Regional logistics prediction is the key step in regional logistics planning and logistics resources rationalization. Since regional economy is the inherent and determinative factor of regional logistics demand, it is feasible to forecast regional logistics demand by investigating economic indicators which can accelerate the harmonious development of regional logistics industry and regional economy. In this paper, the PSORBFNN model, a radial basis function neural network (RBFNN) combined with particle swarm optimization (PSO) algorithm, is studied. The PSORBFNN model is trained by indicators data in a region to predict the regional logistics demand. And the corresponding results indicate the model’s applicability and potential advantages.
With the rapid economic development and the continuous advancement of information and technology, modern logistics industry is developing fast on a global scale. Therefore, logistics industry is considered to be the foundation as well as the basic industry of national economic development. Meanwhile, its level of development becomes an essential symbol of measuring a country’s modernization and comprehensive economic strength.
Regional logistics demand prediction system is a crucial part of regional logistics system planning and logistics rational allocation process of resources. This is because the regional logistics demand prediction system provides the necessary basis for decision making of the government. It also provides support for the construction of logistics infrastructure. Scholars at home and around the world established more predictive models for macrologistics needs, for example, the spacetime multinomial probity model of forecasting freight transportation [
Many domestic and foreign scholars have conducted researches on the prediction of regional logistics demand. It is basically divided into two categories: time series prediction method and causality prediction method. Time series prediction method is a kind of approach based on the evolution rules of the predicted object, which are found out from the historical data of the time series. Commonly used models include moving average, exponential smoothing, and grey model. Causality prediction method is to infer the developing trend of things by establishing the appropriate causality forecasting model, based on the relationship between variables of prediction object and variables of its related things found out from historical data, and using the causal relationship of things development. Commonly used models include elastic coefficient method, linear regression model, and artificial neural network model. Commonly used prediction methods and the applicable situation are shown in Table
Common forecasting methods.
Forecasting methods  The applicable situation 

Moving average [ 
Suitable for spot prediction 
Exponential smoothing [ 
Repeated prediction with or without a change in seasons 
Grey model [ 
Development of time series showing exponential trend 
Elastic coefficient method [ 
Two factors between 
Linear regression model [ 
A linear relationship between independent variables and dependent variables 
Artificial neural network model [ 
Being able to make prediction of nonlinear corresponding relationship 
Time series forecasting method does not consider the influence of other economic development indicators. It disregards that the regional logistics demand is of derivation. Hence, there are often serious prediction errors. On the other hand, compared with the macrologistics, regional logistics demand prediction has its own characteristics: there exists a high degree of nonlinearity between logistics demand and the impact of logistics demand indicators, as well as greater volatility than macrologistics. Due to these features, the traditional time series forecasting methods (such as grey model) and linear prediction methods (such as linear regression model) do not work effectively. Consequently, artificial neural network (ANN) model is more suitable. Furthermore, it is exactly the complexity and nonlinearity of regional logistics demand system that make a single prediction model function not well [
In this paper, a regional logistics demand prediction index system with economic indicators and logistics indicators and a regional logistics demand prediction model based on radial basis function neural network (RBFNN) combined with particle swarm optimization (PSO) algorithm will be built. The PSORBFNN model will be trained with processed data from Sichuan province and will be applied to predict the regional logistics demand in the very area as well. The prediction result will be evaluated and compared with a backpropagation (BP) neural network and regular RBFNN. Eventually, the results and conclusions drawn from the PSORBFNN prediction model will be discussed and summarized.
In order to enhance the investment environment, to increase the attraction of foreign investment, to solve the employment pressure, and to improve the comprehensive competitiveness of urban areas, multiple regions in China have adopted a variety of planning policies to encourage the development of logistics and construction of logistics infrastructure. Nonetheless, China’s logistics started late, and the related policies, strategies, and planning are not mature. Planners’ understanding of the development of modern logistics concept and mode of operation is still not unified, especially in the field of logistics demand and so on. When formulating logistics development policies and studying the feasibility of logistics infrastructure, scholars ascertain that the lack of quantitative data about logistics demand results in numerous problems in the planning process, for instance, the imbalance between actual supply capacity of logistics and logistics demand, repeated construction and sedimentation of money caused by tremendous waste of resources, and false prosperity of logistics industry. Overall, predicting regional logistics demand is critical for the sustainable development of regional logistics industry.
Therefore, the quantitative prediction of the scale and development trends of logistics demand is essential. To begin with, this kind of predictions can purposefully guide social investment into the field of logistics. Various types of logistics infrastructure can be rationally planned and constructed; logistics supply system and network layout can be improved. Moreover, the predictions continuously provide the basis for the supply to meet the demand, so as to maintain a relative balance between supply and demand for logistics services and to make the regional logistics maintain high efficiency.
Currently, there is no uniform view for the definition of regional logistics. Dong [
The regional logistics system.
Compared with the national logistics systems and enterprise logistics system, the regional logistics system is an organic integrated logistics system within the range of the economic region. The basic structural unit of the regional logistics system is a microenterprise supply, sales, logistics, and so on. Meanwhile, it is a vital part of the national logistics, international logistics, and other macrologistics systems. The regional logistics system, which is mesolevel, becomes the convergence of the microscopic and macroscopic logistics systems. Its purpose is to apply the logistics chain management solutions to address a variety of logistical problems beyond a single enterprise, so as to achieve logistics rationalization in a region or in a wider range of areas [
Internal structure of regional logistics system.
Logistics demand prediction is based on the relationship between past and current logistics market demand information and factors affecting the changes in the logistics market demand. It uses sound judgment experience, technical methods, and predictive models on the basis of historical data and statistical information to derive some regularity trends and intrinsic link trends among the factors, which predicts indicators reflecting market demand trends. Logistics demand prediction is preestimates and predictions of the cargo traffic, source, flow, velocity, and other goods constituting in the area which have not occurred or is not yet clear, so as to meet the scale of regional logistics demand and hierarchy of needs. Finally, it provides decisionmaking basis for the regional logistics planning.
Before modeling, we select suitable regional logistics demand prediction indicators, thereby keeping accuracy and reliability of regional logistics demand prediction.
The regional logistics demand scale indicator is the most important indicator in regional logistics demand indicators. It reflects the development of the logistics industry and the supply of logistics services in the region, namely, the size and level of total demand for logistics. It is also the most significant data the government and corporate decisionmakers should first master. Generally, scale indicators of regional logistics demand can be set from several different angles, as demonstrated in Table
Regional logistics demand indicators.
Indicator species  Classification standards  Setting indicators 

Indicators of logistics demand scale  Freight scale  Volume of freight traffic and freight turnover 
Logistics costs  Total logistics costs and the proportion of logistics costs in GDP  
Investment in fixed assets  Total investment in logistics fixed assets  
Industry personnel  The proportion of the number of employees in 
According to the logistic current situation and the principle of regional logistic prediction indicators, we select total freight traffic (TFT,
Regional economic indicators are the economic indicators utilized in the prediction and have tremendous impacts on regional logistics demand. The total regional economy, regional economic structure, and distribution are major economic factors impacting regional logistics demand. In addition, intraregional trade, regional income per capita, and consumption level are also important influencing factors. Hence, when setting regional economic indicators, we select as many related indicators as we can to make prediction more effective. Meanwhile, we have to consider that indicators’ data should be relatively easy to obtain from the regional statistical yearbook. Regional economic indicators are set using the measures illustrated in Table
Logistics demand forecast economic indicators.
Indicator species  Setting indicators 

Indicators of economic scale  Gross domestic product (GDP) and GDP per capita 
Indicators of industrial structure  Primary industry output value, secondary industry output value, and tertiary industry output value 
Indicators of trade  Regional retail sales and total volume of regional foreign trade 
Indicators of household consumption level  Consumption level per capita and income per capita 
Combined with the previous analysis and taking into account the availability of statistical data limits, in this research we select total freight traffic (TFT,
Regional logistics demand prediction index system.
The artificial neural network (ANN) is a nonlinear information processing system which imitates human brain structure and function. According to the potential law, ANN is able to extrapolate new output by using new input. Hence, ANN has the ability to adapt to the changing environment and to achieve real value mapping of any complex functions. ANN is widely utilized to resolve problems such as pattern recognition, forecasting and prediction, optimization control, and intelligent decisionmaking. The feedforward neural networks are one of the most widely used ANNs. Backpropagation (BP) network, radial basis function neural network (RBFNN), and group method of data handling (GMDH) network are the typical feedforward neural networks.
The radial basis function neural network (RBFNN) was proposed by Moody and Darken [
The architecture of RBFNN.
The essential feature of the RBFNN is that it utilizes the distance (Euclidean distance) function as the basis function and the radial basis function (such as Gaussian function) as activation functions. The radial basis function is a radial symmetry about a center point in
Like the human brain’s neural network, RBFNN’s functions are obtained through continuous learning. As the property of the neural network depends on network topology and connection weights between nodes, and the topological structure is often chosen according to specific applications, the RBFNN learning problem is to adjust the connection weights between nodes. Weights can be determined by two methods: (a) determined when RBFNN is designed; (b) determined by learning (or training) according to certain rules. Overall, the latter is mainly applied because the RBFNN obtained by learning has better adaptability. RBFNN’s topology and basis function have some advantages.
RBFNN has a good capability to approximate any nonlinear mapping and processing system’s inherent regularity which is difficult to express. For noisefree data, RBFNN has better fitting capability and higher prediction accuracy. For data with noise, RBFNN’s fitting error and prediction error are smaller, and the convergence rate is faster than other neural networks, such as BP neural network.
RBFNN topology can not only improve the learning speed but also avoid the local minimum. In addition, RBFNN’s transfer function adopts radial basis functions, particularly the Gaussian function. As the Gaussian function has a simple representation, so even a multivariable input would not add much complexity. And it is easy to theoretically analyse.
RBFNN has a selflearning, selforganizing, selfadaptive capability, and a fast learning speed. RBFNN can achieve a wide range of data fusion and data parallel processing at high speed.
The particle swarm optimization (PSO) algorithm is an evolutionary technique first proposed by Kennedy and Eberhart [
Evolutionary algorithm is varied. Generalized evolutionary algorithm includes genetic algorithms, particle swarm optimization, and ant colony algorithm, in which genetic algorithm and particle swarm algorithm are most typical. In comparison with other evolutionary algorithms such as genetic algorithm, PSO algorithm has the following advantages: (a) the algorithm is simple and easy to implement; (b) computation amount of the algorithm is small; (c) the computational efficiency of the algorithm is high.
Suppose in
Standard PSO algorithm procedures [
Initialize the particles
Calculate the fitness value of each particle via the fitness function. There are many options when choosing a fitness function, but finding a good one often requires trial and error.
Compare the particle’s fitness value with the particle’s best position
Compare the individual particle’s fitness with the population’s global best position
Update the particles’ positions and velocities by (
Repeat Step
In this paper, we use real code to make neural network connection weights and threshold values expressed as particle parameters. The specific encode mode is as follows: let the number of input nodes be
The threshold vector from the input layer to hidden layer is
The threshold vector from the hidden layer to output layer is
As the PSO algorithm can easily fall into local optimum, it fails to achieve global optimum. The PSO algorithm is not theoretically rigorous proof of convergence to any type of functions’ global extreme point; hence it may be difficult to obtain satisfactory results of complex test functions. When the PSO algorithm is running, if the parameter design of the algorithm or the selection of particles is in error, it will lead to a rapid disappearance of the diversity of particles, resulting in an algorithm “premature” phenomenon, further restricting the algorithm from converging to the global extreme point.
Meanwhile, the PSO algorithm’s convergence speed is slow. In practical problems, it is necessary to reach the appropriate accuracy within a certain period of time, and it is not worth taking a long time to get feasible solution. This slow convergence speed is caused by the PSO using an individual optimum and the global optimum at each iteration.
Therefore, combining ANN and PSO will overcome their own shortcomings and achieve better prediction and optimization results. ANN and PSO are two different methods and have big difference in their information processing, and the complementariness between them is high. The two principal ways to combine them are (a) using PSO algorithm’s global searching capability to optimize ANN’s topology, connection weights and learning rules, improving the generalization capability and learning efficiency, which improve the ANN’s global searching performance and (b) embedding ANN into the PSO algorithm and using ANN’s good learning performance to enhance the performance of PSO optimization. In this study, we adopt the PSO algorithm to optimize the RBFNN’s connection weights and thresholds, as revealed in Figure
The physical model for the regional logistics demand.
The procedures are as follows.
Collect networking training specimens.
Build the topology structure of RBFNN, that is, to determine the number of input, output, and hidden nodes.
Initialize population.
Calculate the fitness value of each particle.
Compare the particle’s fitness value with the particle’s best position
Compare the individual particle’s fitness with the population’s global best position
Update the particles’ positions and velocities by (
Repeat Step
Decode the population’s global best position. The optimized values are RBFNN’s connection weights and threshold values. Then train the RBFNN.
The algorithm flowchart is shown in Figure
The algorithm flowchart.
In this section, the proposed PSORBFNN model will be applied to predict regional logistics demand in Sichuan province, China. The data are selected from the Sichuan Province Statistical Yearbook from 1994 to 2008, as exhibited in Table
The logistics demand indicators and regional economic indicators statistical data.
Year 










1994  200.141  59.737  78.277  62.127  72474.08  2916.45  1367.17  723.36  497 
1995  244.321  66.246  98.091  79.984  93636.51  2358.72  1646.27  671.54  565 
1996  287.165  77.002  115.601  94.562  109144.85  2148.83  1879.6  520.04  536 
1997  324.147  88.028  126.532  109.587  121236.99  1790.05  2077.74  569.35  549 
1998  347.409  91.224  132.401  123.784  129856.95  2093.28  2243.41  507.59  568 
1999  364.912  92.603  134.963  137.346  138258.69  2470.69  2347.53  501.42  574 
2000  392.82  94.558  143.311  154.951  152374.90  2545.17  2550.48  549.43  597 
2001  429.35  98.168  157.201  173.981  168040.41  3099.16  2707.15  541.41  648 
2002  472.501  104.795  173.338  194.368  185005.76  4469.19  2914.39  572.97  704 
2003  533.309  112.861  201.48  218.968  209105.43  4469.19  3203.36  572.00  699 
2004  637.963  137.992  249.317  250.654  238395.15  5638.62  3656.2  655.80  804 
2005  738.511  148.114  306.723  283.674  298137.34  6871.62  4130.08  703.64  898 
2006  863.781  160.348  377.519  323.914  342164.83  7904.76  4501.34  742.00  891 
2007  1030.530  203.200  464.130  383.200  401557.46  11020.97  5259.22  799.40  979 
2008  1260.123  221.615  582.339  456.169  480076.38  14384.61  6072.00  1145.13  1513 
2009  1415.136  223.591  670.774  520.770  527835.10  24227.28  6817.42  1026.35  1913 
Before using these indicators, the correlation between regional economic indicators and logistics demand indicators should be verified. The verification result of the correlation is indicated in Table
The correlation between indicators.






 

















From Table
As the selected indicators have different attributes and dimensions, the input and output data should be preprocessed to accelerate the network’s training speed and convergence and improve the prediction accuracy of PSORBFNN. In this paper, we adopt normalization processing:
After the normalization processing, the input data is shown in Table
The normalized data.
Year 










1994  0.0001  0.0001  0.0001  0.0001  0.0001  0.0502  0.0001  0.4228  0.0001 
1995  0.0364  0.0397  0.9154  0.0389  0.0404  0.0253  0.0512  0.3241  0.0480 
1996  0.0716  0.1054  0.6798  0.0707  0.0747  0.0160  0.0940  0.0355  0.0275 
1997  0.1021  0.1727  0.5911  0.1035  0.1014  0.0000  0.1304  0.1294  0.0367 
1998  0.1212  0.1922  0.6308  0.1344  0.1205  0.0135  0.1608  0.0118  0.0501 
1999  0.1356  0.2006  0.6761  0.1640  0.1390  0.0303  0.1799  0.0001  0.0544 
2000  0.1586  0.2125  0.7462  0.2024  0.1702  0.0337  0.2171  0.0915  0.0706 
2001  0.1887  0.2345  0.8043  0.2439  0.2049  0.0583  0.2459  0.0762  0.1066 
2002  0.2242  0.2750  0.8152  0.2883  0.2423  0.1194  0.2839  0.1363  0.1462 
2003  0.2742  0.3242  0.8458  0.3420  0.2956  0.1194  0.3369  0.1345  0.1427 
2004  0.3603  0.4776  0.7545  0.4111  0.3603  0.1715  0.4200  0.2941  0.2168 
2005  0.4431  0.5394  0.8215  0.4830  0.4924  0.2265  0.5069  0.3852  0.2832 
2006  0.5462  0.6140  0.8896  0.5708  0.5897  0.2725  0.5751  0.4583  0.2782 
2007  0.6835  0.8756  0.7806  0.7000  0.7209  0.4114  0.7141  0.5677  0.3404 
2008  0.8724  0.9879  0.8831  0.8591  0.8945  0.9058  0.8632  0.8453  0.7175 
2009  0.9999  0.9999  0.9999  0.9999  0.9999  0.9999  0.9999  0.9999  0.9999 
To avoid the extreme data 0 and 1 disrupting prediction result, we set the maximum normalized value as
On the determination of nodes in the hidden layer, there is no uniform standard. Consequently, we use a trialanderror method based on empirical principles: let
The PSORBFNN model structure.
To determine the PSORBFNN learning factors, we have a parametric test of the learning factors
The normalized data.


Training error 


Training error 

4  0.7  0.014683  1.7  0.7  0.002705 
0.5  0.008015  0.5  0.003474  
0.4  0.011149  0.4  0.003087  
0.2  0.008810  0.2  0.001945  


3  0.7  0.002918 

0.7  0.002310 
0.5  0.03043  0.5  0.003224  
0.4  0.019198  0.4  0.003011  
0.2  0.003097 

0.001291  


2  0.7  0.002679  1.3  0.7  0.003241 
0.5  0.002578  0.5  0.002053  
0.4  0.003098  0.4  0.002703  
0.2  0.002796  0.2  0.003204 
In order to train the PSORBFNN, we chose data from the 1994
The transfer function of hidden layer utilizes S type tangent function:
Training vectors and transfer function.
After training, we test the PSORBFNN model’s fitness and prediction capability. Fitness test uses the model to fit to historical data and to estimate the preprediction error. Extrapolation test utilizes postprediction error to estimate the preprediction error. In the actual prediction, historical data are divided into two groups with most of the data being a sample to build the predictive model and the other small parts of the data being used for the extrapolation test.
The data collected from the 1994~2004 yearbooks are selected as fitness test specimens. The fitness error is under
Various prediction models’ capability can be measured by MAPE and the range of MAPE. The prediction accuracy is shown in Table
The MAPE range and prediction evaluation.
MAPE range  Prediction evaluation 


Precision prediction 

Good prediction 

Feasible prediction 

Error prediction 
The fitting and predicting error.
To prove the PSORBFNN’s good prediction capability, we compare the prediction capability among PSORBFNN, a regular BP (backpropagation) network, and a regular RBFNN model. All the inputs and outputs are the same in each model. The prediction errors are shown in Figure
The prediction errors in different models.
The training errors in different RBFNNs.
For the purpose of predicting the regional logistics demands in 2010
The prediction outcomes for the Sichuan province regional economy are illustrated in Table
2010~2015 economic indicators prediction.
Year  GDP  PIO  SIO  TIO  RRS  TIE  PCC 

2010  1612.237  244.157  774.057  600.072  600980.67  27899.82  7588.22 
2011  1836.791  266.614  893.241  691.451  684262.49  32129.06  8446.17 
2012  2092.621  291.137  1030.778  796.745  779085.23  36999.40  9401.12 
2013  2384.083  317.916  1189.491  918.072  887048.17  42608.02  10464.04 
2014  2716.140  347.157  1372.642  1057.875  1009972.24  49066.83  11647.14 
2015  3094.447  379.088  1583.994  1218.968  1149930.71  56504.72  12964.00 
Total freight traffic and freight turnover prediction results.
Year  2010  2011  2012  2013  2014  2015 

TFT (10 000 tons)  104337  108129  110364  114438  115782  118621 
FT (billion tonkm)  2077  2320  2514  2796  3013  3298 
According to Tables
In particular, the “5.12 Wenchuan Earthquake” inflicted heavy loss on Sichuan province. Hence, after the reconstruction process is completed, logistics demand is expected to increase sharply with the result that the regional logistics industry will be highlighted in the growth of the regional economy. Further, as “The 12th FiveYear Program on National Economic and Social Development” proposes, industrial optimization will be China’s top priority. To achieve this optimization, China will need to speed up the development of the modern service industry, in which the logistics industry is the principal development focus.
Logistics is a pioneer in the development of logistics demand. During the process of conducting logistics development planning, regional planners’ lack of correct understanding of the logistics demand will result in the imbalance between supply and demand. Furthermore, it will cause the phenomenon of insufficient supply and overinvestment. It will also hinder the development of the logistics industry. Therefore, studying the forecast of regional logistics demand has vital practical significance. In this paper, based on the theory of regional logistics demand and its prediction, the characteristics and the main content of regional logistics demand prediction are analyzed; the PSORBFNN prediction model is built; and an empirical research of logistics demand in Sichuan province is conducted. The principal conclusions are as follows.
(1) By feasibility analysis and empirical research, it is proved that a PSORBFNN model, which introduces a PSO algorithm to optimizing the RBF neural network connecting weights and thresholds, is scientific and practical. Combining RBFNN with PSO overcomes their own shortcomings and achieves better prediction and optimization results. (2) Through correlation analysis, the strong correlation between the regional economy and regional logistics demand is proven. The rapid development of the regional economy will drive the rapid development of regional logistics. (3) In the empirical research, we applied the PSORBFNN model to predict the regional logistics demand of Sichuan province from 2010 to 2015. After inputting the regional logistics demand prediction indicators values into the PSORBFNN model, valid results are calculated in Table
Nevertheless, our study should be improved in terms of the index system of regional logistics demand prediction. It is not enough to establish indicators only based on the perspective of economic indicators and freight volume, even though these indicators are easy to be collected. Other indicators such as logistics cost GDP ratio should also be studied. Further, we predict the scale of regional logistics demand, rather than the structure and quality of regional logistics demand. In future research, the structure and quality of regional logistics demand will be investigated.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (Grant no. 71301109), the Western and Frontier Region Project of Humanity and Social Sciences Research, Ministry of Education of China (Grant no. 13XJC630018), and the Initial Funding for Young Teachers of Sichuan University (Grant no. 2013SCU11014).