# A Convenient Tool for District Heating Route Optimization Based on Parallel Ant Colony System Algorithm and 3D WebGIS

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## Abstract

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## 1. Introduction

#### 1.1. District Heating Optimization

#### 1.2. Intelligent Algorithms

#### 1.3. GIS Tools for Designers

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. DH Route Planning Indicator (DHRPI) Definition

_{i}

_{,j}(or c

_{j,i}) is the sum of the weights of the pixels that the real road segment covered, as shown in Equation (1):

_{p}refers to the exact road pixel, and the value is set to one. wr represents the weights of the road.

_{i}

_{,j}(or c

_{j,i}) is the sum of the weights of the pixels that the linear segment from i to j (or j to i)covered, as shown in Equation (2):

_{p}is 1, and IV

_{p}, IW

_{p}, and IB

_{p}are 0, so only the wbl has an effect on the c

_{ij}.

_{n×n}, as shown in Equation (3):

_{ij}means the cost of the edge connecting node i and j.

_{n,n+1}is the cost of the specific segment, and it can be traced to c

_{i,j}by the index of the node.

#### 2.3. Data Preparation

#### 2.4. Parallel ACS Algorithm

#### 2.4.1. Parameter Initialization

#### 2.4.2. Route Searching

_{allowed}is the size of the allowed vector. ${P}_{next}({X}_{next},{Y}_{next})$ is one of the points from the allowed vector, while ${P}_{this}({X}_{this},{Y}_{this})$ and ${P}_{last}({X}_{last},{Y}_{last})$ are the current point and the previous point. After the angle screening step, a subset of the allowed vector, namely sub_allowed, is acquired, and used for the subsequent calculations.

_{o}is a constant. Here, we set q

_{0}= 0.9 as a reference [16]. i is the current node, while j is any one candidate node from the sub_allowed vector. ${\tau}_{ij}(t)$ is the intensity of the pheromone between i and j at time t. ${\eta}_{ij}(t)$ is the heuristic information between i and j at time t. sub_allowed

_{k}stores the candidate nodes. α and β are two constantsthat can be described as the weighted values of the pheromone (${\tau}_{ij}(t)$) and heuristic information (${\eta}_{ij}$), respectively. Here, we set α = 0.1 and β = 2 as references [16].

_{0}, we directly set the next visited node to the one with the maximum value, as shown in (7-1). Otherwise, when q > q

_{0}, the roulette wheels method is executed. For every j belongs to sub_allowed

_{k}, ${p}_{ij}^{k}(t)$ is calculated by Equation (7-2), given a random generated number p, and the node with ${p}_{ij}^{k}(t)$≥ p is chosen as the next visited node. If j doesn’t belong to sub_allowed

_{k}, ${p}_{ij}^{k}(t)$ is set to 0 as shown in Equation (7-3). We can determine that the search is finished for one ant when Ep is chosen as the next visited node.

#### 2.4.3. Pheromone Updating

#### 2.5. Interactive 3D WebGISTool

## 3. Results and Discussion

#### 3.1. Comparation with the Manually Designed Route

#### 3.2. Comparation with the Corresponding Sequential Algorithm

#### 3.3. Comparation with ArcGIS Network Analyst Tool

#### 3.4. Interactive Design Results of the 3D WebGIS Tool

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Abbreviation | Full Name |

3D | three-dimensional |

ABC | artificial bee colony |

ACO | ant colony optimization |

ACS | ant colony system |

AS | ant system |

ASrank | rank-based ant system |

CS | cuckoo search |

CVRP | capacitated vehicle routing problem |

DH | district heating |

DHRPI | district heating route planning indicator |

GA | genetic algorithm |

GIS | Geographic Information System |

GPUs | graphics processing units |

ID | identification numbers |

IWD | intelligent water drops algorithm |

MMAS | max–min ant system |

OSM | OpenStreetMap |

PSO | particle swarm optimization |

SI | Swarm intelligence |

TSP | traveling salesman problem |

## Nomenclature

Symbol | Description | Equation |

c_{i,j} | the cost between node i and node j | (1) |

IR_{p} | IR is thebinary image of road.For the exact pixel p, if p is the road pixel, IR_{p} is set to 1; else, if p is not the road pixel, IR_{p} is set to 0. | (1) |

IBL_{p} | IBL is thebinary image of bare land. For the exact pixel p, if p is the bare land pixel, IBL_{p} is set to 1; else, if p is not the bare land pixel, IBL_{p} is set to 0. | (2) |

IV_{p} | IV is thebinary image of vegetable. For the exact pixel p, if p is the vegetable pixel, IV_{p} is set to 1; else, if p is not the vegetable pixel, IV_{p} is set to 0. | (2) |

IB_{p} | IB is thebinary image of building. For the exact pixel p, if p is the building pixel, IB_{p} is set to 1; else, if p is not the building pixel, IB_{p} is set to 0. | (2) |

IW_{p} | IW is thebinary image of water. For the exact pixel p, if p is the water pixel, IW_{p} is set to 1; else, if p is not the water pixel, IW_{p} is set to 0. | (2) |

wr | the weight of the road pixel | (2) |

wbl | the weight of the bare land pixel | (2) |

wv | the weight of the vegetation pixel | (2) |

wb | the weight of the building pixel | (2) |

ww | the weight of the water pixel | (2) |

C | the cost matrix | (3) |

D_{n,n+1} | D_{n,n+1} is the cost of the specific segment that composed a candidate route. It can be traced to c_{i,j} by the index of the node. | (4) |

f_{ind} | the function of the DH route planning indicator | (2) |

${\tau}_{0}$ | the initial value of pheromone | |

m | the number of ants | |

Sp | the start point of the route | |

Ep | the end point of the route | |

Tabu | a matrix that storesthe index of visited nodes | |

visited | a vector that stores the index of the visited nodes for the current ant | |

allowed | a vector that stores the index of the candidate nodes for the current ant | |

N_{allowed} | the size of the allowed vector | (6) |

${P}_{next}({X}_{next},{Y}_{next})$ | one of the candidate nodes from the allowed vector | (6) |

${P}_{this}({X}_{this},{Y}_{this})$ | the current visited node | (6) |

${P}_{last}({X}_{last},{Y}_{last})$ | the previous visited node | (6) |

sub_allowed | a subset of the allowed vector after the angle screening step | |

q | a random number | (7) |

qo | a constant | (7) |

${\tau}_{ij}(t)$ | the intensity of the pheromone between node i and node j at time t | (7) |

${\eta}_{ij}(t)$ | the heuristic information between node i and node j at time t | (7) |

α | a constant that can be described as the weighted value of the pheromone (${\tau}_{ij}(t)$) | (7) |

β | a constant that can be described as the weighted value of the heuristic information (${\eta}_{ij}$) | (7) |

${p}_{ij}^{k}(t)$ | a probability | (7) |

ρ | a parameter for the local updating rule | (8) |

α | a parameter for the global updating rule | (9) |

$\u25b3{\tau}_{ij}^{}$ | We set $\u25b3{\tau}_{ij}^{}$ the same as the initial value of pheromone (${\tau}_{0}$) | (8) |

${L}_{best}$ | the DH route planning indicator of the best route | (10) |

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**Figure 2.**Classification data of the study area. (

**a**) The downloaded data from OSM; (

**b**) The reprocessed classification maps.

**Figure 4.**Classification maps of the study area. (

**a**) Binary image of roads; (

**b**) Binary image of buildings; (

**c**) Binary image of water; (

**d**) Binary image of vegetation; (

**e**) Binary image of bare land; (

**f**) Distribution of nodes.

**Figure 7.**Scheme comparison interface with alternative routes of the three sub zones (green ones for the first zone, yellow ones for the second zone, and blue ones for the third zone).

**Figure 8.**District heating (DH) routes by manual design and the algorithm (cost function value sorted from the smallest to the biggest). (

**a**) The manually designed route; (

**b**) The route with minimum cost function value; (

**c**) The 28th route; (

**d**) The 29th route.

**Figure 9.**The cost function value variation from thefirst iteration to the 100th iteration for the 10 repetitions.

No. | Indicators | No. | Indicators | No. | Indicators |
---|---|---|---|---|---|

1 | 29.2184 | 11 | 36.5449 | 21 | 38.8374 |

2 | 30.2141 | 12 | 36.7126 | 22 | 39.1459 |

3 | 30.7896 | 13 | 36.9894 | 23 | 39.8428 |

4 | 31.9826 | 14 | 37.1286 | 24 | 39.905 |

5 | 32.0779 | 15 | 37.2763 | 25 | 41.9456 |

6 | 32.3144 | 16 | 37.4986 | 26 | 42.3429 |

7 | 32.6468 | 17 | 37.9436 | 27 | 44.4666 |

8 | 33.5068 | 18 | 38.231 | 28 | 45.2416 |

9 | 36.2242 | 19 | 38.5003 | 29 | 47.052 |

10 | 36.3235 | 20 | 38.6646 | 30 | 48.335 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Zhang, G.; Zhao, H.; Cao, Y.; Liu, Q.; Shen, Z.; Li, A. A Convenient Tool for District Heating Route Optimization Based on Parallel Ant Colony System Algorithm and 3D WebGIS. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 225.
https://doi.org/10.3390/ijgi8050225

**AMA Style**

Zhang Y, Zhang G, Zhao H, Cao Y, Liu Q, Shen Z, Li A. A Convenient Tool for District Heating Route Optimization Based on Parallel Ant Colony System Algorithm and 3D WebGIS. *ISPRS International Journal of Geo-Information*. 2019; 8(5):225.
https://doi.org/10.3390/ijgi8050225

**Chicago/Turabian Style**

Zhang, Yang, Guoyong Zhang, Huihui Zhao, Yuming Cao, Qinhuo Liu, Zhanfeng Shen, and Aimin Li. 2019. "A Convenient Tool for District Heating Route Optimization Based on Parallel Ant Colony System Algorithm and 3D WebGIS" *ISPRS International Journal of Geo-Information* 8, no. 5: 225.
https://doi.org/10.3390/ijgi8050225