# Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs)

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## Abstract

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## 1. Introduction

#### 1.1. Problem Statement

#### 1.2. Our Contribution

## 2. Related Works

#### 2.1. Data Dissemination Algorithms in VANETs

#### 2.2. Probabilistic Data Dissemination Algorithms for VANETs Based on Distance

**p**is the retransmission probability of the receiver to retransmit an incoming message,

**R**is the vehicles’ wireless communication range and

**d**is the relative Euclidean distance between two vehicles

_{ik}**i**and

**k**. A simple evolution of p-persistence scheme is the polynomial scheme [22], which uses an exponent

**b**to calculate the retransmission probability according to the following equation:

**i**and

**k**, and

**v**is a tuning parameter to adjust the retransmission probability. The value of ${\mathit{F}}_{{\mathit{x}}_{\mathit{i}\mathit{j}}}$ depends on the spatial distribution of the vehicles in the VANET. In ref. [18], the authors demonstrate that exponential and lognormal distributions are likely to be found in VANET scenarios. In the case of the exponential distribution, the retransmission probability can be determined as follows:

**v**the mentioned adjusting parameter. Other data dissemination schemes based on the irresponsible forwarding scheme can be found in [19,23]. In ref. [19], the authors modified the expression (4) to reflect that vehicles may have different wireless communication ranges. The resulting expression is:

**R**is the wireless communication range of the

_{i}**i**th receiving vehicle and the ratio

**R**/

**R**represents the differences in the vehicles’ wireless communication areas.

_{i}## 3. Dissimilarity Metrics Based on Neighboring Information

**i**and

**k**vehicles (sender and receiver or vice-versa), if m is placed inside the wireless communication ranges of

**i**and

**k**(see Figure 1). It is worth indicating that the probability of a neighbor vehicle

**m**of being within the overlapping area (IA in Figure 1) of both vehicles

**i**and

**k**depends on the Euclidean distance

**d**between both vehicles and the density of vehicles in the VANET. In general, the size of IA decreases with the relative distance between two vehicles. Consequently, it is more probable to find more vehicles in the IA for a given VANET scenario. In addition, the dissimilarity between two vehicles can be defined as the contrary of the similarity. Notice that these definitions of similarity and dissimilarity between vehicles are also valid in case that the wireless communication range of vehicles is not an ideal circle as represented in Figure 1. Therefore, it is an important feature of the use of dissimilarity metrics, since they do not rely on wireless technology parameters or ideal circumstances. Consequently, they will adapt their performance to the real conditions in terms of connectivity among vehicles.

**a**accounts for the number of neighbor vehicles shared by the vehicles

_{ik}**i**and

**k**, the term

**a**determines the number of neighbor vehicles of the vehicle

_{i}**i**that are not neighbors of the vehicle

**k**, and

**a**is the number of neighbor vehicles of the vehicle

_{k}**k**that are not neighbors of the vehicle

**i**. With respect to Figure 1,

**a**is the number of vehicles placed within the region IA,

_{ik}**a**is the number of vehicles inside the I vehicle’ communication range (I in Figure 1), and

_{i}**a**is the number of vehicles within the region

_{k}**K**.

#### 3.1. Definition of Classical Dissimilarity Metrics

**λ**in (6) several classical similarity/dissimilarity metrics can be obtained. In addition, it is essential to notice that the relation between a similarity metric S and its equivalent dissimilarity metric DM is DM = 1 – S if S ∈ [0, 1].

**Jac**and distance

**Jacd**between two vehicles

**i**and

**k**can be formulated as:

**Dic**and distance

**Dicd**between two vehicles

**i**and

**k**can be expressed as:

**Kul**and distance

**Kuld**between two vehicles i and k can be formulated as:

**Fow**and distance

**Fowd**between two vehicles

**i**and

**k**can be expressed as:

**Sok**and dissimilarity

**Sokd**can be determined as:

#### 3.2. New Dissimilarity Metrics

## 4. Genetic Programming

**b**(see Equation (2)) for a given scenario. However, the exponential relation between the Euclidean distance between two vehicles and the retransmission probability may not be the best one for the considered scenario. Then, we may run a GP algorithm to find the best relation between the Euclidean distance and retransmission probability (exponential, logarithmic, etc.). Therefore, when using a GP approach, we do not seek for the optimal values of certain variables or tuning parameters; we search for their optimal relation instead. In our case, the objective of the GP is to determine the optimal combination among the aforementioned terms

**a**,

_{i}**a**, and

_{k}**a**.

_{ik}Algorithm 1. Genetic programming. |

1: Objective function = PCC(M, D) |

2: Encode the solution into a tree (string) |

3: Generate the initial population |

4: Set crossover (pc) and mutation (pm) probabilities |

5: While (t < Max. of generations) |

6: Parents selection |

7: Crossover with pc |

8: Mutation with pm |

9: Evaluate offspring |

10: Update t = t + 1 |

11: End While |

12: Decode the results and visualization |

#### 4.1. Representation of the Solutions

**a**terms described in Section 3 and the red nodes determine the relationships among

**a**terms. In this paper, the primitive set of operations is composed of {summation, subtraction, multiplication, safe division, safe root square, safe logarithm}. Safe operators avoid the singularities of division by zero and root square and logarithm of a negative number. Furthermore, the depth of the tree and the number of operations is limited for computational reasons. Otherwise, the GP would converge to a solution impossible to implement (see Section 5 for more details).

#### 4.2. Fitness Function

**X**and

**Y**is calculated as:

**cov**(

**X**,

**Y**) is the covariance between

**X**and

**Y**, and

**σ**is the standard deviation. In this paper, the fitness function is obtained by averaging out the absolute value of

**PCC**(

**M**,

**D**) in several representative VANET scenarios obtained by varying the density of nodes (more details in Section 5).

**M**represents the sample of dissimilarity values between each pair of neighbor nodes for a given new metric $\mathit{m}=\mathit{f}\left({\mathit{a}}_{\mathit{i}\mathit{k}},{\mathit{a}}_{\mathit{i}},{\mathit{a}}_{\mathit{k}}\right)$, and

**D**is the sample of the Euclidean distances among each pair of neighbor nodes. Two vehicles are neighbors if they are within the wireless communication range of each other, so

**d**<

**R**. Therefore, the fitness function of the GP implementation is:

**n**is the number of VANET scenarios. Thus, the optimization problem is defined as:

#### 4.3. Genetic Operators

_{c}and p

_{m}in Algorithm 1) and along with the selection mechanism, they determine the exploration and exploitation power of the optimization GP algorithm. Since there is no consensus in the literature regarding the optimal values of p

_{c}and p

_{m}, several values have been tested in Section 5.

#### 4.4. Stopping Criterion and Time Complexity

**I**. The number of simulations required to obtain a suitable solution is

**G**×

**I**. Appropriated values should be selected in order to achieve suitable solutions in a reasonable time. Further details about the selected values are given in the next section.

## 5. Simulation Results

**p**used is within the interval [0.6, 0.8] with a step of 0.1. The p

_{c}_{m}tested is within the interval [0.05, 0.2] with a step of 0.5. Therefore, 12 different parameter settings of the GP have been evaluated. The limit of operations among the a terms is 100.Both the depth of the trees and the number of operations reduces the algorithmic complexity of the proposed approach. Higher values of both terms will lead to solutions very difficult to implement in real-life scenarios. The number of generations is 100 and each setting is evaluated with 10 different seeds of random numbers. Regarding the VANET scenarios, they are based on real maps using C4R tool [34]. The density of vehicles varies within the interval [100, 200] in steps of 10. The VANET scenario is based on a real map of the city of Seville in Spain, which is shown in Figure 3. The size of the scenario is 2 km × 2 km. The vehicle’s communication range

**R**is 250 m and the unit disk model is used. To measure the correlation, we consider that the vehicles are static during the simulation. Notice that this assumption will not affect the correlation results between the Euclidean distance and the obtained dissimilarity metric in real mobile scenarios.

#### 5.1. Correlation Results

#### 5.2. Data Dissemination Results

Algorithm 2. P-persistence algorithm based on dissimilarity metric. |

1: Whenever a message g is received |

1: If g is new: |

3: Retrieve neighboring list from g |

4: Calculate a, _{ik}a, _{i}a_{k} |

5: Calculate p as $p=D{M}_{ik}$ |

6: If p ≥ Rand [0,1] |

7: Include neighboring list in g |

8: Rebroadcast g |

9: Else: |

10: Eliminate g |

11: End if |

12: Else: |

13: Eliminate g |

12: End if |

**Re**than in the cases that used classical dissimilarity metrics and the Euclidean distance. The percentage of improvement with respect to the best classical dissimilarity metric (Sokal-Sneath) is within the interval [0.7, 6]. In addition, the obtained new metric clearly outperforms the results of the Euclidean based p-persistence. Regarding redundancy, the proposed approach outperforms flooding and it is closed to Sokal-Sneth metric.

**b**is 2 since higher values of

**b**have been already tested, showing low performances [30]. Figure 8 shows the obtained simulation results in terms of

**Re**. It can be observed that the majority of classical dissimilarity metrics do not work well when used in polynomial scheme. However, the new dissimilarity metric suits quite well when applied to polynomial scheme. However, it requires a higher number of messages to obtain a suitable Re (see Figure 9).

Algorithm 3. Polynomial algorithm based on dissimilarity metric. |

1: Whenever a message g is received |

1: If g is new: |

3: Retrieve neighboring list from g |

4: Calculate a, _{ik}a, _{i}a_{k} |

5: Calculate p as $p={(D{M}_{ik})}^{b}$ |

6: If p ≥ Rand [0,1] |

7: Include neighboring list in g |

8: Rebroadcast g |

9: Else: |

10: Eliminate g |

11: End if |

12: Else: |

13: Eliminate g |

12: End if |

**v**, it has been fixed to 20, which has already been demonstrated to provide good results in terms of reachability [30]. Notice that the most optimal configuration of polynomial and irresponsible schemes is out of the scope of the paper. Figure 10 includes the obtained simulation results for irresponsible scheme in terms of

**Re**, which again validate the obtained dissimilarity metric. Figure 11 contains the obtained results in terms of number of redundant messages. The proposed approach outperforms flooding, but it requires a higher number of messages compared with classical dissimilarity metrics.

Algorithm 4. Irresponsible algorithm based on dissimilarity metric. |

1: Whenever a message g is received |

2: If g is new: |

3: Retrieve neighboring list from g |

4: Calculate a, _{ik}a, _{i}a_{k} |

5: Calculate p as $p=\mathrm{exp}\left(-\frac{{n}_{b}\left(1-(D{M}_{ik}\right)}{v}\right)$ |

6: If p ≥ Rand [0,1] |

7: Include neighboring list in g |

8: Rebroadcast g |

9: Else: |

10: Eliminate g |

11: End if |

12: Else: |

13: Eliminate g |

12: End if |

#### 5.3. Future Work

- Combine the proposed approach with online approaches based on learning policies like [35]. The idea is to reduce the number of messages exchanged among nodes by updating the hyper-parameters of learning models.
- Evaluate the proposed approach under different wireless and sensor technologies for VANETs, such as IEEE 802.11p, IEEE 802.11ax, and IEEE 802.15.4, among others.
- Since in majority of cases the proposed approach outperforms the other algorithms in terms of
**Re**, but with an increase of redundancy, we plan to extend the work by considering a multi-objective genetic programming approach [40]. Therefore, both reachability and redundancy can be balanced.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**An illustration of a shared node between two vehicles. The vehicle in yellow is shared by both

**i**and

**k**vehicles.

**Figure 4.**Best solution obtained by the GP approach,

**a**=

_{0}**a**,

_{ik}**a**=

_{1}**a**, and

_{i}**a**=

_{2}**a**.

_{k}**Figure 6.**Comparison of Reachability results for the p-persistence scheme based on the different dissimilarity metric.

**Figure 7.**Comparison of redundancy results for the p-persistence scheme based on the different dissimilarity metric.

**Figure 8.**Comparison of Reachability results for the polynomial scheme based on the different dissimilarity metric.

**Figure 9.**Comparison of redundancy results for the polynomial scheme based on the different dissimilarity.

**Figure 10.**Comparison of Reachability results for the irresponsible scheme based on the different dissimilarity metric.

**Figure 11.**Comparison of redundancy results for the irresponsible scheme based on the different dissimilarity metric.

Metric | Correlation |
---|---|

Jaccard | 0.661357 |

Dice | 0.622318 |

Kulczynski | 0.616629 |

Fowlkes-Mallows | 0.620337 |

Sokal-Sneath | 0.620337 |

GP Metric (Depth = 4, p_{c} = 0.7, p_{m} = 0.1) | 0.738470 |

GP Metric (Depth = 5, p_{c} = 0.8, p_{m} = 0.15) | 0.741575 |

GP Metric (Depth = 6, p_{c} = 0.8, p_{m} = 0.2) | 0.740777 |

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**MDPI and ACS Style**

Gutiérrez-Reina, D.; Sharma, V.; You, I.; Toral, S.
Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs). *Sensors* **2018**, *18*, 2320.
https://doi.org/10.3390/s18072320

**AMA Style**

Gutiérrez-Reina D, Sharma V, You I, Toral S.
Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs). *Sensors*. 2018; 18(7):2320.
https://doi.org/10.3390/s18072320

**Chicago/Turabian Style**

Gutiérrez-Reina, Daniel, Vishal Sharma, Ilsun You, and Sergio Toral.
2018. "Dissimilarity Metric Based on Local Neighboring Information and Genetic Programming for Data Dissemination in Vehicular Ad Hoc Networks (VANETs)" *Sensors* 18, no. 7: 2320.
https://doi.org/10.3390/s18072320