# An IndoorGeoBML Model Based IORP Algorithm for Indoor Operation

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## Abstract

**:**

## 1. Introduction

## 2. The Design of IndoorGeoBML Model

#### 2.1. Geometry Information

#### 2.2. Navigation Information

#### 2.3. Semantic Information

- IGBMLSpace is the entity used to represent a space as the area or volume of a functional region. It is often associated with entities with empty space (e.g., hall, room, bathroom). The speed ${s}_{sp}$ within those entities can be around 30 m per minute, and we can set the military difficulty factor ${\psi}_{sp}$ of those entities as a standard unit 1.
- IGBMLElevator is a vertical entity, which merges or splits the space. Although the use of elevators is discouraged in operations with fire, some research still shows that they are a necessity and their usage is unavoidable, especially when we can monitor it with IoT technology. The speed ${s}_{el}$ within those entities can be at an average of 6 m per second, the military difficulty factor ${\psi}_{el}$ of those entities is higher, such as 15, in comparison with IGBMLSpace entities.
- IGBMLStair also represents a vertical passage allowing for movement from one floor to the other. It can contain an intermediate landing. The speed ${s}_{st}$ within those entities is considered at 15 m per minute, the military difficulty factor ${\psi}_{st}$ of those entities is a little bit higher, at 5, compared to IGBMLSpace entities.

#### 2.4. Outdoor Information

#### 2.5. Intelligence Information

- IGBMLPeople is the detailed information about the enemy and victims (for some rescue operations). This includes the number of enemy and victims, the military ranks and positions of enemy, etc.
- IGBMLWeapon describes the number and categories of the enemy’s weapons.
- IGBMLLocation is the location of people and weapons.

#### 2.6. Event Information

## 3. IORP Algorithm for Indoor Operation Route Planning

#### 3.1. The Core Concept of IORP Algorithm

#### 3.1.1. Route Selection

#### 3.1.2. Parameters Setting

#### 3.1.3. Pheromone Update

#### 3.2. IORP Algorithm for Single Destination Short Route Planning

**Step 1:**Construct IndoorGeoBML model:

**Step 2:**Confirm the algorithm parameters:

**Step 3:**Confirm the initial and terminating condition of the algorithm:

**Step 4:**Choose next node:

_{p}, ${N}_{i}^{p}$, $\mu $

_{w}, ${N}_{i}^{w}$, and ${P}_{i}^{w}$ (the parameters of coefficient and number of people); calculate the enemy capability ${C}_{xy}^{E}$ of the possible associate nodes respectively.

**Step 5:**Update pheromone and parameters:

**Step 6:**Check the terminating condition:

Algorithm 1. Pseudo code of IORP algorithm for the single destination route planning | |

1. | initialization; |

2. | while not terminate condition do |

3. | calculate fitness values associated with each squad; |

4. | choose next node; |

5. | if next node != target node then |

6. | update pheromone; |

7. | update parameters; |

8. |
end |

9. | end |

#### 3.3. IORP Algorithm for Whole Searching Route Planning

#### 3.3.1. Implementation Steps of IORP Algorithm for Whole Searching Route Planning

**Step 1:**Construct IndoorGeoBML model:

_{w}, the number of IGBMLWeapon of the node ${N}_{i}^{w}$, and the damage ability of IGBMLWeapon of the node ${P}_{i}^{w}$ in Equation (11).

**Step 2:**Confirm the algorithm parameters:

**Step 3:**Confirm the initial and terminating condition of the algorithm:

**Step 4:**Choose next node:

**Step 5:**Calculate casualties:

**Step 6:**Check if all nodes are visited:

**Step 7:**Update pheromone and parameters:

**Step 8:**Check terminating condition:

#### 3.3.2. Simplified Code of IORP Algorithm for Whole Searching Route Planning

Algorithm 2. Pseudo code of IORP algorithm for whole searching route planning | |

1. | initialization; |

2. | while not terminate condition do |

3. | calculate fitness values associated with each squad; |

4. | if not all squads have completed tour then |

5. | choose next node; |

6. | if next node violates constrains then |

7. | return to closest exit; |

8. | assign a new squad from start node; |

9. |
else |

10. | add a new node to current route; |

11. | if not all nodes are visited then |

12. | choose next node; |

13. | continue while loop; |

14. |
else |

15. | update pheromone; |

16. | update parameters; |

17. | solution and initialize squads; |

18. |
end |

19. | end |

#### 3.3.3. Flow Chart of IORP Algorithm for Whole Searching Route Planning

## 4. Experiment and Result Analysis

#### 4.1. Experimental Design

#### 4.2. The Single Destination Route Planning Result

#### 4.3. The Whole Searching Route Planning Result

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Meaning | Meaning of Subscript and Superscript | |

V | Geometry entities vector | None |

v_{i} | Geometry entity coordinate | i: node number |

A_{G} | Geometry entity attribute vector | G: geometry entity |

${a}_{G}^{i}$ | Geometry entity attribute node | i: node number G: geometry entity |

G(V,A_{G}) | Geometry information vector | V: geometry entity coordinate A _{G}: geometry entity attribute |

g_{i} | Geometry information node | i: node number |

E | Navigation entities vector | None |

e_{j} | Navigation entity coordinate | j: node number |

A_{N} | Navigation entity attribute vector | N: navigation entity |

${a}_{N}^{i}$ | Navigation entity attribute node | i: node number N: navigation entity |

N(E,A_{N}) | Navigation information vector | E: navigation entity coordinate A _{N}: navigation entity attribute |

g_{j} | Navigation information node | j: node number |

U(G,N) | Matrix of relationship between geometry and navigation information | G: geometry information vector N: navigation information vector |

S_{G} | Semantic information of geometry entities | G: geometry information |

S_{N} | Semantic information of navigation entities | N: navigation information |

s_{x} | Speed of entity | x: type of entity, sp represents IGBMLSpace, el represents IGBMLElevator, st represents IGBMLStair, ro represents road |

ψ_{x} | Military difficulty factor | x: type of entity, sp represents IGBMLSpace, el represents IGBMLElevator, st represents IGBMLStair, ro represents road |

${L}_{ij}^{x}$ | Judge if node in route | x: type of entity, sp represents IGBMLSpace, el represents IGBMLElevator, st represents IGBMLStair, ro represents road ij: node number |

B | Outdoor information vector | None |

b_{p} | Outdoor entity coordinate | p: node number |

μ_{y} | Coefficient in intelligence information | y: type of coefficient, p represents IGBMLPeople, w represents IGBMLWeapon |

${N}_{i}^{p}$ | Number of IGBMLPeople | p: represents IGBMLPeople i: node number |

${N}_{i}^{w}$ | Number of IGBMLWeapon | w: represents IGBMLWeapon i: node number |

${P}_{i}^{w}$ | Power of IGBMLWeapon | w: represents IGBMLWeapon i: node number |

${C}_{xy}^{E}$ | Enemy capability | E: represents enemy xy: node number |

a_{xy} | Nodes can accessible or not | xy: node number |

t_{xy} | Traversing time between nodes | xy: node number |

d_{xy} | Distance between nodes | xy: node number |

θ_{xy} | Cost between nodes | xy: node number |

D | Event information tuple | None |

f | Function of event information | None |

${C}_{S}^{O}$ | Own max casualty can bear | O: represents own s: represents casualty |

${P}_{xy}^{k}$ | Probability to choose next node | k: squad number xy: node number |

${\tau}_{xy}^{\alpha}$ | Probability influence τ | α: parameter to control τ xy: node number |

${\theta}_{xy}^{\beta}$ | Probability influence θ | β: parameter to control θ xy: node number |

I_{max} | Total number of iterations | max: total number |

I | Current number of iterations | None |

$\gamma $ | Coefficient with enemy’s capability and own side capability | None |

$\delta $ | Coefficient with enemy’s capability and own side capability | None |

$\sigma $ | Coefficient with enemy’s capability and own side capability | None |

$\xi $ | Coefficient with enemy’s capability and own side capability | None |

${\tau}_{{P}_{xy}^{k}}^{0}$ | Initial pheromone value | 0: initial state ${P}_{xy}^{k}$: Probability to choose next node |

τ_{0} | Initial value | 0: initial state |

d_{H,max} | Maximum distance of horizontal | H,max: horizontal maximum |

d_{V,max} | Maximum distance of vertical | V,max: vertical maximum |

$len\left({P}_{xy}^{k},L\right)$ | Distance from the node to the straight line L | ${P}_{xy}^{k}$: Probability to choose next node L: straight line |

λ | Map scale factor | None |

len(k) | Path length of the kth squad | k: the kth squad |

rank(k) | The rank of ant k | k: the kth squad |

ϑ · M | Number of squads to be updated | None |

ρ | Pheromone volatility factor | None |

Q | Pheromone constant | None |

ρ(k) | The kth squad pheromone update | k: the kth squad |

${\rho}_{min}$ | Preset value of pheromone volatilization rate | min: preset value |

${R}_{xy}^{k}$ | Route vector | k: the kth squad xy: node number |

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**Figure 1.**Geometry, navigation, and semantic information in a building. (

**a**) draws geometry information with blue circles. (

**b**) adds navigation information (green lines). (

**c**) adds semantic information with vector ${S}_{G}$, where the purple points represent the windows, and the cyan points represent the doors to enter the building. (

**d**) adds semantic information with vector ${S}_{N}$, where green lines represent the IGBMLSpace, the red lines represent the IGBMLElevator, and the orange lines represent the IGBMLStair.

**Figure 3.**As event information reveals that the elevators no longer work, red lines (representing elevators) in the IndoorGeoBML model turn into gray lines.

**Figure 4.**IORP algorithm flow chart for single destination route planning. The terminate condition is depicted in detail in implementation Step 3.

**Figure 5.**IORP algorithm flow chart for the whole searching route planning. The terminate condition is depicted in detail in implementation Step 3.

**Figure 7.**Experiment result of Dijkstra, PSO, GSA, BSA, and IORP for the single destination route planning.

**Figure 8.**Distance and time comparison between Dijkstra, PSO, GSA, BSA, and IORP algorithms for the single destination route planning.

**Figure 9.**Enemy capability and own casualties comparison between Dijkstra, PSO, GSA, BSA, and IORP algorithms for the single destination route planning.

**Figure 10.**A minimum of five squads will be required to accomplish the mission. The completed tour paths of these five squads are shown from (

**a**–

**e**) respectively.

**Table 1.**Dijkstra, PSO, GSA, BSA, and IORP algorithms for the single destination route planning result comparison.

Algorithm | Distance (m) | Enemy Capability | Time (s) | Casualties |
---|---|---|---|---|

Dijkstra | 75.8 | 1049.0 | 925 | 14.1 |

PSO | 120.1 | 1211.1 | 1073 | 15.9 |

GSA | 125.7 | 864.8 | 882 | 13.5 |

BSA | 155.1 | 887.3 | 902 | 13.8 |

IORP | 139.6 | 779.2 | 801 | 12.5 |

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**MDPI and ACS Style**

Su, M.; Wang, G.; Chen, L.; Zhang, X.
An IndoorGeoBML Model Based IORP Algorithm for Indoor Operation. *Sustainability* **2022**, *14*, 5760.
https://doi.org/10.3390/su14105760

**AMA Style**

Su M, Wang G, Chen L, Zhang X.
An IndoorGeoBML Model Based IORP Algorithm for Indoor Operation. *Sustainability*. 2022; 14(10):5760.
https://doi.org/10.3390/su14105760

**Chicago/Turabian Style**

Su, Mingzhan, Guangxia Wang, Lingyu Chen, and Xin Zhang.
2022. "An IndoorGeoBML Model Based IORP Algorithm for Indoor Operation" *Sustainability* 14, no. 10: 5760.
https://doi.org/10.3390/su14105760