Immunological Algorithm-based Neural Network Learning for Sales Forecasting

Figures & data

FIGURE 1 The flowchart of the proposed VIS algorithm.

FIGURE 2 The pseudocode for the proposed VIS algorithm.

TABLE 1 Three Continuous Test Functions Used in This Experiment

Continuous Test Function (Shelokar et al. 2007)	Equation
Rosenbrock
Griewank
B2

TABLE 2 Parameters Setup for Three Continuous Function Testing Experiments

		Continuous Test Function
Parameter	Description	Rosenbrock	B2	Griewank
DS	Search domain	[−5, 5]	[−100, 100]	[−300, 600]

TABLE 3 The Setting of Parameters in the Proposed VIS Algorithm

Parameter	Description	Value
	The maximum number of generations	1000
	The number of the RBFN hidden node centers	min(training set/3, 100)
	Population size	50
	Clone ratio	0.1
	Recruit ratio	0.06
	Initial recruitment count	20
	RBF initial width	max(input domain width)/20
	Suppression threshold	||RBF initial width||

TABLE 4 Result Comparison Among Three Algorithms Used in This Experiment

Test Function	Rosenbrock Function		Griewank		B2
Algorithm	Training Set	Validation Set	Training Set	Validation Set	Training Set	Validation Set
RBFN-OLS(Chen, Wu, and Luk 1999)	11880 ± 1343.4	12731 ± 2555.7	26.394 ± 2.359	27.85 ± 3.777	5791.5 ± 403.7	5848.8 ± 673.66
AIS-Based(Diao and Passino 2002)	1176.2 ± 136.78	1970.4 ± 354.59	6.917 ± 11.099	50.944 ± 9.981	2199 ± 123.76	2778.7 ± 438.27
VIS	1039.1 ± 104.32	1785.8 ± 293.75	5.848 ± 10.153	25.337 ± 7.482	1277.6 ± 103.98	1422.5 ± 327.16

TABLE 5 The Setting of Parameters in the Proposed VIS Algorithm

Parameter	Description	Value
	The maximum number of generations	1000
	The number of the RBFN hidden node centers	min(training set/3, 100)
	Population size	40
	Clone ratio	0.25
	Recruit ratio	0.075
	Initial recruitment count	20
	RBF initial width	max(input domain width)/20
	Suppression threshold	||RBF initial width||

TABLE 6 The Error Comparison of Relevant Algorithms

Error
Algorithm	RMSE	MAE	MAPE (%)
RBFN-OLS (Chen, Wu, and Luk 1999)	610.771	528.731	9.07%
AIS-Based (Diao and Passino 2002)	861.561	657.674	11.81%
ARMA (2, 1) mode	519.607	401.858	6.73%
VIS	472.579	363.289	5.46%

TABLE 7 The Statistical Results for Paired Sample Test (t-test) Among Relevant Algorithms in This Exercise

	Paired Differences
Algorithm	Mean	Standard Deviation	t	Significant (2-Tailed)
RBFN-OLS (Chen, Wu, and Luk 1999)	−611.240	638.021	−3.030	0.014*
AIS-Based (Diao and Passino 2002)	−433.308	522.681	−2.622	0.028*
ARMA (2, 1) mode	−206.875	565.985	−1.156	0.278
VIS	−194.837	558.402	−1.036	0.681

*5% significance level.

Shelokar, P. S., P. Siarry, V. K. Jayaraman, and B. D. Kulkarni. 2007. Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Applied Mathematics and Computation 188 (1):129–42. doi:10.1016/j.amc.2006.09.098.

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Chen, S., Y. Wu, and B. L. Luk. 1999. Combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks. IEEE Transactions on Neural Networks 10 (5):1239–43. doi:10.1109/72.788663.

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Diao, Y., and K. M. Passino. 2002. Immunity-based hybrid learning methods for approximator structure and parameter adjustment. Engineering Applications of Artificial Intelligence 15:587–600. doi:10.1016/S0952-1976(03)00003-4.

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