# A Low-Carbon Decision-Making Algorithm for Water-Spot Tourists, Based on the k-NN Spatial-Accessibility Optimization Model

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Scenic Water Spot Classification Model Based on k-NN Mining

**Definition**

**1.**

**Definition**

**2.**

- (1)
- When $S(1,{i}_{1})\in {C}_{(u)}$, there should be $S(1,{i}_{1})\notin {C}_{{(}^{\neg}u)}$;
- (2)
- Arbitrary $\forall {C}_{(u)}\ne \varnothing $;
- (3)
- $\forall {C}_{(u)}\cap \forall {C}_{{(}^{\neg}u)}=\varnothing $, ${C}_{(1)}\cup {C}_{(2)}\cup ...\cup {C}_{(p)}={{S}_{1}}^{(1)}$;
- (4)
- The number of the classification ${C}_{(u)}$ is defined as $q(u)$. It stands for the element $S(1,{i}_{1})$ number in the No. $u$ classification ${C}_{(u)}$.

- (1)
- The No. $u$ row of ${{S}_{1}}^{(2)}$ stores the elements $S(1,{i}_{1})$ of the No. $u$ classification ${C}_{(u)}$;
- (2)
- The storage method for the arbitrary No. $u$ row in the matrix is that the element ${{S}_{1}}^{(2)}(u,y)$ footmark $y$ is increased by column;
- (3)
- If the element $S(1,{i}_{1})$ number $q(u)$ of the current ${C}_{(u)}$ row meets $q(u)<\mathrm{max}q(u)$, the latter $\mathrm{max}q(u)-q(u)$ number of elements are set 0;
- (4)
- The rows or the columns of ${{S}_{1}}^{(2)}$ are nonlinear-correlated; the row rank meets $rank({{S}_{1}}^{(1)}{)}_{ro}=p$; the column rank meets $rank({{S}_{1}}^{(2)}{)}_{co}=\mathrm{max}q(u)$.

**Definition**

**3.**

- (1)
- The No. $u$ row of ${S}_{2}$ stores the elements $S(2,{i}_{2})$ of the No. $u$ classification ${C}_{(u)}$;
- (2)
- The storage method for the arbitrary No. $u$ row in the matrix is that the element ${S}_{2}(u,y)$ footmark $y$ is increased by column;
- (3)
- If the element $S(2,{i}_{2})$ number $t(u)$ of the current ${C}_{(u)}$ row meets $t(u)<\mathrm{max}t(u)$, the latter $\mathrm{max}t(u)-t(u)$ number of elements are set 0;
- (4)
- The rows or the columns of ${S}_{2}$ are nonlinear-correlated; the row rank meets $rank({S}_{2}{)}_{ro}=p$; the column rank meets $rank({S}_{2}{)}_{co}=\mathrm{max}t(u)$.

**Definition**

**4.**

**Definition**

**5.**

**Input:**$m$ number of $S(1,{i}_{1})$, $n$ number of $S(2,{i}_{2})$, the set ${{S}_{1}}^{(2)}$.

**Output:**Matrix ${S}_{2}$.

**Step 1:**Initialize a transition matrix ${}^{\Delta}{{S}_{1}}^{(2)}$ with the same dimension as ${{S}_{1}}^{(2)}$; the dimension is $p\times \mathrm{max}q(u)$.

**Step 2:**Calculate the feature distance $d(S(1,{i}_{1}),S(2,1))$ between the No.1 element $S(2,1)$ and the set data, traverse ${i}_{1}$ in $(0,m]$;

**Step 3:**Confirm the $k$ number of the nearest neighborhood element $S(1,{i}_{1})$ for k-NN mining. Search the distance values $d(S(1,{i}_{1}),S(2,1))$ in ${}^{\Delta}{{S}_{1}}^{(2)}$; note the counter for the classification ${C}_{(ui)}$ as $count({C}_{(ui)})$ and the total number as $count({C}_{(u)})$.

- (1)
- Other than the element ${}^{\Delta}{{S}_{1}}^{(2)}(x,y)$ with $\mathrm{min}d(S(1,{i}_{1}),S(2,1))$, if there is no ${{}^{\neg}}^{\Delta}{{S}_{1}}^{(2)}(x1,y1){~}^{\neg}d(x1,y1)$ that makes ${}^{\neg}d(x1,y1)<d(x1,y1)$, the searching ends. Note the row number $x~ui$ and column number $y$ of ${\forall}^{\Delta}{{S}_{1}}^{(2)}(x1,y1)~d(x1,y1)$. Iterate $count({C}_{(ui)})=count({C}_{(ui)})+1$, $count({C}_{(u)})=count({C}_{(u)})+1$.
- (2)
- Other than the element ${}^{\Delta}{{S}_{1}}^{(2)}(x,y)$ with $\mathrm{min}d(S(1,{i}_{1}),S(2,1))$, if there is a ${{}^{\neg}}^{\Delta}{{S}_{1}}^{(2)}(x1,y1){~}^{\neg}d(x1,y1)$ which makes ${}^{\neg}d(x1,y1)<d(x1,y1)$, continue searching until the condition is not tenable. Output the current row number $x~ui$ and column number $y$ of ${\forall}^{\Delta}{{S}_{1}}^{(2)}(x1,y1)~d(x1,y1)$. Iterate $count({C}_{(ui)})=count({C}_{(ui)})+1$, $count({C}_{(u)})=count({C}_{(u)})+1$.

**Step 4:**Iterate to output $count({C}_{(ui)})$, $0<{u}_{i}\le p$, ${u}_{i},p\in N$. Traverse to search the maximum number in $count({C}_{(ui)})$. The related $C(ui)$ is the classification that the element $S(2,1)$ belongs to. Store $S(2,1)$ into the No. $ui$ row No.1 column in ${S}_{2}$.

**Step 5:**Turn back to the above Step 2~Step 4, continue calculating the feature distance $d(S(1,{i}_{1}),S(2,{i}_{2}))$ between the No. ${i}_{2}$ element $S(2,{i}_{2})$ and the training set data, traverse ${i}_{1}$ in $(0,m]$, ${i}_{2}$ in $(0,n]$. Calculate the classification ${C}_{(ui)}$ for $S(2,{i}_{2})$ and store $S(2,{i}_{2})$ into the No. $ui$ row No. $y$ column in ${S}_{2}$. When search till ${i}_{2}=n$, output the matrix ${S}_{2}$.

#### 2.2. Scenic Water Spot Spatial-Accessibility Optimization Model Based on Classification Matrix

**Definition**

**6.**

**Definition**

**7.**

**Definition**

**8.**

**Definition**

**9.**

- (1)
- The No. $u$ row of ${{S}_{2}}^{opt}$ stores the elements $S(2,{i}_{2})$ of the No. $u$ classification ${C}_{(u)}$;
- (2)
- The storage method for the arbitrary No. $u$ row in the matrix is that the element ${S}_{2}{}^{opt}(u,y)$ footmark $y$ is increased by column;
- (3)
- If the element $S(2,{i}_{2})$ number $t(u)$ of the current ${C}_{(u)}$ row meets $t(u)<\mathrm{max}t(u)$, the latter $\mathrm{max}t(u)-t(u)$ number of elements are set 0;
- (4)
- The rows or the columns of ${{S}_{2}}^{opt}$ are nonlinear-correlated; the row rank meets $rank{(}_{S}2{}^{opt}{)}_{ro}=p$; the column rank meets $rank({S}_{2}{}^{opt}{)}_{co}=\mathrm{max}t(u)$.

**Input:**$n$ number of elements $S(2,{i}_{2})$, matrix ${S}_{2}$.

**Output:**Matrix ${{S}_{2}}^{opt}$.

**Step 1:**Confirm the starting point $A$, spatial coordinates $(l,B)$ of the scenic water spots $S(2,{i}_{2})$. Initialize the matrix ${{S}_{2}}^{opt}$ as an empty matrix, ${{S}_{2}}^{opt}=0$;

**Step 2:**Set up the spatial-accessibility optimization model for the classification ${C}_{(1)}$. Calculate the accessibility factors of ${S}_{2}(1,1)~S(2,{i}_{2})$.

**Step 3:**Calculate the accessibility factors of ${S}_{2}(1,2)~S(2,{i}_{2})$ and make comparison.

- (1)
- If ${\lambda}_{(3,1)}>{\lambda}_{(3,2)}$, the spatial accessibility of ${S}_{2}(1,1)~S(2,{i}_{2})$ is stronger than that of ${S}_{2}(1,2)~S(2,{i}_{2})$, store ${S}_{2}(1,1)~S(2,{i}_{2})$ scenic water spot in the element ${{S}_{2}}^{opt}(1,1)$ of the first row ${C}_{(1)}$ in ${{S}_{2}}^{opt}$; store ${S}_{2}(1,2)~S(2,{i}_{2})$ scenic water spot in the element ${{S}_{2}}^{opt}(1,2)$ of the first row ${C}_{(1)}$ in ${{S}_{2}}^{opt}$.
- (2)
- If $\lambda (3,1)<\lambda (3,2)$, the spatial accessibility of ${S}_{2}(1,2)~S(2,{i}_{2})$ is stronger than that of ${S}_{2}(1,1)~S(2,{i}_{2})$, store ${S}_{2}(1,2)~S(2,{i}_{2})$ scenic water spot in the element ${{S}_{2}}^{opt}(1,1)$ of the first row ${C}_{(1)}$ in ${{S}_{2}}^{opt}$; store ${S}_{2}(1,1)~S(2,{i}_{2})$ scenic water spot in the element ${{S}_{2}}^{opt}(1,2)$ of the first row ${C}_{(1)}$ in ${{S}_{2}}^{opt}$.

**Step 4:**Traverse the column element of $y~(3,t(u)]$, and calculate the accessibility factors ${\lambda}_{(3,y)}$ of ${S}_{2}(1,y)~S(2,{i}_{2})$ and make comparison.

- (1)
- Search the maximum value in ${\lambda}_{(3,y)}$, $y\in (0,t(u)]$; store the related scenic water spot into ${{S}_{2}}^{opt}(1,1)$;
- (2)
- Search the second maximum value in ${\lambda}_{(3,y)}$, $y\in (0,t(u)]$; store the related scenic water spot into ${{S}_{2}}^{opt}(1,2)$;
- (3)
- Continue searching ${\lambda}_{(3,y)}$ in the descending order, and store them into ${{S}_{2}}^{opt}(1,y)$. When $y=t(u)$, the searching ends.
- (4)
- The searching process of the first row in ${{S}_{2}}^{opt}$ is completed; turn to Step 5.

**Step 5:**In line with the method from the Step 2 to Step 4, the spatial-accessibility optimization model of ${C}_{(u)}$ is constructed, traversing $u~(1,p]$. When $u=p$, the searching ends, and the matrix ${{S}_{2}}^{opt}$ is constructed.

#### 2.3. Low-Carbon Decision-Making Algorithm for Water-Spot Tourists, Based on the k-NN Spatial-Accessibility Optimization Matrix

**Definition**

**10.**

**Definition**

**11.**

**Definition**

**12.**

- (1)
- The $F$ dimension is $1\times (v+1)$, the row rank is $rank(F{)}_{ro}=1$, and the column rank is $rank(F{)}_{co}=v+1$;
- (2)
- The first element of $F(1)$ stores the starting point $A$, and it is not involved in the $2-opt$ algorithm;
- (3)
- From the second element to the No. $v+1$ element, they are used to store the $v$ number of scenic water spots $S(2,{i}_{2})$;
- (4)
- Arbitrary two elements $\forall {F}_{(i)}$ and $\forall {F}_{(j)}$ in the vectors ${F}_{(2)}~{F}_{(v+1)}$ can operate $2-opt$ dynamic algorithm, $i,j\in (1,v+1]$.

**Definition**

**13.**

- (1)
- The dimension is $1\times a$, the row rank is $rank(M{)}_{ro}=1$, and the column rank is $rank(\mathbf{M}{)}_{co}=a$;
- (2)
- In the process of the algorithm, the function $f(x,y)$ values are dynamically stored, and the finally stored values are the optimal $a$ number of $f(x,y)$.

**Input:**Matrix ${{S}_{2}}^{opt}$. Tourists choose classifications ${C}_{(u)}$, the number $v$ of the scenic water spots to be visited, the transportation modes $r$.

**Output:**Vector $M$.

**Step 1:**Based on ${{S}_{2}}^{opt}$, ${C}_{(u)}$ and $v$, the system recommends the optimal scenic water spots in each ${C}_{(u)}$ and accumulates to the number $v$; Initialize $F=0$, $\mathbf{M}=0$;

**Step 2:**Confirm the starting point $A$, store it in the No.1 element ${F}_{(1)}$ of $F$. Randomly store the recommended $v$ number scenic water spots $S(2,{i}_{2})$ in the No.2 to No. $v+1$ elements ${F}_{(2)}~{\mathbf{F}}_{(v+1)}$, get the initialized vector ${F}_{0}$.

**Step 3:**Based on the randomly chosen transportation mode $r$ in each road section, calculate the tourist spatial decision influence factor $\epsilon {(i,j)}^{(r)}$ and the normalization factor $\tau {(i,j)}^{(r)}$ for each section of scenic water spot $\forall S(2,{i}_{2})$ and $\forall S(2{,}^{\neg}{i}_{2})$. Then calculate each section’s function value ${}^{\Delta}f(x,y)$.

**Step 4:**Calculate $f(x,y)$, initialize the full ranked vector $M$.

- (1)
- If ${F}_{1}\ne {F}_{2}\wedge {F}_{1}\ne {F}_{0}$, calculate the $f(x,y)$ of the vector ${F}_{2}$, store the function value into No.3 element $M(3)$ of $M$;
- (2)
- If ${F}_{1}={F}_{2}\vee {F}_{1}={F}_{0}$, perform $2-opt$ dynamic algorithm again.

**Step 5:**Continue the $2-opt$ dynamic algorithm; do hill-climbing algorithm to search the optimal $M$.

- (1)
- If ${f}_{{F}_{a+1}}(x,y)<\forall M(i)~{f}_{{F}_{i}}(x,y)$, delete the maximum peak value $\mathrm{max}f(x,y)cu$ in current $M$, store ${f}_{{F}_{a+1}}(x,y)$ into vector $M$;
- (2)
- If ${f}_{{F}_{a+1}}(x,y)>\forall M(i)~{f}_{{F}_{i}}(x,y)$, turn to Sub-step 2 and continue searching.

- (1)
- If ${f}_{{F}_{a+2}}(x,y)<\forall {M}_{(i)}~{f}_{{F}_{i}}(x,y)$, delete the maximum peak value $\mathrm{max}f(x,y)cu$ in current $M$, store ${f}_{{F}_{a+2}}(x,y)$ into vector $M$;
- (2)
- If ${f}_{{F}_{a+2}}(x,y)>\forall {M}_{(i)}~{f}_{{F}_{i}}(x,y)$, turn to Sub-step 3 and continue searching.

- (1)
- If ${f}_{{F}_{k}}(x,y)<\forall {M}_{(i)}~{f}_{{F}_{i}}(x,y)$, delete the maximum peak value $\mathrm{max}f(x,y)cu$ in current $M$, store ${f}_{{F}_{k}}(x,y)$ into vector $M$;
- (2)
- If ${f}_{{F}_{k}}(x,y)>\forall {M}_{(i)}~{f}_{{F}_{i}}(x,y)$, continue searching until $k=A(v,v)$, the searching ends.

**Step 6:**Output the vector $M$. The $a$ number of elements in $M$ are the $a$ number of minimum peak values in all of the $A(v,v)$ number of peak values after the overall $2-opt$ dynamic algorithm performances on $F$.

## 3. Experiment, Results and Discussions

#### 3.1. Data Collection and Analysis of the Scenic Water-Spot Classification Results

- (1)
- The results of the experimental data collection.

- (2)
- The results of the scenic water-spot classification

#### 3.2. Calculation Results and Analysis of Scenic Water Spot Spatial Accessibility

- (1)
- The calculation results of the scenic water spot spatial accessibility.

- (2)
- The discussions of the classification of the scenic water-spot spatial accessibility.

#### 3.3. The Comparison Analysis of the Water-Spot Tourist Spatial Decision-Making Results

- (1)
- The results of the water-spot tourist spatial decision-making.

- (2)
- The discussions of the water-spot tourist spatial decision-making.

#### 3.4. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Abbreviation | Definition |

$S(1,{i}_{1})$ | Element of scenic water-spot classification training set |

${{S}_{1}}^{(1)}$ | Scenic water-spot initial training set |

${C}_{(u)}$ | Scenic water-spot classification |

${{S}_{1}}^{(2)}$ | Scenic water-spot classification training set |

$S(2,{i}_{2})$ | The to-be-classified scenic water-spot element |

${S}_{2}$ | Scenic water-spot classification matrix. |

${k}_{(i)}$ | Scenic water-spot feature attribute |

$k$ | Feature-attribute vector |

$\delta {(}_{k(i)})$ | Feature-attribute normalization parameter |

$d{(}_{S(1,{i}_{1}),S(2,{i}_{2})})$ | k-NN element feature distance |

${\lambda}_{(1)}$ | Starting-distance accessibility factor |

${\lambda}_{(2)}$ | Average traveling-distance accessibility factor |

${\lambda}_{(3)}$ | The weighted average accessibility factor |

${{S}_{2}}^{opt}$ | Scenic water spot accessibility optimization matrix |

$\epsilon {(i,j)}^{(r)}$ | Tourism spatial decision influence factor |

$\tau {(i,j)}^{(r)}$ | Normalization factor |

${}^{\Delta}{f}_{(i)}(x,y)$ | Spatial decision-making section cost function |

$f(x,y)$ | Spatial decision-making cost function |

$F$ | Tourism spatial decision-making $2-opt$ dynamic vector |

$M$ | Optimal peak-value storage vector |

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**Figure 2.**The modeling process of the scenic water-spot classification algorithm, based on k-NN mining.

**Figure 3.**The modeling process of the scenic water spot accessibility optimization matrix ${{S}_{2}}^{opt}$.

**Figure 5.**Spatial decision-making algorithm for water-spot tourists process, combined with $2-opt$ dynamic algorithm and hill-climbing algorithm.

**Figure 6.**The distribution of the scenic water spots, and the main roads connecting scenic water spots in Leshan City: (

**a**) shows the distribution of the scenic water spots. Different colors on the map annotation for the names of scenic water spots in the figure represent different classifications; the orange color represents humanity scenic water spots; the blue color represents lakes and valleys; and the pink color represents mountains and rivers; (

**b**) shows the spatial distribution of the roads around the scenic water spots.

**Figure 7.**The fluctuating curve graph of the accessibility factors for the scenic water spots: (

**a**) the fluctuating curve graph of the starting-distance accessibility factor ${\lambda}_{(1)}$; (

**b**) the fluctuating curve graph of the average traveling-distance accessibility factor ${\lambda}_{(2)}$; (

**c**) the fluctuating curve graph of the weighted average accessibility factor ${\lambda}_{(3)}$. Scenic water spots in the table: a. Dongfeng Weir–Thousand Buddha Rock; b. Leshan Giant Buddha–Three-River View; c. JiaYang Alsophila Spinulosa Lake; d. Dadu River–Jinkouhe Gorge; e. Muchuan Bamboo Sea; f. Heizhu Ravine; g. Emei Mountain–E Xiu Lake; h. Tianfu Sightseeing Tea Garden; i. Zhuyeqing Ecological Tea Garden; j. Ping Qiang Small Three Gorges.

**Figure 8.**Spatial decision-making results for the optimal route and sub-optimal routes under the two different transportation modes. (

**a**) shows the extracted research range of the recommended scenic water spots; (

**b**) represents the optimal route for self-driving travel; (

**c**,

**d**) represent the sub-optimal routes for self-driving travel; (

**e**) represents the optimal route for public bus travel; (

**f**,

**g**) represent the sub-optimal routes for public bus travel.

**Table 1.**The classifications of the tourists’ previously visited scenic water spots, and the weighted values of the feature attributes for each scenic water spot.

Previously Visited Water Scenic | ${\mathit{k}}_{(1)}$ | ${\mathit{k}}_{(2)}$ | ${\mathit{k}}_{(3)}$ | ${\mathit{k}}_{(4)}$ | ${\mathit{k}}_{(5)}$ | ${\mathit{k}}_{(6)}$ | ${\mathit{k}}_{(7)}$ | ${\mathit{k}}_{(8)}$ | |
---|---|---|---|---|---|---|---|---|---|

Humanity scenic water spot | The Summer Palace | 0.50 | 0.94 | 0.30 | 0.30 | 1.00 | 1.00 | 0.00 | 1.00 |

Suzhou Gardens | 0.50 | 0.92 | 0.80 | 0.20 | 0.00 | 1.00 | 0.00 | 1.00 | |

Guangzhou Chimelong | 0.50 | 0.96 | 2.50 | 0.80 | 0.00 | 0.00 | 0.00 | 1.00 | |

Yu Garden, Shanghai | 0.40 | 0.94 | 0.40 | 0.20 | 0.00 | 1.00 | 0.00 | 1.00 | |

Tang Paradise | 0.50 | 0.88 | 0.00 | 0.20 | 1.00 | 1.00 | 0.00 | 1.00 | |

Baotu Spring | 0.50 | 0.9 | 0.40 | 0.20 | 1.00 | 1.00 | 0.00 | 1.00 | |

Lakes and valleys | Qiandao Lake | 0.50 | 0.88 | 1.20 | 0.50 | 1.00 | 0.00 | 1.00 | 0.00 |

Qinglong Lake–Sansheng Flower Town | 0.40 | 0.78 | 0.00 | 0.40 | 1.00 | 0.00 | 1.00 | 0.00 | |

Xinyang Nanwan Lake | 0.40 | 0.82 | 0.60 | 0.20 | 1.00 | 0.00 | 1.00 | 0.00 | |

West Lake | 0.50 | 0.94 | 0.00 | 0.20 | 1.00 | 1.00 | 1.00 | 0.00 | |

Qinghai Lake | 0.50 | 0.92 | 0.00 | 0.20 | 1.00 | 0.00 | 1.00 | 0.00 | |

Mountains and rivers | Zhengzhou Yellow River Tourist Area | 0.40 | 0.84 | 0.60 | 0.30 | 1.00 | 1.00 | 1.00 | 1.00 |

Juzhou Park–Xiangjiang River scenery | 0.50 | 0.90 | 0.00 | 0.20 | 1.00 | 0.00 | 1.00 | 0.00 | |

Tengwangge–Ganjiang River scenery | 0.50 | 0.90 | 0.50 | 0.20 | 1.00 | 1.00 | 0.00 | 0.00 | |

Longmen Grottoes–Yihe River scenery | 0.50 | 0.92 | 0.90 | 0.20 | 1.00 | 1.00 | 0.00 | 1.00 | |

Huangguoshu Waterfall | 0.50 | 0.9 | 1.80 | 0.30 | 1.00 | 0.00 | 1.00 | 0.00 | |

Xiaolangdi of the Yellow River | 0.40 | 0.86 | 0.40 | 0.20 | 1.00 | 1.00 | 0.00 | 1.00 | |

Du Fu thatched cottage–Huanhua Creek | 0.40 | 0.92 | 0.50 | 0.20 | 1.00 | 1.00 | 0.00 | 1.00 |

**Table 2.**The classification results of the scenic water spots in the research range, and the weighted values of the feature attributes for each scenic water spot.

Classification Name | Scenic Water Spot in the Research Range | $\mathit{k}(1)$ | $\mathit{k}(2)$ | $\mathit{k}(3)$ | $\mathit{k}(4)$ | $\mathit{k}(5)$ | $\mathit{k}(6)$ | $\mathit{k}(7)$ | $\mathit{k}(8)$ |
---|---|---|---|---|---|---|---|---|---|

Humanity water scenic spot | Leshan Giant Buddha—Three-River View | 0.50 | 0.90 | 0.80 | 0.30 | 1.00 | 1.00 | 1.00 | 1.00 |

Zhuyeqing Ecological Tea Garden | 0.30 | 0.86 | 0.20 | 0.20 | 0.00 | 0.00 | 1.00 | 1.00 | |

Lakes and valleys | Ping Qiang Small Three Gorges | 0.10 | 0.88 | 0.00 | 0.30 | 1.00 | 0.00 | 1.00 | 0.00 |

Dadu River–Jinkouhe Gorge | 0.40 | 0.88 | 0.00 | 0.30 | 1.00 | 0.00 | 1.00 | 0.00 | |

Heizhu Ravine | 0.40 | 0.88 | 0.48 | 0.30 | 1.00 | 0.00 | 1.00 | 0.00 | |

Mountains and rivers | Tianfu Sightseeing Tea Garden | 0.40 | 0.88 | 0.30 | 0.20 | 1.00 | 0.00 | 1.00 | 1.00 |

Dongfeng Weir–Thousand Buddha Rock | 0.40 | 0.88 | 0.50 | 0.20 | 1.00 | 1.00 | 1.00 | 1.00 | |

Emei Mountain–E Xiu Lake | 0.50 | 0.92 | 1.60 | 0.30 | 1.00 | 1.00 | 1.00 | 0.00 | |

JiaYang Alsophila Spinulosa Lake | 0.40 | 0.80 | 1.00 | 0.20 | 1.00 | 1.00 | 1.00 | 0.00 | |

Muchuan Bamboo Sea | 0.30 | 0.90 | 0.39 | 0.20 | 1.00 | 0.00 | 1.00 | 0.00 |

**Table 3.**The calculated starting-distance accessibility factor λ

_{(1)}, the average traveling-distance accessibility factor λ

_{(2)}and the weighted average accessibility factor λ

_{(3)}. Scenic water spots in the table: a. Dongfeng Weir–Thousand Buddha Rock; b. Leshan Giant Buddha–Three-River View; c. JiaYang Alsophila Spinulosa Lake; d. Dadu River–Jinkouhe Gorge; e. Muchuan Bamboo Sea; f. Heizhu Ravine; g. Emei Mountain–E Xiu Lake; h. Tianfu Sightseeing Tea Garden; i. Zhuyeqing Ecological Tea Garden; j. Ping Qiang Small Three Gorges.

Scenic Water Spot | a | b | c | d | e |

$${\lambda}_{(1)}$$
| 0.0333 | 0.0769 | 0.0131 | 0.0086 | 0.0099 |

$${\lambda}_{(2)}$$
| 0.0165 | 0.0161 | 0.0109 | 0.0091 | 0.0084 |

$${\lambda}_{(3)}$$
| 0.0249 | 0.0465 | 0.0120 | 0.0089 | 0.0091 |

Scenic Water Spot | f | g | h | i | j |

$${\lambda}_{(1)}$$
| 0.0070 | 0.0319 | 0.0366 | 0.0398 | 0.0415 |

$${\lambda}_{(2)}$$
| 0.0076 | 0.0172 | 0.0149 | 0.0173 | 0.0147 |

$${\lambda}_{(3)}$$
| 0.0073 | 0.0246 | 0.0258 | 0.0286 | 0.0281 |

**Table 4.**Scenic water-spot accessibility optimization matrix. Scenic water spots in the table: a. Dongfeng Weir–Thousand Buddha Rock; b. Leshan Giant Buddha–Three-River View; c. JiaYang Alsophila Spinulosa Lake; d. Dadu River–Jinkouhe Gorge; e. Muchuan Bamboo Sea; f. Heizhu Ravine; g. Emei Mountain–E Xiu Lake; h. Tianfu Sightseeing Tea Garden; i. Zhuyeqing Ecological Tea Garden; j. Ping Qiang Small Three Gorges.

Classification Name | Classification Results | Weighted Average Accessibility Factor | Sequence of Spatial Accessibility Intensity |
---|---|---|---|

Humanity scenic water spot | b | 0.0465 | 1 |

i | 0.0286 | 2 | |

Lakes and valleys | j | 0.0281 | 1 |

d | 0.0089 | 2 | |

f | 0.0073 | 3 | |

Mountains and rivers | h | 0.0258 | 1 |

a | 0.0249 | 2 | |

g | 0.0246 | 3 | |

c | 0.0120 | 4 | |

e | 0.0091 | 5 |

**Table 5.**Optimal route and sub-optimal routes, section cost function value, total cost result comparison and the cost different comparison under the two transportation modes.

Transportation Mode | Tour Route | Section Cost Function Value | Total Cost | Cost Difference | |||

$i=1$ | OR 1: 12453 | 0.6907 | 1.4863 | 1.1408 | 1.3983 | 4.7161 | |

OR 2: 12543 | 0.6907 | 1.5062 | 1.1408 | 1.5416 | 4.8794 | 0.1633 | |

OR 3: 12354 | 0.6907 | 1.7500 | 1.3983 | 1.1408 | 4.9799 | 0.2638 | |

Transportation mode | Tour Route | Section cost function value | Total cost | Cost difference | |||

$i=2$ | OR 1: 15324 | 1.9970 | 3.6020 | 3.3420 | 2.9390 | 11.8800 | |

OR 2: 13524 | 1.5630 | 3.6020 | 3.8040 | 2.9390 | 11.9080 | 0.0280 | |

OR 3: 14235 | 2.4030 | 2.9390 | 3.3420 | 3.6020 | 12.2860 | 0.4060 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, X.; Wen, B.; Su, M.; Tian, J.
A Low-Carbon Decision-Making Algorithm for Water-Spot Tourists, Based on the *k*-NN Spatial-Accessibility Optimization Model. *Water* **2022**, *14*, 2920.
https://doi.org/10.3390/w14182920

**AMA Style**

Zhou X, Wen B, Su M, Tian J.
A Low-Carbon Decision-Making Algorithm for Water-Spot Tourists, Based on the *k*-NN Spatial-Accessibility Optimization Model. *Water*. 2022; 14(18):2920.
https://doi.org/10.3390/w14182920

**Chicago/Turabian Style**

Zhou, Xiao, Bowei Wen, Mingzhan Su, and Jiangpeng Tian.
2022. "A Low-Carbon Decision-Making Algorithm for Water-Spot Tourists, Based on the *k*-NN Spatial-Accessibility Optimization Model" *Water* 14, no. 18: 2920.
https://doi.org/10.3390/w14182920