3.1 A modified AHP by evolutionary algorithms
It is the first time that Satty et al. (Saaty and Kearns 1985)proposed a multicriteria decision-making method named Analytic Hierarchy Process(AHP), which is considered to be a reasonable and effective method of determining power in the existing weight evaluation methods(Saaty 2008). Because AHP adopts the qualitative analysis of the expert scoring method and the appropriate mathematical model for quantitative analysis, multiple objectives and multiple criteria can be reasonably quantitatively analyzed simultaneously. (Saaty and Vargas 2012) The way includes four main steps: 1.Establish the analytic hierarchy model. 2. Building model comparison matrix. 3. Calculate the weight of each factor in the model. 4. Results consistency test. However, the subjective influence of expert evaluation in AHP leads to the qualitative aspects too many ingredients and reduces the reliability of this method(Zhao J and Dan Q 2003). This study uses evolutionary algorithms(EA) further to optimize the weight determination process of AHP and improve the rationality of the quantitative evaluation of each factor.
As described in Figure 3, the modified AHP uses evolutionary algorithms to calculate the optimal compare matrix with the best consistency(the black dotted line), instead of expert scoring and checking consistency in the traditional AHP (the red dotted line). As a result, the modified AHP method is more objective than the evaluation result of the traditional method.
Through the improvement of traditional AHP methods, the step of the modified AHP is organized as follows. Firstly, determining the evaluation indicators(X1, X2,..., Xn) of judgment matrix X. And then, obtaining the importance range by pairwise comparison of indicators refer to Table 1. At last, the fuzzy judgment matrix is assembled by the importance range. It is worthy to note that the importance of the two evaluation indicators is between two scales, so we construct the fuzzy scoring matrix by the expert scoring interval and determine the comparison matrix with the optimal consistency within the scope of the fuzzy scoring matrix.
Table 1 The standard for quantitative judgment of importance for index
Scale
|
Meaning
|
1
|
Indicating that two factors are equally important
|
3
|
Indicating that one factor is slightly more important than the other
|
5
|
Indicating that one factor is significantly more important than the other
|
7
|
Indicating that one factor is more important than the other
|
9
|
Indicating that one factor is extremely more important than the other
|
2,4,6,8
|
Indicating the transition value between importance judgments
|
Reciprocal
|
The factor i is compared with j to obtain the judgment bij. The factor j is compared with i to obtain the judgment bji=1/bij.
|
The borders of the evolutionary algorithm are defined by fuzzy judgment matrix, the same as traditional AHP, consistency ratio CR calculated by equation 1-4 as the single optimization objective of EA.
①Expand the judgment matrix by row:
![](https://myfiles.space/user_files/69515_16346c490bab499e/69515_custom_files/img1628827844.png)
②Normalized judgment matrix:
![](https://myfiles.space/user_files/69515_16346c490bab499e/69515_custom_files/img1628827866.png)
③Solving the maximum eigenvalue of the judgment matrix:
![](https://myfiles.space/user_files/69515_16346c490bab499e/69515_custom_files/img1628827901.png)
④Calculating the consistency indicator CR:
![](https://myfiles.space/user_files/69515_16346c490bab499e/69515_custom_files/img1628827925.png)
CI is the consistency ratio, λmax is the maximum eigenvalue, and n is the matrix order. RI is the ratio of average random consistency to random consistency reflected in the number of evaluation indicators. The judgment matrix would be ragard as satisfactory consistency, and the weight values are reasonable if CR < 0.1 in the traditional method. However, If CR>0.10, the data will not generate meaningful outcomes unless reexamined, which always leads the evaluation procedure complicated. So we could take CR as the only optimization objective to find a consistent optimal matrix as a single objective evolutionary problem, and directly calculate the consistent optimal judgment matrix by evolutionary algorithms method. So the result of modified AHP will be more objective than traditional way.
3.2 Buliding the evaluation index system
According to the post-earthquake geological environment background, ecological environment, distribution of disaster points, and social development in the region, the evaluation system of geological environment carrying capacity is constructed based on ten evaluation index layers in three aspects of geological environment, ecological environment, and social environment. Then the content of the evaluation index system of geological environment carrying capacity is calculated at different levels. Pingwu county geological environment carrying capacity evaluation index system structure, as shown in Figure 4, includes three subsystems: geological environment subsystem, ecological environment subsystem, and social-economic subsystem.
As can be seen in Figure 4, the prerequisite of building AHP evaluation system requires that the selected factors are independent of each other. Therefore, we select four factors related to geological environment carrying capacity for the geological environment criterion layer. Because the ecological environment is an essential part of environmental geology, the ecosystem is regarded as the second criterion layer, including water resources and tourism resources. The third criterion layer is social economy, including population and basic facilities. Obviously, it is not comprehensive enough that evaluating regional geological environment carrying capacity just considering the potential of natural hazards and environmental resources(Liu et al. 2009; Wang and Yi 2009). The social environment and ecological environment are also key criterion layers in the quantitative model of eco-geological environment carrying capacity evaluation system. Therefore, we could comprehensively evaluate eco-geological environment carrying capacity of study area based on this new evaluation index system.
3.3 Calculating weight of index by evolutionary algorithms
According to the evaluation indexes of eco-geological environment carrying capacity in the last section and standard for quantitative judgment in Table 1, we determine the fuzzy judgment matrix referring to the expert scoring of AHP evaluation index in previous studies(Chen et al. 2004; Wang and Yi 2009). The fuzzy scoring matrix reflects the advantages of quantitative evaluation of expert scoring and reduces the objectivity caused by human factors in the scoring process. Table 2 shows the details about the fuzzy judgment matrix.
Table 2 Fuzzy judgment matrix of evaluation indexs
Index layer
|
Geological Structure
|
Lithology
|
Topography
|
Natural Hazard
|
Water Resources
|
Mine Resources
|
Population
|
Basic Facilities
|
Geological Structure
|
1
|
0-1
|
0-1
|
0-1
|
4-5
|
0-1
|
0-1
|
0-1
|
Lithology
|
|
1
|
0-1
|
0-1
|
4-5
|
0-1
|
0-1
|
0-1
|
Topography
|
|
|
1
|
0.5-1.5
|
4-5
|
0-1
|
0-1
|
0-1
|
Natural Hazard
|
|
|
|
1
|
4-5
|
0-1
|
0.5-1.5
|
0-1
|
Water Resources
|
|
|
|
|
1
|
0-1
|
0-0.5
|
0-0.5
|
Mine Resources
|
|
|
|
|
|
1
|
0-0.5
|
0-0.5
|
Population
|
|
|
|
|
|
|
1
|
1-2
|
Basic Facilities
|
|
|
|
|
|
|
|
1
|
In fact, it is a single-objective optimization problem of a complex process to select the consistent optimal matrix in the fuzzy matrix. CR is the optimization objective of evolutionary algorithms in this study. We set the number of individuals to 1000 and increase the generations of evolution step by step. As shown in Fig. 5, With the increase of evolutionary generations, the mean and standard deviation of CR in the last generation generations decrease continuously.
(a) 50 generations; (b)100 generations; (c) 200 generations; (d) 500 generations
Indeed, the optimal solution and standard deviation of CR are stable while the generation increases to five hundred (<10-4 ). Therefore, We use the comparison matrix corresponding to the minimum CR value of the five hundred generations evolutionary algorithm as the optimal comparison matrix to calculate the weight of each parameter. The calculation results are shown in Table 3.
Table 3 Weight of index layer
Target Layer
|
Criterion Layer
|
Index Layer
|
Weight
|
Evaluation System of Geological Environment Carrying Capacity of
Pingwu County
|
Geological Environment
|
Geological Structure
|
0.10676812
|
Geological Structure
|
0.10782611
|
Topography
|
0.10727444
|
Natural hazard
|
0.10834189
|
Ecosystem
|
Water Resources
|
0.02623324
|
Mine Resources
|
0.10817181
|
Social Economy
|
Population
|
0.21682408
|
Basic Facilities
|
0.21856031
|
3.4 Results of Geological Eco-Environment Carrying Capacity in Pingwu County
Based on the nine evaluation indexes in the three criteria of geological environment, ecological environment, and social environment, Figure 6 shows the results of GIS raster visualization. And then, we determinate the weight of each index by modified AHP method that used evolutionary algorithms. We calculated and superimposed multiple values of indicators through the GIS grid and finally obtained the geological environment carrying capacity map of Pingwu County.
(a) Lithology; (b) Topography; (c) Natural hazards; (d) Geological structure.
There are four indexes in geological environment criterion layer, as shown in Figure 6. Topography and geological structure contain two secondary factors, respectively. The geological structure mainly includes the influence of seismic faults, and it is quantified as fault distance and classification of ground shock. Similarly, Slope and elevation are select to represent the characteristics of topography. Other indexes can be expressed directly by a single factor which including natural hazards density and lithology.
According to the genetic type, material composition, structural characteristics, and physical and mechanical properties of the strata, the lithology is divided into five geological rock groups: clastic rock, carbonate rock, metamorphic rock, magmatic rock and pebble, which could be considered as hard rock, medium-hard rock, hard/soft interphase, soft rock and pebble soil,respectively. Topography index include slope range from to and elevation range from 600m to 5440m, and they are divided into four levels. The main purpose of this study is to understand the geological carrying capacity after the Wenchuan earthquake, so the natural disaster index analyzes the disaster density distribution after the earthquake, mainly including debris flow, landslide, collapse and other disasters, and geological structure index includes fault distance and ground shock, which belong to quantitative indicators directly related to earthquake.
Figure 7 gives visualization results of two indexes in the ecological environment criterion layer, including water resources and mine resources. Water resources mainly come from the Fujiang River running through Pingwu County with a total length of 157 km, which is the largest tributary of the Jialing River. Moreover, there are 15 Fujiang tributaries and 428 streams in the region, such as Qingyi River and Duobu River, the total river network density is up to 0.3 km / km2. So it is a critical criterion of river distance for water resources. The study area is rich in iron, lead, zinc, manganese, gold, and other mineral resources. On the one hand, In the process of mine underground mining, mine roof caving, gushing water, precipitation induced groundwater level decline, part of the open-pit mining lead the natural slope instability eventually forms landslide. On the other hand, the arbitrary accumulation of abandoned soil and slag formed by mining provides more material sources for disasters such as collapse, landslide, and debris flow triggered by rainstorm and destroys the ecological environment.
The population density and basic facilities belong to the social economy criterion layer. Population density shows the degree of population aggregation in Pingwu County. As is shown in figure 7, the Population of Pingwu mainly concentrated in Longan Town, Crystal Town, Nanba Town, and radioactive reduction in population density centered on these areas. The population density of Tucheng Town and Xiangyan Town decreased sharply to below 50 people per square kilometer. The infrastructure in Pingwu County is mainly distributed along the river basin, in which Longan Town is the most concentrated. It is distributed linearly along the main river channel and tributaries of the Fujiang River. The infrastructure is mainly highway traffic, town construction, and ancillary facilities.
Indeed, we use the weight of each index (Table 3) obtained by the optimal comparison matrix and implement grid superposition to draw the geological eco-environment carrying capacity map of Pingwu County.
The carrying capacity of the eco-geological environment in Pingwu County involves four categories, there are high, medium, low, and very low, respectively. Furthermore, these categories can be divided into two states: equilibrium (critical overload) and surplus (non-overload). The equilibrium state includes high and medium carrying capacity, which means the geological disasters in the region are relatively developed, and the development area is limited. Moreover, both low and very low carrying capacity all belong to the surplus state, and the areas of this state are usually less developed with low population density. As can be seen in Figure 8, high carrying capacity areas mainly located along the Fujiang River and both sides of the Pingtong River, including slope sections on both sides of the valley and human activities to the buffer zone of nature reserves, as well as some low-mountain and hilly landform areas. The critical overload capacity in these areas mainly due to frequent geological disasters and human activities. Similarly, The areas in Pingwu County with low population density and fewer geological disasters belong to the surplus state, mainly including nature reserves in Baima Town, Tucheng Town, and Huya Town.