Abstract: Complex section route scheme selection of mountainous expressway is the key to overall design of expressway. It not only determines the quality of expressway alignment, as well as the expressway construction cost control factors. According to the basic principles of expressway route selection, combining with the terrain and geological conditions of mountains, it analyses and establishes the optimization model of complex section route scheme selection of mountainous expressway based on multi-objective decision making method. The relative weight of indicators is determined by the method Analytic Hierarchy Process (AHP) and the pattern vectors to be tested and characteristic matrix of indicators are established based on Grey Correlation Degree Process (GRAP) and the correlation degree is calculated and the optimal route is determined according to the size of correlation degree. This method is validated by a case study of complex section route selection of mountainous expressway in Chinese. The practice proves that the method for complex section route selection of mountainous expressway is feasible.
INTRODUCTION
Mountainous expressway route selection is not only directly related to the project investment of expressway itself and transportation efficiency, as well as whether it can plays a proper role in the expressway network. In the mountains, complex section route scheme selection of mountainous expressway is the soul of overall design of expressway; it fundamentally determines the route direction of mountainous expressway. Mountainous expressway route selection commonly used technical indicators, economic indicators and social and political environment indicators and every indicator contains different quantitative or qualitative and other indicators. A study of section Route scheme of mountainous expressway based on AHP method considering that topography and geology condition, construction technology factors, based on multi-objective decision making method, it constructs optimization model of complex section route scheme selection of mountainous expressway and provides scientific basis for final decision. So that complex section route scheme selection of mountainous expressway tend to be more reasonable and constantly improve, for lower the project cost, reducing the project’s impact on the environment and so on that has the important meaning.
MULTI-OBJECTIVE DECISION MAKING OPTIMIZATION MODEL
The establishment of evaluation index system: In the mountainous area expressway route scheme complex section selection, the establishment of evaluation index system is very important. The established to index system should be based on comprehensive, scientific, feasibility and applicability of the principle. Evaluation index is not only to reflect the main contradiction but also to get attention to the secondary contradiction. The index system should as far as possible reaction its objective characteristics and it should be fair and comparable to each alternative evaluation scheme and to obtain easily and quantification. In the process of evaluation, quantitative analysis is given priority, quantitative indicators must be quantitative, not quantitative indicators uses qualitative analysis, in the middle of evaluation index system, it includes the qualitative and quantitative indicators. According to the above principles, based on a large number of actual survey material and extensively draw the expert research achievement, the AHP-GRAP method unifies, comprehensive induction, comparison analysis and study, it sets up the evaluation index system of expressway scheme selection including the target layer, index layer, the second index layer and scheme layer (Fig. 1) (Yang et al., 2010; Sun et al., 2011; Xu et al., 2012; Suh et al., 2011).
| Fig. 1: | Evaluation index system of expressway route scheme selection |
The evaluation model of expressway scheme selection: Analytic Hierarchy Process(AHP) is a kind of systematic and hierarchical analysis problem of multi-objective decision-making method, The whole system is divided into target layer, criterion layer and scheme layer and then every scheme comparison, the judgment matrix is used to evaluate relatively, finally the comprehensive comparison is carried on and the superiority of these schemes will be discharged. At the same time, Grey Correlation Degree Process (GRAP) is a relative sequence analysis, its basic thought is to judge whether the contact closely based on sequence curve the geometry of the similar degree, curve is closer, the correlation between the corresponding sequence is the greater and the smaller. The AHP-GRAP method unifies is used in complex section route scheme selection of mountainous expressway and establish the evaluation model. Its basic thought is: Firstly, the structure levels relationship is established with AHP method, As shown in Fig. 1. The judgment matrix is constructed based on the analysis of the indexes of each scheme and calculate the relative weight of the criterion layer, the second criterion layer and scheme layer each index. Secondly, it calculates the correlation degree with GRAP method, the relative weight of each evaluation index of the second criterion layer constitutes waiting for test mode vector and the relative weight of each evaluation index of the scheme layer constitutes the risk characteristic matrix and the correlation degree is calculated, the scheme is sorted based on the correlation degree, the maximal correlation degree is the optimal route scheme:
| • | Establish hierarchy model: By using AHP method to analyze problems, the problem is resolved into some layers according to the causal relationship, the complex section route scheme selection of mountainous expressway is divided into the target layer, criterion layer, the second criterion layer and the scheme layer (Fig. 1) |
| • | Structure judgment matrix: To establish the hierarchical structure model, it can compare one element to another element in each layer and each index. step by step and Structure judgment matrix, the judgment matrix is showed , as follows (Sheng and Qun-Qi, 2007; Ping et al., 2011; Liu et al., 2005; Chen and Song, 2012; Zhang 2006): |
| Table 1: | The corresponding RI value of matrix order number |
For a single criterion, the comparison of two indicators can be disputed good and bad. The coefficient value is showed, as follows:
When Pi and Pj is quite, bij = 1; When Pi is better than Pi, bij = 3;
When Pi is more better than Pj, bij = 5; When Pi is further better than Pj, bij = 7;
When Pi is best than Pj, bij = 9.
In a similar way, when Pi is worse than Pj, bij can obtain the reciprocal of above corresponding value (the good and bad of 2, 4, 6, 8 is between 1, 3, 5, 7. the value is based on specific conditions).
The judgment matrix can be used critical thinking mathematical and can simplify
the analysis of the problem. But in order to avoid the extreme violation of
common sense and in order to guarantee the Analytic Hierarchy Process (AHP)
to get the rationality of the analysis conclusion, the consistency of the judgment
matrix must be checked. In middle of AHP method, the consistency check of the
judgment matrix applies to
| • | Layer sort and consistency check: According to the judgment matrix, for above layer correlation the elements of this layer, the weight value of elements of this layer is calculated (Sheng and Qun-Qi, 2007; Ping et al., 2011; Liu et al., 2005; Chen and Song, 2012; Zhang, 2006). The procedure is as follows: |
| • | Calculate each line of the judgment matrix product: |
| (1) |
| • | Calculate the n root of Mi: |
| (2) |
| • | Regularization |
| (3) |
The value of W = [W1, W2 ..., Wn]T is the weight value of each element.
| • | Calculate the biggest characteristic root of the judgment matrix: |
| (4) |
One of them, (AW)i expresses the i element of the vector AW.
| • | Grey relational analysis: The weight coefficient of the index of the layer is ascertained by Analytic Hierarchy Process (AHP) method. Then the calculation of Grey Correlation Degree Process (GRAP) includes these weight coefficients, in other words , the correlation coefficient takes the weighted average instead of the average value last date (Zhang, 2006). The specific procedure is as follows: |
| • | Ascertain characteristic matrix of indicators: In the middle of complex section route scheme selection of mountainous expressway, the relative weight of scheme layer composes the characteristic matrix of indicators, the form is as follows: |
Ascertain waiting for test vector matrix: In the middle of complex section route scheme selection of mountainous expressway, the relative weight of the criterion layer composes the waiting for test vector matrix, the form is as follows:
| • | Calculate the grey correlation degree: The grey correlation degree is a kind of indicators on behalf of similarity between grey system. Its calculation formula is as follows: |
| (5) |
One of them, εij (k)is the grey correlation coefficient, Its calculation formula is as follows:
| (6) |
This, Δij (k) expresses the absolute difference value of two series in k moment. namely Δij (k) = |Xi(k)-Xj(k)|, Δmax is the maximum of the absolute difference value in each moment, Δmin is the minimum of the absolute difference value in each moment, general Δmin = 0, ρ is respective cofficient, 0<ρ<1, genetal ρ = 0.5.
| • | Judge good and bad of scheme. According to the calculation results, the scheme is sorted bases on the correlation degree size, the greater the correlation scheme more close to the optimal reference scheme and it is the optimum scheme too. |
APPLICATION EXAMPLE
Original material: Take a expressway complex section as an example. The topographic feature of the 44 kilometers in middle of the route is canyon terrain, narrow valley, the indicators of the alignment are low, this complex section lies in here, the ratio of curve is 80%, plenty of radius of circular curve is between 450-1130 m. The complex section route selection arranges around the arrangement of Water quality of the reservoir. The scheme not only considers the harm to the water quality of the reservoir in expressway construction and operation period but also considers the fatal harm to the reservoir when toxic substances is transported, at the same time, the expressway operation safety must be considered when the reservoir impound. Based on above ideas, combined specific conditions of complex section, there are three schemes now, it will choose the optimum scheme according to comprehensive analysis and evaluation, the specific technical, economic and environment indicators of three schemes are in Table 2.
| Table 2: | The value of the indicators of three schemes |
| Table 3: | The judgement matrix of the criterion layer on the target layer and W value |
| A-the mountains area expressway route scheme evaluation Bi , Ci- in the table 2; W---weight | |
Structure judgment matrix and determine the weight coefficient of each layer: According to the specific indicators of three schemes in Table 2, the score value of the criterion layer on the target layer will be ascertained and the second criterion layer on the criterion layer and the scheme layer on the second criterion layer, the score value structure the judgment matrix, according to the above formula, the weight coefficient of each indicator can be calculated, Table 3, 4 and 5 show the value, at the same time, to check the consistency of the judgment matrix check. Table 6 shows the specific value, according to the value, the consistency is satisfied. Finally, the weight coefficient of the target layer on each specific indicator ascertains, C1 = 0.0824, C2 = 0.0327, C3 = 0.0582, C4 = 0.0582, C5 = 0.0327.
Ascertain characteristic matrix of indicators and waiting for test vector matrix: Complex section route scheme selection model of mountainous expressway chooses sixteen indicators and three schemes, then characteristic matrix of indicators consists of the weight coefficient of each scheme in Table 5, the matrix is three lines and sixteen row, as follows:
| Table 4: | The judgement matrix of second criterion layer on criterion layer and W value |
| Bi, Ci--- in the Table 2, C6=0.0327,C7=0.1419, C8=0.0770, C9=0.0698,C10=0.0379, C11=0.1054, C12=0.0698, C13=0.0379, C14=0.0881, C15=0.0485, C16=0.0267 | |
| Table 5: | The judgement matrix of the scheme layer on second criterion layer and W value |
| sch-scheme; Ci--- in the Table 2 | |
| Table 6: | The consistency check value of the judgment matrix check |
| ë--- the biggest characteristic root of the judgment matrix, CI--- the consistency index of the judgment matrix, RI--- the average random consistency index, CR--- the ratio of random consistency, S---scheme | |
| Table 7: | Correlation degree calculation of three schemes |
At the same time, waiting for test vector matrix consists of the weight coefficient of each specific indicator, the matrix is one line and sixteen row, as follows:
[XT] = {XT} = [0.0824 0.0327 ... 0.0267]
Calculate the correlation degree: According to formula (5) and (6), the correlation degree of three schemes is calculated, Table 7 shows their specific value, the correlation degree of the scheme 1, 2 and 3, respectively are 11.9, 10.8, 10.2. the correlation degree of the scheme 1 is the biggest, so the scheme 1 is the optimal scheme.
CONCLUSION
Because of the special geological conditions of the mountainous terrain, it is very important for mountainous area expressway to build a technical and economic feasible route. This paper establishes evaluation index system of mountainous area expressway and establishes complex section route scheme selection model of mountainous area expressway by AHP-GRAP method and ascertains the optimal scheme. The method is convenient and scientific, it provides a quantitative analysis basis for complex section route scheme selection of mountainous area expressway.
ACKNOWLEDGMENTS
This work was financially supported by The National Natural Science Foundation (51078250).