Abstract
Railway freight transportation is an important part of the national economy. Accurate forecast of railway freight volume is significant to the planning, construction, operation, and decision making of railways. After analyzing the application status of generalized regression neural network (GRNN) in the prediction method of railway freight volume, this paper improves the performance of this model by using improved neural network. In the improved method, genetic algorithm (GA) is adopted to search the optimal spread, which is the only factor of GRNN, and then the optimal spread is used for forecasting in GRNN. In the process of railway freight volume forecasting, through this method, the increments of data are taken in the calculation process and the goal values are obtained after calculation as the forecasted results. Compared with the results of GRNN, a higher prediction accuracy is obtained through the GA-improved GRNN. Finally, the railway freight volumes in the next 2 years are forecasted based on this method.
1 Introduction
Freight transportation is one of the core businesses in railways, and this method of transportation plays an important role in the conveying of goods throughout the state. The railway’s “twelfth five-year” development plan for logistics puts forward 10 key tasks, such as strengthening the construction of railway logistics infrastructure, and so on. It has determined to construct 42 national railway logistics node cities and 98 regional railway logistics node cities.
The national railway freight center was set up in 2013 and is facing new development opportunities. China is currently developing its strategy of “One Belt and One Road”, which is being paid much attention, while the rail network is actively involved in considerable planning and construction. Similarly, multiple railways are being re-organized to promote an efficient resource configuration, which will consequently have a profound influence on railway freight transportation throughout the whole nation.
Railway freight volume is determined by the level of demand for this type of transport and illustrated in the national macro-economic, which is the basis for the railway infrastructure’s investment decision making for further construction. It is an important factor in the success of a railway’s operation and is necessary in the process of making various policies.
With the development of China’s railway reform, on the basis of existing railway hardware facilities, in order to adapt to the railway development and to find a new economic growth point, the railway freight system is necessary to improve its operational management level. To anticipate the future demand for railway freight volume is particularly urgent, and therefore accurate forecasts should be predicted by using existing things and new resources. At present, there are many available methods in the prediction of railway freight volume, including traditional forecasting methods and numerous modern intelligent algorithms. American scholars Brockweil and Davis analyzed and compared several commonly used time series models and found that the autoregressive integrated moving average model could successfully predict the effect of traffic flow [2].
Babcock et al. [1] established a time series model that is used to forecast the number of railway grain loading. Godfrey and Powell [4] established an exponential smoothing model to forecast the daily demand for cargo transport. Among the domestic scholars, Li and Liu [6, 7] have demonstrated the feasibility fractal theory and rough set theory for China’s railway freight volume forecast, and have proposed two methods to enhance this forecasting process. Zhao et al. [13, 14] established the railway freight volume forecast, generalized regression neural network (GRNN) model, and the support vector machine model. Moreover, Liu et al. [9] used the radial basis function neural network for freight volume analysis and forecast.
Other scholars, including Yonge et al. [13], Huawen and Fuzhang [6], Lin and Chen [8] and Zhang and Zhou [12] have used the “gray model” and the Markov’s chain combination method to predict China’s railway freight volume. Based on the analysis of the influencing factors of freight volume, Geng et al. [3] proposed the least square support vector machine model based on gray correlation analysis. Guo et al. [5] proposed the concept of the economic cycle stage parameter, thus establishing the Elman neural network forecast model based on the economic cycle.
Based on the above literature, the researches highlight that railway transportation is a complex dynamic system. There are many complex factors that affect railway freight transport, and the relationship between the factors and the volume of rail freight is not entirely or obviously consistent with any distribution pattern or rule hypothesized by predicting models.
Therefore, in this paper, based on the GRNN forecasting method, we introduce the genetic algorithm (GA) to improve research with the hope that the improved algorithm can provide a new approach for railway freight volume forecasting, railway freight reform in China, railway planning, and construction. It also provides reference for the establishment of related policies.
2 Performance Analysis of Railway Freight Volume Forecasting with GRNN
The traditional approach is to rely on historical data to build a model and use it to predict future variables. Therefore, these models assume that the future is very similar to the past. Conventional models sometimes assume the overall distribution of the form, and these assumptions may or may not be consistent with the facts. For example, the interval estimation based on the regression model assumes that the base population is in the normal distribution.
Railway freight volume and its influencing factors are not in line with the distribution law of a certain forecasting model hypothesis. Therefore, the traditional forecasting method based on an accurate model is difficult to adapt to the demand of railway freight volume prediction under complex conditions.
GRNN was proposed by Dr. Specht in 1991. In GRNN, a number of programming examples are input to the computer, which covers the relationship between all variables that may affect the outcome of a variable. Neural network procedures absorb these examples, and strive to build the basic relationship through the knowledge they have learned. The theoretical advantage of GRNN as a predictive tool is that it does not need to be specified in advance, because the method uses the complex relationships provided by the examples to learn. At the same time, unlike many traditional methods of prediction, GRNN does not require any assumptions about the overall distribution of the foundation, which can be used to calculate the incomplete data.
GRNN is based on non-linear regression, and the implementation of Parzen non-parametric estimation is based on the principle of maximum probability of computing network output. GRNN was used as it possesses a strong learning ability, good non-linear approximation performance, robustness, and the ability to be fault tolerant.
GRNN has these characteristics and advantages, compared to other methods. It is particularly suitable for railway freight volume forecast. Training samples are taken in order to ascertain the GRNN, network structure, and the neurons between the connection weights with the input. The GRNN needed to be adjusted as the parameters indicate only a smooth σ factor, with large computational advantage. However, the prediction results have a great influence in determining the improper smoothing factor. Specht [11] had proposed a method called multiple test methods to determine σ.
Let the smooth factor in a range set up ahead of the (σmin, σmax) in arithmetic changes. Then, remove a few or individual training samples, and use the remaining samples to train the neural network. Next, σ arithmetic is performed to remove minor or individual samples. This is to predict the value and between sample values. Owing to a square error in the evaluation index, a σ error minimum value is used as the optimal smoothing factor, for the final GRNN predictive. This method is the most common method in the practical application of GRNN prediction; however, the results are not satisfactory when this method is used to predict the railway freight volume.
Another way is the selection of smoothness factor, i.e. conducting optimizing through function. Seng et al. [10] proposed to seek for optimum value through gradient descent. However, when using this method, local extremum often causes failure in optimization.
3 Volume of Railway Freight Genetic Progress GRNN Model
GA is synchronous searching for possible solution groups instead of starting from single values through traditional optimizing methods. This search strategy allows GA to be more suitable for large-scale parallel computing, and furthermore enhances the optimization capability and processing speed.
Meanwhile, GAs are conducted for “optimization” purposes. Information exchange takes place between individuals to identify possible solutions in order to avoid excessive dependence on gradient information. These features allow the GA to be suitable for solving complex and non-linear optimization problems and, in addition, reduce the possibility of local optimization.
Finally, GA uses probabilistic transition rules to guide the search direction, providing results of a high fit, which are both enlightening and probabilistic. GA is widely used in areas such as combination optimization, machine learning, adaptive control, planning, design, and artificial life. It is especially adaptable to use with neural networking systems, and offers feasible solutions to enable better performance.
This paper therefore uses GA to optimize GRNN smooth factors, to seek an optimal solution to overcome the weaknesses of the conventional theory σ value optimization method, and apply this method in railway freight volume forecasting in order to enhance the accuracy.
3.1 Improved Method of Forecasting Process
The proposed improved method of the prediction process is divided into two parts. The first part uses GA to find the only optimum value of GRNN parameter smooth factors. GA is the main subject. The input is parameter values of GA. This produces a random generation of smooth factor groups. The output is the optimum value of smooth factors. The second part involves conducting a GRNN prediction on optimal values of smooth factors. GRNN is the main subject. The input is index system data relevant to forecast and optimal smooth factor. The output is the prediction result.
The first part is to achieve an improvement of GA on GRNN. It is designed based on the genetic progress GRNN model. The basic procedure of the improved prediction method is shown in Figure 1.
Genetic Improvement GRNN Method Forecast Flowchart.
3.2 Genetic Improvement of Optimal Smoothing Factor
As for randomly generated smooth factor groups, GA is conducted for screening, based on fitness levels through selection, crossover, and mutation in inheritance. In this way, variables possessing the best fitness levels can be maintained, while those with low fitness levels will be omitted. New groups inherit information from the previous generation and supersede the previous ones in terms of performance.
This cycle is repeated until all conditions are met. GA consists of CODEC, individual fitness evaluation, and genetic operation. Genetic operation includes the selection, crossover, and mutation of chromosomes. Based on basic GA, this paper adopts the following technologies for optimization.
3.2.1 Encoding and Decoding
Encoding is the method for transferring feasible solutions of smooth factors in solution space to identify space that algorithms can handle.
Binary code not only conforms to the principles of computer information processing, but also facilitates the crossover and mutation operations on chromosomes. The paper adopts the binary encoding method to search for randomly generated individuals within the prescribed scope. Each individual is given the value of smooth factor σ. In crossover and mutation operations, binary values can be directly applied. As for the calculation of individual fitness value, binary values should be decoded to decimal values.
3.2.2 Fitness Evaluation
Fitness is used to measure the excellence degree of optimum values that smooth factors may attain or get relatively close to. The method used to calculate individual fitness is called fitness function. This method is an evaluation function used in guiding the searching process in GA.
How to construct the fitness function is one of the most notable problems in GA. In this paper, GRNN is established through fitness function. The adjacent five samples are selected and monitored. The target values of three samples adjacent to the previous five samples are predicted. The reciprocal of the Euclidean distance between the prediction results and the true value is used here as the fitness function.
The smaller the value of Euclidean distance, the larger values form the fitness value. X is the true value, and x is the prediction value. The fitness value is
3.2.3 Genetic Operation
3.2.3.1 Choice
The selection of determining crossover or mutation individuals.
The method used in this paper is for smooth factor group S with the scale of N, based on the selective probability of xi∈S determined by each chromosome P(xi), randomly selected N chromosome from S.
The computational formula of selectiveprobability is
Based on selective probability, randomly choose chromosomes and use the method ofroulette wheel selection.
Generate a uniform distribution of random numbers in the (0, 1) interval r. If r≤q1 is established, then the chromosome x1 is selected. If qk−1<r<qk(2≤k≤N) is established, then the chromosome xk is selected, where qi is the cumulative probability of chromosome xi(i=1, 2, …, N). The formula is
3.2.3.2 Overlapping
Crossing is the exchange of two genes that are selected from some of the genes on the chromosome, enabling new individuals to be generated through the combination of information from the parent.
3.2.3.3 Variation
Mutation is carried out to change certain genes in chromosomes, i.e. by changing 0 to 1 and 1 to 0. In fact, offspring genes change based on small disturbances.
The mutation process is similar to the crossover process. Based on preset mutation probability, whether or not to conduct a mutation operation should be decided. If conducted, a mutation position will be randomly produced. If not conducted, the mutation operation will not be activated.
3.3 Termination Principle of Genetic Algorithm
The termination of GA involves several principles. For instance, when the largest artificial evolutionary algebra is reached, it should then accordingly be terminated. Another example is when the fitness function value exceeds certain levels, it should similarly be terminated.
In this paper, GA predestinates the largest possible evolutionary algebra. Optimization will be terminated if the largest evolutionary algebra value is reached. GA also takes into consideration the overall fitness value changes of consecutive multiple generations. If the largest fitness value of consecutive multiple generations does not highlight obvious changes, and the average value of the fitness value for each generation remains close to the largest fitness value, then the process should be terminated and considered effective. Alternatively, GA should be performed again.
4 Example of Railway Freight Volume Forecast
To verify the effectiveness of theoretical algorithm, an algorithm program is compiled under the context of MATLAB (The MathWorks, Natick, MA, USA). Moreover, MATLAB neural network tools are used to establish two prediction models: genetically improved GRNN model and unimproved GRNN model.
4.1 Index System
There are many influencing factors of railway freight volumes. After calculating the degree of gray incidence, those influential factors with a degree of gray incidence >0.6 to railway freight volumes should be selected.
Factors that most affect this are domestic products (100 million yuan), industrial products (100 million yuan), total coal production (million tons of standard coal, iron, and steel, including pig iron, crude steel, steel production; 10,000 tons), crude oil output (10,000 tons), grain total output (10,000 tons), coke yield (10,000 tons), railway freight car ownership (cars), railway operating mileage (million kilometers), double track railway (%), railway freight cargo volume share (%; a total of 11 elements all in all, respectively, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, and X11), and railway freight volume (10,000 tons) expressed by Y.
As the 2014 statistical data has not yet been fully released, in addition to the 1990 data not being fully comprehensive, this paper selected the years 1990–2013 as its relevant data, all derived from the statistical yearbook of China (Table 1).
Railway Freight Volume and Its Influencing Factors in 1990–2013.
| Serial Number | Year | Y | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 | X11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1990 | 150,681 | 18,667.8 | 6858.0 | 77,110.1 | 18,026.0 | 13,831.0 | 44,624.3 | 7328.0 | 364,966 | 5.79 | 24.4 | 15.52 |
| 2 | 1991 | 152,893 | 21,781.5 | 8087.1 | 77,689.4 | 19,503.0 | 14,099.0 | 43,529.3 | 7352.0 | 370,054 | 5.78 | 25.0 | 15.51 |
| 3 | 1992 | 157,627 | 26,923.5 | 10,284.5 | 79,691.2 | 22,380.0 | 14,210.0 | 44,265.8 | 7984.0 | 373,233 | 5.81 | 25.5 | 15.07 |
| 4 | 1993 | 162,794 | 35,333.9 | 14,188.0 | 82,183.7 | 25,411.0 | 14,524.0 | 45,648.8 | 9320.0 | 390,097 | 5.86 | 26.6 | 14.59 |
| 5 | 1994 | 163,216 | 48,197.9 | 19,480.7 | 88,571.8 | 27,430.0 | 14,608.0 | 44,510.1 | 11,477.0 | 415,919 | 5.90 | 28.7 | 13.83 |
| 6 | 1995 | 165,982 | 60,793.7 | 24,950.6 | 97,162.6 | 29,045.1 | 15,005.0 | 46,661.8 | 13,510.0 | 432,731 | 6.24 | 31.0 | 13.44 |
| 7 | 1996 | 171,024 | 71,176.6 | 29,447.6 | 99,774.0 | 30,184.6 | 15,733.4 | 50,453.5 | 13,643.0 | 443,893 | 6.49 | 32.5 | 13.17 |
| 8 | 1997 | 172,149 | 78,973.0 | 32,921.4 | 99,160.8 | 32,384.5 | 16,074.1 | 49,417.1 | 13,731.0 | 437,686 | 6.60 | 33.1 | 13.47 |
| 9 | 1998 | 164,309 | 84,402.3 | 34,018.4 | 95,168.3 | 34,160.5 | 16,100.0 | 51,229.5 | 12,806.0 | 439,326 | 6.64 | 34.2 | 12.96 |
| 10 | 1999 | 167,554 | 89,677.1 | 35,861.5 | 97,500.0 | 37,075.0 | 16,000.0 | 50,838.6 | 12,073.7 | 436,236 | 6.74 | 36.1 | 12.96 |
| 11 | 2000 | 178,581 | 99,214.6 | 40,033.6 | 98,855.1 | 39,097.5 | 16,300.0 | 46,217.5 | 12,184.0 | 439,943 | 6.87 | 36.5 | 13.14 |
| 12 | 2001 | 193,189 | 109,655.2 | 43,580.6 | 105,028.8 | 46,785.3 | 16,395.9 | 45,263.7 | 13,130.7 | 449,921 | 7.01 | 38.3 | 13.78 |
| 13 | 2002 | 204,956 | 120,332.7 | 47,431.3 | 110,732.2 | 54,572.8 | 16,700.0 | 45,705.8 | 14,279.8 | 446,707 | 7.19 | 38.7 | 13.82 |
| 14 | 2003 | 224,248 | 135,822.8 | 54,945.5 | 130,992.4 | 67,708.3 | 16,960.0 | 43,069.5 | 17,775.7 | 503,868 | 7.30 | 39.2 | 14.33 |
| 15 | 2004 | 249,017 | 159,878.3 | 65,210.0 | 151,615.6 | 87,097.8 | 17,587.3 | 46,946.9 | 20,619.0 | 520,101 | 7.44 | 39.1 | 14.59 |
| 16 | 2005 | 269,296 | 184,937.4 | 77,230.8 | 167,785.9 | 107,470.3 | 18,135.3 | 48,402.2 | 25,411.7 | 541,824 | 7.54 | 39.4 | 14.46 |
| 17 | 2006 | 288,224 | 216,314.4 | 91,310.9 | 180,625.9 | 130,053.4 | 18,476.6 | 49,804.2 | 29,768.3 | 558,483 | 7.71 | 39.8 | 14.15 |
| 18 | 2007 | 314,237 | 265,810.3 | 110,534.9 | 192,135.8 | 153,141.3 | 18,631.8 | 50,160.3 | 33,553.4 | 571,078 | 7.80 | 40.5 | 13.81 |
| 19 | 2008 | 330,354 | 314,045.4 | 130,260.2 | 200,103.9 | 158,590.5 | 19,043.1 | 52,870.9 | 32,031.5 | 584,961 | 7.97 | 41.6 | 12.78 |
| 20 | 2009 | 333,348 | 340,902.8 | 135,239.9 | 212,280.5 | 181,907.1 | 18,949.0 | 53,082.1 | 35,510.1 | 594,388 | 8.55 | 43.8 | 11.80 |
| 21 | 2010 | 364,271 | 401,512.8 | 160,722.2 | 227,437.7 | 203,732.9 | 20,241.4 | 54,647.7 | 38,864.0 | 622,284 | 9.12 | 44.8 | 11.24 |
| 22 | 2011 | 393,263 | 473,104.0 | 188,470.2 | 247,393.9 | 221,198.8 | 20,287.6 | 57,120.8 | 43,270.8 | 644,677 | 9.32 | 45.2 | 10.64 |
| 23 | 2012 | 390,438 | 519,470.1 | 199,670.7 | 253,863.7 | 234,320.5 | 20,571.1 | 58,958.0 | 44,778.9 | 664,333 | 9.76 | 46.2 | 9.52 |
| 24 | 2013 | 396,697 | 568,845.2 | 210,689.4 | 257,040.0 | 255,563.3 | 20,946.9 | 60,193.8 | 47,932.0 | 715,492 | 10.31 | 47.8 | 9.68 |
Data sources: China Statistical Yearbook.
4.2 Data Processing
In the prediction process, in most cases, prediction of incremental data can produce better output effects than direct prediction of data. To establish the actual railway freight volume, the improved algorithm is used to forecast the data increment. According to the actual situation of railway freight volume, the improved algorithm is used to forecast the data increment.
Using X1–X11 and Y values from the years 1991–2013, minus relevant values from last year respectively, incremental data X1–X11 and Y are obtained for the 23 years. The paper conducts an input and forecast on the aforementioned incremental data. Incremental data of 9 consecutive years should be placed in a group. The former 8 years’ data will be used in the optimization of smooth factor and GRNN training. The 9th year data will be used in the forecast.
In this way, the incremental data were divided into 15 groups, in order to predict the 1999–2013 railway freight increment. In order to prevent increase in network training time caused by outlier sampledata, normalizationprocessing should conducted on various data, i.e. convert data to numerical values between 0 and 1.
In Eq. (4), the normalized value x′, as the original value xi, affects the same element xi in the minimum value xmin and affects the same element value xi of the maximum value xmax. After obtaining the predictive value, the range is between 0 and 1; therefore, the predicted value y′ should be reduced to the actual value by Eq. (5).
For the normalized value, the minimum value ymin of the network is the direct output value and the maximum value ymax of the network is the output value.
4.3 Forecasting Process
Utilizing GA optimization smooth factor, the operating parameters were set as smooth σ factor range of [0.05, 1], precision arithmetic of 0.0001, population size of 50, biggest genetic algebra of 12, crossover probability of 0.9, and mutation probability of 0.09.
In terms of fitness function, the incremental data of each group of the first 8 years is divided into two parts: the first part relates to the first 5 years and the second part for the last 3 years. The first part of training GRNN is thus used to predict the second part of the freight increment value.
4.4 Forecast Results
Observations were made of the biggest fitness curve and average fitness curve in genetic arithmetic. No large-scale vibrations were evident. Algorithm convergence progressed smoothly. In the evolution process, two curves showed a similar tendency, and the maximum adaptation of individual successive generations did not evolve, suggesting that populations were mature.
A curve graph is selected, as shown in Figure 2. Other years have similar predictions. It does not need to be repeated here.
Smooth Factor Fitness Curve of the Railway Freight Increment in 2006.
The GA, the respective smooth factor by GRNN, and the prediction results were obtained for the railway freight increment. The actual freight volume of the year before the year of the incremental forecast results can be predicted by the railway freight volume, as shown in Table 2.
Prediction Results of GRNN and Genetic Improvement in GRNN.
| Year | Volume of freight traffic | Smoothing factor σ | Prediction results | Absolute value of percentage error | |||
|---|---|---|---|---|---|---|---|
| GRNN | Genetic improvement GRNN | GRNN | Genetic improvement GRNN | GRNN | Genetic improvement GRNN | ||
| 1999 | 167,554 | 0.1 | 0.41712 | 164,310 | 165,195 | 1.94% | 1.41% |
| 2000 | 178,581 | 0.1 | 0.99942 | 167,550 | 169,627.9 | 6.18% | 5.01% |
| 2001 | 193,189 | 0.1 | 0.095404 | 178,581 | 183,748 | 7.56% | 4.89% |
| 2002 | 204,956 | 0.1 | 0.99577 | 193,189 | 199,882.4 | 5.74% | 2.48% |
| 2003 | 224,248 | 0.1 | 0.67724 | 204,956 | 217,000 | 8.6% | 3.23% |
| 2004 | 249,017 | 0.1 | 0.42477 | 224,248 | 242,987 | 9.95% | 2.42% |
| 2005 | 269,296 | 0.1 | 0.21694 | 249,017 | 273,786 | 7.53% | 1.67% |
| 2006 | 288,224 | 0.1 | 0.063511 | 269,296 | 289,575 | 6.57% | 0.47% |
| 2007 | 314,237 | 0.1 | 0.41828 | 288,224 | 308,047 | 8.28% | 1.97% |
| 2008 | 330,354 | 0.1 | 0.69742 | 314,237 | 333,277 | 4.88% | 0.88% |
| 2009 | 333,348 | 0.1 | 0.7528 | 330,354 | 349,612 | 0.9% | 4.88% |
| 2010 | 364,271 | 0.1 | 0.75077 | 333,348 | 353,300 | 8.49% | 3.01% |
| 2011 | 393,263 | 0.1 | 0.068266 | 364,271 | 390,284 | 7.37% | 0.76% |
| 2012 | 390,438 | 0.1 | 0.10973 | 393,263 | 409,380 | 0.72% | 4.85% |
| 2013 | 396,697 | 0.1 | 0.58754 | 390,438 | 405,699 | 1.58% | 2.27% |
| Average | 5.75% | 2.68% | |||||
As average GRNN uses fitting degree of training samples to determine smooth factor within range from 0.1 to 0.5, average GRNN smooth factor often reaches the value of 0.1. Moreover, in the year of prediction, when the actual value of GRNN is almost equal to that of last year, prediction accuracy is relatively high. When they are not almost equal to each other, prediction accuracy is relatively low. In the 15 years of prediction, the absolute value relative error of genetically improved GRNN only accounts for 5.01% of the whole year. The rest absolute value relative errors are all below the level of 5%. In addition, when average value of absolute value relative error is lower than 3%, prediction accuracy is relatively enhanced.
4.4.1 Extended Forecast
In this paper, a new method of genetic improvement based on the GRNN is proposed and applied to railway freight volume forecasting. However, in general situations, it will take some time to obtain the statistical data of these 11 influencing factors. This would impact the promptness of predicting railway freight volumes, thus reducing the significance of prediction results.
The solution is to consider real-timesupervision in order to obtain statistical data of relevant influencing factors. Other suitable prediction methods can also adopted to predict the values of 11 influencing factors. Moreover, the prediction values of these influencing factors can be regarded as the input value, and then the prediction of railway freight volumes can be conducted.
As most influencing factors of railway freight volumes indicate stability, few change or show certain obvious tendency, such as gross domestic product. Based on the development of the national economy, and macroeconomicregulationandcontrol, increases are achieved between 6% and 8%. Thus, the method of exponentialsmoothing can be used to predict the 11 influencing factors. Then, the prediction value of influencing factors can be substituted into the improved algorithm, in order to obtain the forecast value of railway freight volumes.
Such a way of prediction – data obtained through traditional prediction methods before using the improved algorithm – is utilized to obtain the desired final prediction result, which is also scientific, because while using influencing factors to predict railway freight volumes, the influencing factors have non-linear relations with target values. Moreover, it is in conformity with the mathematical model set by the traditional prediction method.
As for the prediction of influencing factors, based on the above analysis, it is suitable for the traditional prediction method. In other words, as for the prediction of different target values, different suitable prediction methods should be adopted to fit different target values.
Based on the scientific and reasonable target prediction values obtained by the traditional prediction method, it is reasonable to select these prediction results and regard them as the influencing factors, because the next prediction process is not related to the prediction results of the previous one, as long as the previous prediction results are scientific, reasonable, and reliable.
Based on the above analysis, forecast is conducted on railway freight volumes in 2015 and 2016. Considering that Chinese economic growth has entered the new normal state, and the overall international economicdevelopment has slowed down, while using SPSS software to predict influencing factors, the method of exponential smoothing is adopted. The prediction values of railway freight volume influencing factors from 2014 to 2016 are shown in Table 3.
Influencing Factors of Railway Freight Volume in 2014–2016.
| Year | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 | X11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2014 | 619,666.9 | 225,525.2 | 259,892.8 | 273,348.6 | 21,226.9 | 60,717.3 | 50,490.1 | 740,316 | 10.78 | 48.7 | 9.29 |
| 2015 | 670,485.1 | 240,360.2 | 262,455 | 291,674.5 | 21,526.7 | 61,240.6 | 52,908.9 | 765,139 | 11.25 | 49.7 | 9.13 |
| 2016 | 721,300 | 255,194.9 | 264,756.3 | 309,982 | 21,826.4 | 61,763.5 | 55,195.4 | 789,963 | 11.71 | 50.6 | 9.01 |
In 2015 and 2016, the smooth factor fitness curve of the railway freight increment is predicted, as shown in Figures 3 and 4.
2015 Smoothing Factor of Railway Freight: Incremental Fitness Curve Prediction.
2016 Smoothing Factor of Railway: Freight Incremental Fitness Curve Prediction.
GA was used to predict the 2015 and 2016 railway freight incremental GRNN smooth σ factor, and the smooth σ factor was substituted into GRNN. The rail freight incremental predictive results are shown in Table 4.
Railway Freight Volume Forecast in 2015 and 2016.
| Year | Smoothing factor σ | Railway freight increment prediction results | Railway freight increment prediction results |
|---|---|---|---|
| 2015 | 0.93685 | 11,633 | 392,967 |
| 2016 | 0.81694 | 8942.3 | 401,909.3 |
From the website of National Bureau of Statistics, it can be learned that in 2014, the railway freight volume reached 3.81334 billion tons. Then, the railway freight volumes of 2015 and 2016 can be obtained through relevant calculations.
5 Conclusion
In this paper, a new method of genetic improvement based on the GRNN is proposed, and it is applied to railway freight volume forecasting.
Compared to the former method, GA is more highly effective because it takes into consideration the subjective factors. The prediction results show that using the same number of training samples, and forecasting the same target, the genetic improvement of the GRNN model prediction accuracy is better in predicting target values and therefore indicates a large improvement in forecast accuracy.
The set of improved algorithm to calculate fitness function forms an innovative method by using a “5+3” mode, namely to establish a GRNN, with the continuous five training samples, capable of predicting the next five samples. The predicted results and the real value of the reciprocal of Euclidean distance as the fitness function ensure a smooth factor optimization that can be used to forecast any change in trend of the target data.
Finally, a forecast of incremental data is calculated, rather than using direct projections of the data, and then the prediction results are calculated. It is concluded that this system is suitable to forecast the target. Furthermore, this method of data processing makes forecasting more sensitive, as well as brings prediction results closer to their real value.
Acknowledgements:
This work was supported by the science research project of Liaoning Provincial Department of Education with the project number “JDL2016032”.The authors wish to acknowledge the support and efforts of all authors which are present and involved in this paper, in particular expresses our sincere gratitude to all those who have helped improving the content and format of the paper.
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