# Strategic Sensor Placement in Expansive Highway Networks: A Novel Framework for Maximizing Information Gain

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

^{n}while preserving the network topology. To enhance the topological embedding, we introduce additional dimensions (R

^{m}) to account for segment-specific features such as AADT, functional class, and the number of lanes. This dimensional augmentation results in a joint vector space (R

^{(n+m)}), highlighted by the shaded blue box in Figure 1. As a result, the inherent distance metric between two nodes (or segments) in this joint vector space incorporates both their topological relationship and segment attributes.

#### 2.1. Graph Representation of Highway Network

#### 2.2. Topological Embedding of Graphs

#### 2.3. Construction of Joint Vector Space

#### 2.4. Kernel Density Estimation

#### 2.5. Optimization Problem Formulation

#### 2.6. Solution Algorithm

#### 2.6.1. Physics-Guided Random Walk

#### 2.6.2. Genetic Algorithm

Algorithm 1. Pseudocode of GA with penalty trick. |

1: Initialize population P with size ${N}_{p}$ |

2: For generation $i=1$ to ${N}_{g}$: |

3: For $j=1$ to ${N}_{p}$: |

4: If (the number of “1” gene in individual ${x}_{j}$) ! = (the desired number of sensors): |

5: assign a low fitness score (e.g., 0.00001) to individual ${x}_{j}$. |

6: Else: compute the fitness score for individual ${x}_{j}$. |

7: End for |

8: Select the best m individuals in the population P and save them as population, ${P}_{1}$ |

9: //crossover operation// |

10: For $j=1$to $\left({N}_{p}-m\right)$: |

11: randomly select two individuals ${x}_{a}$ and ${x}_{b}$ from population P |

12: generate ${x}_{a}^{\prime}$ and ${x}_{b}^{\prime}$ by crossover. |

13: save ${x}_{a}^{\prime}$ and ${x}_{b}^{\prime}$ to population ${P}_{2}$ |

14: End for |

15: //mutation operation// |

16: For $j=1$to $\left({N}_{p}-m\right)$: |

17: select an individual ${x}_{j}$ from ${P}_{2}$ |

18: apply mutation to obtain individual ${x}_{j}^{\prime \prime}$ |

19: replace ${x}_{j}$ with ${x}_{j}^{\prime \prime}$ in ${P}_{2}$ |

20: End for |

21: update population ${P=P}_{1}+{P}_{2}$ |

22: End for |

23: Return the best individual, ${x}_{best}$ in population P |

## 3. Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The KDE of the Savannah highway network on 3D UMAP embeddings: (

**a**) bandwidth 0.4, (

**b**) bandwidth 0.2, (

**c**) bandwidth 0.1, (

**d**) bandwidth 0.05.

**Figure 9.**Visualization of GA results. (Note: orange segments denote the reduced search space by the PGRW, green triangles denote the existing sensor locations, blue circles indicate the locations selected by the GA method, and red dots are the locations from the ES method).

Parameter | Value | Description |
---|---|---|

${l}_{wl}$ | 30 | Walk length, i.e., the number of nodes in each walk |

${N}_{nw}$ | 200 | Number of walks per node |

$p$ | 1 | The likelihood of backtracking the walk and immediately revisiting a node in the random walk |

$q$ | 1 | The In-Out parameter q allows the traversal calculation to differentiate between inward and outward nodes |

${d}_{dim}$ | 8 | The output Node2Vec embeddings dimension |

Parameter | Value |
---|---|

Number of generations | 100 |

Number of parents mating | 30 |

Population size | 100 |

Gene space | [0, 1] |

Parent selection | roulette wheel |

Crossover | single point |

Mutation | random |

Mutation percent for genes | 5 |

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**MDPI and ACS Style**

Yang, Y.; Yang, J.J.
Strategic Sensor Placement in Expansive Highway Networks: A Novel Framework for Maximizing Information Gain. *Systems* **2023**, *11*, 577.
https://doi.org/10.3390/systems11120577

**AMA Style**

Yang Y, Yang JJ.
Strategic Sensor Placement in Expansive Highway Networks: A Novel Framework for Maximizing Information Gain. *Systems*. 2023; 11(12):577.
https://doi.org/10.3390/systems11120577

**Chicago/Turabian Style**

Yang, Yunxiang, and Jidong J. Yang.
2023. "Strategic Sensor Placement in Expansive Highway Networks: A Novel Framework for Maximizing Information Gain" *Systems* 11, no. 12: 577.
https://doi.org/10.3390/systems11120577