Combining SOM and evolutionary computation algorithms for RBF neural network training

Abstract

This paper intends to enhance the learning performance of radial basis function neural network (RBFnn) using self-organizing map (SOM) neural network (SOMnn). In addition, the particle swarm optimization (PSO) and genetic algorithm (GA) based (PG) algorithm is employed to train RBFnn for function approximation. The proposed mix of SOMnn with PG (MSPG) algorithm combines the automatically clustering ability of SOMnn and the PG algorithm. The simulation results revealed that SOMnn, PSO and GA approaches can be combined ingeniously and redeveloped into a hybrid algorithm which aims for obtaining a more accurate learning performance among relevant algorithms. On the other hand, method evaluation results for four continuous test function experiments and the demand estimation case showed that the MSPG algorithm outperforms other algorithms and the Box–Jenkins models in accuracy. Additionally, the proposed MSPG algorithm is allowed to be embedded into business’ enterprise resource planning system in different industries to provide suppliers, resellers or retailers in the supply chain more accurate demand information for evaluation and so to lower the inventory cost. Next, it can be further applied to the intelligent manufacturing system to cope with real situation in the industry to meet the need of customization.

Appendix: Four continuous test functions (Shelokar et al. 2007; Whitehead and Choate 1996)

The first experiment, Rosenbrock function (Shelokar et al. 2007) is expressed as follows:

$$\begin{aligned} RS(x_j ,x_{j+1} )=\sum _{j=1}^{n-1} {[100(x_j^2 -x_{j+1} )^{2}+(x_j -1)^{2}],n=2}\nonumber \\ \end{aligned}$$

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• (a) search domain: $-5\leqq x_j \leqq 5, j = 1$;

• (b) one global minimum: $(x_1 ,x_2 ) = (1, 1); RS(x_1 ,x_2)=0$.

In the second experiment, Griewank function (Shelokar et al. 2007) is expressed as follows:

$$\begin{aligned} GR(x_j ,x_{j+1} )=\sum _{j=1}^n {\frac{x_j^2 }{4000}-\prod _{j=1}^n {\cos \left( \frac{x_{j+1} }{\sqrt{j+1}}\right) } +1} ,n=1\nonumber \\ \end{aligned}$$

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• (a) search domain: $-300 \leqq x_j \leqq 600, j$= 1;

• (b) one global minimum: ($x_1 ,x_2 )$ = (0, 0); $GR(x_1 ,x_2 )$= 0.

In the third experiment, B2 function (Shelokar et al. 2007) is expressed as follows:

$$\begin{aligned} B2(x_j ,x_{j+1} )= & {} x_j^2 +2x_{j+1}^2 -0.3\cos (3\pi x_j )\nonumber \\&-0.4\cos (4\pi x_{j+1} )+0.7 \end{aligned}$$

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• (a) search domain: $-100\leqq x_j \leqq 100, j = 1$;

• (b) one global minima: $(x_1 ,x_2 )= (0, 0); B2(x_1 ,x_2 )= 0$.

In the fourth experiment, the Mackey-Glass time series (Whitehead and Choate 1996) is expressed as follows:

$$\begin{aligned} \frac{dx(t)}{d(t)}=0.1x(t)+0.2\cdot \frac{x(t-17)}{1+x(t-17)^{10}} \end{aligned}$$

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The research for the retrieved time step was in the range from 118 to 1118 with the Mackey-Glass time series function, from which 1000 samples were generated randomly.