainty
Algorithms & performance measures	LL, UL	LL, UL	LL, UL	LL, UL	LL, UL	LL, UL	LL, UL	LL, UL

DFP-GSM-(BHHH)
One iteration time	0:02:40	0:01:34	0:01:36	0:01:41	0:01:41	0:01:47	0:01:47	0:01:47
Number of iterations	7	6	6	6	6	6	6	6
Convergence time	0:18:32	0:09:13	0:09:26	0:09:57	0:09:57	0:10:32	0:10:33	0:10:34
DFP-GSM-(BHHH-2)
One iteration time	0:01:21	0:01:36	0:01:36	0:01:42	0:01:42	0:01:47	0:01:49	0:01:46
Number of iterations	7	6	6	6	6	6	6	6
Convergence time	0:09:19	0:09:25	0:09:25	0:10:01	0:10:05	0:10:31	0:10:43	0:10:28
BFGS-GSM-(BHHH)
One iteration time	0:01:12	0:01:16	0:01:16	0:01:18	0:01:20	0:01:24	0:01:25	0:01:22
Number of iterations	5	6	6	6	6	6	6	6
Convergence time	0:07:08	0:07:28	0:07:26	0:07:37	0:07:52	0:08:17	0:08:21	0:08:05
BFGS-GSM-(BHHH-2)
One iteration time	0:01:06	0:01:13	0:01:15	0:01:18	0:01:18	0:01:22	0:01:21	0:01:22
Number of iterations	6	6	6	6	6	6	6	6
Convergence time	0:6:46	0:07:30	0:07:38	0:08:00	0:07:54	0:08:19	0:08:17	0:08:32