Passenger Flow Prediction Based on Newly Adopted Algorithms

Figures & data

Table 1. Reviewed papers in the field of public transport.

Authors	Objective of studies	Number input variables	Number of hidden layer	Number of hidden neurons
Ma et al. (2014)	Prediction	3	Single	10
Guan, Shen, and Wang (2002)	Prediction	14	Single	4
Xie et al. (2014)	Prediction	4	Single	15
Mazloumi et al. (2011)	Prediction	Uncertain	Two	5 and 7
Wei and Chen (2012)	Prediction	3	Single	–
Yu, Lam, and Tam (2011)	Prediction	3–4	Single	5
Jeong and Rilett (2004)	Forecast	3	Single	15
Yuen et al. (2013)	Route choice	3	Single	–
Celebi, Bolat, and Bayraktar (2009)	Prediction	4	Single	At least 20
Lin et al. (2013)	Prediction	4	Single	16
Chien, Ding, and Wei (2002)	Forecast	5	Single	6

Table 2. Parameters of POA based ANN.

Options	Optimal conditions	Options	Optimal conditions
	10		0.01
	100		1
	0.3		3
	2		10
	0.5		1000
Hidden layer Hidden layer	Single hidden layer	Hidden neuron	12
Cpu time (second)	217	Transfer function	Sigmoidal

represents the number of groups, L is the group size, and is the number of candidates.

Table 3. Pseudo code for POA-ANN.

(1)	(5.4)
(2)	(5.5)
(3)	(5.6)
(4)	(5.6.1)
(5)	(5.7)
(5.1)	(5.7.1)
(5.1.1)	(5.8)
(5.1.2)	(6)
(5.2)	(7)
(5.3)	(8)

Table 4. Parameters of IWD-based ANN.

Options	Optimal conditions	Options	Optimal conditions
	1		4
	1	DIS(i,j)	100
	0.01		0.9
	0.01		0.1
	1	i	5
	1		0.001
	2		10
	1000	Transfer function	Sigmoidal
Mc	0	Cpu time (second)	6
Hidden neuron number	12	Hidden layer	Single hidden layer

Table 5. Pseudo code for IWD-ANN.

(1)	(6.2)
(2)	(6.3)
(3)	(6.4)
(4)	(6.5)
(5)	(7)
(6)	(8)
(6.1)	(9)

Table 6. Parameters of GA based ANN.

	Options	Optimal conditions
Population	Creation function	20
	Population size
Fitness scaling		–
Selection		Stochastic uniform
Reproduction	Elite count	2
	Crossover fraction	0.45
Mutation		Gaussian mutation
Crossover		Heuristic crossover
Migration	Direction	Both
	Fraction	0.35
	Interval
Algorithm settings	Initial penalty	10
	Penalty factor	100
Hybrid function		–
Stopping criteria	Generations	1000
	Time limit	1.00e−8
	Fitness limit Stall generations	50
Hidden neuron number	Single hidden layer	12
Cpu time (second)		49

Table 7. Comparison of the three hybrid ANNs with respect to MSE and .

Method	MSE
GA-ANN	0.11781	0.52481
POA-ANN	0.01639	0.60851
IWD-ANN	0.06110	0.63775

Figure 1. Daily passenger amount in Istanbul (except the rail transit).

Figure 2. Graphical representation of the three hybrid algorithms with respect to MSE and .

Figure 3. The number of the expected passengers for hybrid algorithms with regard to different sample sizes.

Table 8. Multivariate tests of the three hybrid ANNs with respect to MSE and .

Source	Dependent variable	Sum of squares	Degree of freedom	Mean square	F	Significance
Method	MSE	0.258	2	0.129	20.961	0.000
		0.344	2	0.172	35.383	0.000
Number of neuron	MSE	0.058	9	0.006	1.054	0.401
		0.025	9	0.003	0.567	0.822
Sample size	MSE	0.004	4	0.001	0.154	0.961
		0.046	4	0.011	2.359	0.057
Error	MSE	0.826	134	0.006
		0.651	134	0.005
Total	MSE	1.146	150
		1.065	150

Table 9. The effect of interaction between the parameters on the ANNs’ performance.

Source	Dependent variable	Sum of squares	Degree of freedom	Mean square
Number of neuron*sample size	MSE	0.211	36	0.006
		0.144	36	0.004
Method*sample size	MSE	0.063	8	0.008
		0.073	8	0.009
Method*number of neuron	MSE	0.115	18	0.006
		0.051	18	0.003
Method*number of neuron*sample size	MSE	0.437	72	0.006
		0.382	72	0.005

Appendix A. Mean square values of POA-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.01272	0.00276	0.01230	0.00660	0.00004
4	0.00325	0.01442	0.00195	0.00126	0.00030
5	0.04635	0.06971	0.00255	0.01327	0.00023
6	0.10029	0.05267	0.01029	0.00216	0.00033
7	0.02532	0.07856	0.00996	0.00068	0.00077
8	0.00233	0.00680	0.01604	0.00025	0.00076
9	0.06895	0.00008	0.01674	0.01816	0.00017
10	0.09442	0.00296	0.00373	0.00474	0.00001
11	0.03210	0.00747	0.00045	0.01126	0.00011
12	0.05430	0.00009	0.00570	0.00016	0.00293

Appendix B. Mean square values of IWD-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.04015	0.04970	0.04592	0.04370	0.04300
4	0.04500	0.05350	0.048175	0.04595	0.04486
5	0.04270	0.05080	0.04720	0.04490	0.04400
6	0.04540	0.05250	0.05906	0.045833	0.044925
7	0.04690	0.05330	0.04980	0.04730	0.04600
8	0.048575	0.05776	0.05976	0.04833	0.04690
9	0.04800	0.05380	0.05054	0.04800	0.04660
10	0.06574	0.06306	0.06236	0.05668	0.06650
11	0.05816	0.06176	0.06002	0.06190	0.55900
12	0.04872	0.05310	0.05272	0.04798	0.04856

Appendix C. Mean square values of GA-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.14540	0.08530	0.11572	0.08994	0.10740
4	0.10940	0.15240	0.10230	0.08490	0.07730
5	0.09100	0.14700	0.10698	0.10486	0.11484
6	0.05010	0.11800	0.10098	0.09688	0.09766
7	0.07700	0.08750	0.12950	0.06938	0.09998
8	0.10480	0.11020	0.12316	0.07142	0.10200
9	0.11970	0.06770	0.14258	0.12526	0.05936
10	0.11770	0.08840	0.10286	0.86680	0.12280
11	0.09660	0.11570	0.13200	0.09638	0.07024
12	0.07920	0.07760	0.14512	0.08138	0.10962

Appendix D. R square values of POA-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.55224	0.62158	0.66500	0.61792	0.64602
4	0.58052	0.64574	0.55494	0.64702	0.61988
5	0.57916	0.50124	0.64760	0.66343	0.55528
6	0.42134	0.58678	0.61032	0.65428	0.66253
7	0.59020	0.53140	0.65702	0.63874	0.63920
8	0.58540	0.64640	0.60420	0.59044	0.57890
9	0.60266	0.48760	0.65165	0.66126	0.65532
10	0.61244	0.66630	0.59960	0.65330	0.63193
11	0.54756	0.66500	0.59294	0.54528	0.56306
12	0.55920	0.66960	0.62952	0.66288	0.67372

Appendix E. R square values of IWD-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.60925	0.63150	0.62964	0.63630	0.65080
4	0.64366	0.65530	0.648725	0.65270	0.65882
5	0.62495	0.64410	0.63910	0.64480	0.65760
6	0.64380	0.65600	0.65056	0.65240	0.66387
7	0.63910	0.65300	0.64640	0.65070	0.66240
8	0.643775	0.65924	0.65098	0.65250	0.66400
9	0.64270	0.65520	0.64830	0.65230	0.66360
10	0.59738	0.63890	0.63492	0.61992	0.56820
11	0.59624	0.58826	0.60084	0.56218	0.60860
12	0.61362	0.66670	0.62568	0.64442	0.64346

Appendix F. R square values of GA-ANN with regard to two different parameters.

Number of hidden neuron	Sample size
	60	70	80	90	100
3	0.31380	0.62230	0.47200	0.58048	0.49206
4	0.48400	0.32520	0.53326	0.60396	0.63456
5	0.57080	0.34930	0.51188	0.51084	0.45710
6	0.76360	0.47760	0.53930	0.54796	0.53822
7	0.63660	0.61270	0.40916	0.67622	0.52726
8	0.50540	0.51210	0.43798	0.66686	0.51762
9	0.43520	0.70000	0.34960	0.41906	0.71935
10	0.44470	0.60840	0.53058	0.59556	0.41940
11	0.54430	0.49770	0.39790	0.55036	0.66782
12	0.62400	0.46640	0.33788	0.62040	0.48164

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