# Emerging Inter-Swarm Collaboration for Surveillance Using Pheromones and Evolutionary Techniques

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## Abstract

**:**

## 1. Introduction

- A new mobility model (ABISS) is designed to be used by unmanned vehicle swarms as a cooperation strategy for mutual inter-swarm collaboration.
- An Evolutionary Algorithm (EA) is specially designed and tuned for optimising the ABISS’ parameters to maximise the coverage of the area under surveillance.

## 2. Related Work

## 3. Attractor Based Inter-Swarm CollaborationS (ABISS)

#### 3.1. Intra-Swarm Mobility

Algorithm 1 Pseudocode of CACOC. |

procedure CACOC$currentstate\leftarrow $“ahead” loop$\rho \leftarrow \mathit{next}\mathit{value}\mathit{in}\mathit{first}\mathit{return}\mathit{map}$ if $\mathit{no}$ then$currentstate\leftarrow CROMM$ elseif $\rho <{P}_{R}$ then$currentstate\leftarrow $“right” else if $\rho <{P}_{R}+{P}_{L}$ then$currentstate\leftarrow $“left” else$currentstate\leftarrow $“ahead” end if$\mathit{move}\mathit{according}\mathit{to}\mathit{the}currentstate$ end ifend loopend procedure |

#### 3.2. Inter-Swarm Mobility

#### 3.3. Model Parameters

## 4. Problem Description

#### 4.1. Objective

#### 4.2. Instances

#### 4.3. Parameter Sensitivity Analysis

## 5. Optimisation Approach

#### 5.1. Evolutionary Algorithm (EA)

Algorithm 2 Pseudocode of the Evolutionary Algorithm (EA). |

procedure EA(${N}_{i},{P}_{c},{P}_{m}$)$t\leftarrow \varnothing $ $Q\left(0\right)\leftarrow \varnothing $ ▹ Q = auxiliary population $P\left(0\right)\leftarrow Initialisation\left({N}_{i}\right)$ ▹ P=population while $\mathit{not}TerminationCondition\left(\right)$ do$Q\left(t\right)\leftarrow Selection\left(P\right(t\left)\right)$ $Q\left(t\right)\leftarrow Crossover(Q\left(t\right),{P}_{c})$ $Q\left(t\right)\leftarrow Mutation(Q\left(t\right),{P}_{m})$ $Evaluation\left(Q\right(t\left)\right)$ $P(t+1)\leftarrow Replacement\left(Q\right(t),P(t\left)\right)$ $t\leftarrow t+1$ end whileend procedure |

#### 5.1.1. Crossover Operator

Algorithm 3 Pseudocode of the crossover operator. |

function Crossover($Q,{P}_{c}$)${Q}^{\prime}\leftarrow \varnothing $ for all $\{\overrightarrow{x},\overrightarrow{y}\}\in Q$ do ▹ all the individuals in Q, taken in pairs${\overrightarrow{x}}^{\prime}=\overrightarrow{x}$ ${\overrightarrow{y}}^{\prime}=\overrightarrow{y}$ if $rnd\left(\right)<{P}_{c}$ then ▹ crossover probability$p\leftarrow randInt(1,L)$ ▹ crossing point p, L is the length of the solution vector for $i\leftarrow p,L$ do ▹i goes from p to Lif $is\_an\_int\_parameter\left(i\right)$then ▹ type of the i-th parameter${\overrightarrow{x}}^{\prime}\left[i\right]=\overrightarrow{y}\left[i\right]$ ${\overrightarrow{y}}^{\prime}\left[i\right]=\overrightarrow{x}\left[i\right]$ else$M\leftarrow randInt(1,10)$ ${\Delta}_{x}\leftarrow \overrightarrow{x}\left[i\right]/M$ ${\Delta}_{y}\leftarrow \overrightarrow{y}\left[i\right]/M$ ${\overrightarrow{x}}^{\prime}\left[i\right]=\overrightarrow{x}\left[i\right]+{\Delta}_{y}-{\Delta}_{x}$ ${\overrightarrow{y}}^{\prime}\left[i\right]=\overrightarrow{y}\left[i\right]-{\Delta}_{y}+{\Delta}_{x}$ end ifend forend if${Q}^{\prime}\leftarrow {Q}^{\prime}\cup \{{\overrightarrow{x}}^{\prime},{\overrightarrow{y}}^{\prime}\}$ end forreturn ${Q}^{\prime}$end function |

#### 5.1.2. Mutation Operator

Algorithm 4 Pseudocode of the mutation operator. |

function Mutation($Q,{P}_{m}$)${Q}^{\prime}\leftarrow \varnothing $ for all $\left\{\overrightarrow{x}\right\}\in Q$do ▹ all the individuals in Q${\overrightarrow{x}}^{\prime}\leftarrow \overrightarrow{x}$ for $i\leftarrow 1,L$ do ▹i goes from 1 to L (the length of the solution vector)if $rnd\left(\right)<{P}_{m}$ then ▹ mutation probability$M\leftarrow randInt(1,10)$ $\Delta \leftarrow getDelta(\overrightarrow{x}\left[i\right],M)$ if $rnd\left(\right)<0.5$ then ▹ increment/decrement$\Delta =-1\ast \Delta $ end if${\overrightarrow{x}}^{\prime}\left[i\right]\leftarrow \overrightarrow{x}\left[i\right]+\Delta $ end ifend for${Q}^{\prime}\leftarrow {Q}^{\prime}\cup \left\{{\overrightarrow{x}}^{\prime}\right\}$ end forreturn ${Q}^{\prime}$end function |

#### 5.2. EA Parameter Optimisation

## 6. Experimental Results

#### 6.1. Random Search (RS)

Algorithm 5 Pseudocode of Random Search (RS). |

procedure RS$best\leftarrow Initialisation\left(\right)$ while $\mathit{not}TerminationCondition\left(\right)$ do$next\leftarrow getRandomConfiguration\left(\right)$ ▹ 4 or 8 parameters depending on the case study if $F\left(next\right)>F\left(best\right)$ then$best\leftarrow next$ ▹ The $best$ configuration found so far, is updated end ifend whileend procedure |

#### 6.2. Coverage Optimisation

#### 6.3. Testing the Best Configuration

#### 6.4. ABISS vs. CACOC

_{0}, which is the initial mobility model presented in [29], not using the parameterisation proposed in our study. CACOC

_{0}uses fixed parameters by design, i.e., ${\tau}_{d}=1.0$, ${\tau}_{r}=0$, ${\tau}_{a}=0$ and ${\tau}_{m}=2$.

_{0}since in the former the vehicles were customised to each case study. Moreover, ABISS improved both coverage metrics (Total area and UZ) for almost all case studies. In 100x100.6z3, as mentioned above, the best result is achieved when not using collaboration between vehicles. We include the second best configuration, marked by asterisks, to show that the total coverage is only 0.1% lower when using collaborations. Note that this is not the best solution found by EA, hence the asterisks.

## 7. Conclusions

_{0}, which cannot be parameterised, the improvements in the coverage are even higher (17.6% on average and 65.8% in UZs).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Attractor Based Inter-Swarm collaborationS (ABISS). In this example, a UAV swarm explores a water surface that UGVs cannot access.

**Figure 2.**Flow diagram of ABISS using attractors, chaotic solutions and pheromones. The parameters affecting each operation are listed next to them.

**Figure 3.**Parameters of ABISS. The UAV has to decide whether to go to explore the water surface where the UGV has left an attractor because it could not enter.

**Figure 4.**Case studies without (

**a**) and with square unreachable zones (

**b**–

**d**). In these examples, there are four vehicles placed at their starting position in the centre of the map.

**Figure 5.**Parameter sensitivity study ($\sigma $ and ${\mu}^{\u2605}$) for the model using four and eight parameters to modify the behaviour and performance of ABISS.

**Figure 7.**Frequency of the tests performed during the irace run for: the number of individuals (

**a**); crossover probability (

**b**); and mutation probability (

**c**).

**Figure 8.**Box plots showing the distribution of values (30 runs) of EA and RS after optimising the proposed 12 case studies. As we are maximising area coverage, the higher the better.

Probability of Action: | Left | Ahead | Right |
---|---|---|---|

${P}_{L}=\frac{total-left}{2\times total}$ | ${P}_{A}=\frac{total-ahead}{2\times total}$ | ${P}_{R}=\frac{total-right}{2\times total}$ |

Parameter | Symbol | Type | Units | Range |
---|---|---|---|---|

Intra-Swarm | ||||

Pheromone decay | ${\tau}_{d}$ | real | % | [0.01–0.20] |

Pheromone radius | ${\tau}_{r}$ | integer | cells | [0–2] |

Pheromone scan angle | ${\tau}_{a}$ | real | radians | [0.00–$\frac{\pi}{4}]$ |

Pheromone scan depth | ${\tau}_{m}$ | integer | cells | [1–10] |

Inter-Swarm | ||||

Collaboration probability | ${\pi}_{c}$ | real | – | [0.00–1.00] |

Attractor scan angle | ${\alpha}_{a}$ | real | radians | [0.00–$\frac{\pi}{4}]$ |

Attractor scan depth | ${\alpha}_{m}$ | integer | cells | [1–20] |

Pheromone in unreachable area | ${\tau}_{u}$ | real | % | [0.00–1.00] |

Case Study | Size | # UZ | # UAV | # UGV |
---|---|---|---|---|

50x50.2 | 50 × 50 | 0 | 1 | 1 |

50x50.4 | 50 × 50 | 0 | 2 | 2 |

100x100.4 | 100 × 100 | 0 | 2 | 2 |

100x100.6 | 100 × 100 | 0 | 4 | 2 |

50x50.2z1 | 50 × 50 | 2 (15 × 15) | 1 | 1 |

50x50.4z1 | 50 × 50 | 2 (15 × 15) | 2 | 2 |

100x100.4z1 | 100 × 100 | 2 (30 × 30) | 2 | 2 |

100x100.4z2 | 100 × 100 | 2 (30 × 30) | 2 | 2 |

100x100.4z3 | 100 × 100 | 2 (30 × 30) | 2 | 2 |

100x100.6z1 | 100 × 100 | 2 (30 × 30) | 4 | 2 |

100x100.6z2 | 100 × 100 | 2 (30 × 30) | 4 | 2 |

100x100.6z3 | 100 × 100 | 2 (30 × 30) | 4 | 2 |

Ranking | # Individuals | P_{c} | P_{m} | Mean Fitness |
---|---|---|---|---|

1st | 20 | 0.92 | 0.22 | 0.8020 |

2nd | 10 | 0.10 | 0.37 | 0.7994 |

3rd | 10 | 0.11 | 0.36 | 0.7984 |

**Table 5.**Results of the optimisation process performed by EA and RS and the Wilcoxon p-value of each statistical test. We report the fitness values obtained from 30 runs of each algorithm on the 12 case studies (four without UZs and eight having two UZs) comprising 30 instances (scenarios) each (720 optimisation runs in total). Best fitness values are in bold.

Case Study | Fitness Values (30 runs) | Wilcoxon p-Value | |||||
---|---|---|---|---|---|---|---|

RS | EA | ||||||

Mean | StDev | Max | Mean | StDev | Max | ||

50x50.2 | 0.844 | 2.80 × 10${}^{-3}$ | 0.847 | 0.851 | 0.00 × 10${}^{0}$ | 0.851 | 0.000 |

50x50.4 | 0.944 | 1.43 × 10${}^{-3}$ | 0.947 | 0.947 | 0.00 × 10${}^{0}$ | 0.947 | 0.000 |

100x100.4 | 0.607 | 5.24 × 10${}^{-3}$ | 0.613 | 0.635 | 0.00 × 10${}^{0}$ | 0.635 | 0.000 |

100x100.6 | 0.755 | 7.08 × 10${}^{-3}$ | 0.766 | 0.775 | 2.64 × 10${}^{-4}$ | 0.775 | 0.000 |

50x50.2z1 | 0.822 | 5.01 × 10${}^{-3}$ | 0.829 | 0.840 | 2.80 × 10${}^{-3}$ | 0.846 | 0.000 |

50x50.4z1 | 0.931 | 2.41 × 10${}^{-3}$ | 0.936 | 0.941 | 1.14 × 10${}^{-3}$ | 0.944 | 0.000 |

100x100.4z1 | 0.607 | 3.65 × 10${}^{-3}$ | 0.619 | 0.622 | 3.12 × 10${}^{-3}$ | 0.629 | 0.000 |

100x100.4z2 | 0.599 | 3.69 × 10${}^{-3}$ | 0.606 | 0.619 | 3.54 × 10${}^{-3}$ | 0.629 | 0.000 |

100x100.4z3 | 0.596 | 4.09 × 10${}^{-3}$ | 0.605 | 0.612 | 2.22 × 10${}^{-3}$ | 0.618 | 0.000 |

100x100.6z1 | 0.742 | 4.43 × 10${}^{-3}$ | 0.756 | 0.757 | 2.55 × 10${}^{-3}$ | 0.761 | 0.000 |

100x100.6z2 | 0.739 | 5.87 × 10${}^{-3}$ | 0.750 | 0.758 | 2.95 × 10${}^{-3}$ | 0.764 | 0.000 |

100x100.6z3 | 0.732 | 5.41 × 10${}^{-3}$ | 0.745 | 0.748 | 3.40 × 10${}^{-3}$ | 0.754 | 0.000 |

**Table 6.**Best configuration for each case study (parameters) followed by the mean, standard deviation and best coverage obtained when testing them in the 30 corresponding scenarios.

Case Study | ${\mathit{\tau}}_{\mathit{d}}$ | ${\mathit{\tau}}_{\mathit{r}}$ | ${\mathit{\tau}}_{\mathit{a}}$ | ${\mathit{\tau}}_{\mathit{m}}$ | ${\mathit{\pi}}_{\mathit{c}}$ | ${\mathit{\alpha}}_{\mathit{a}}$ | ${\mathit{\alpha}}_{\mathit{m}}$ | ${\mathit{\tau}}_{\mathit{u}}$ | Coverage (%) | ||
---|---|---|---|---|---|---|---|---|---|---|---|

Mean | StDev | Best | |||||||||

50x50.2 | 0.01 | 2 | 0.26 | 5 | – | – | – | – | 85.1 | 2.8 | 90.3 |

50x50.4 | 0.01 | 2 | 0.23 | 4 | – | – | – | – | 94.7 | 0.8 | 95.7 |

100x100.4 | 0.01 | 2 | 0.22 | 8 | – | – | – | – | 63.5 | 3.1 | 69.2 |

100x100.6 | 0.01 | 2 | 0.38 | 7 | – | – | – | – | 77.5 | 2.9 | 82.0 |

50x50.2z1 | 0.01 | 2 | 0.36 | 4 | 0.21 | 0.08 | 18 | 0.59 | 84.6 | 4.2 | 89.8 |

50x50.4z1 | 0.01 | 2 | 0.15 | 4 | 0.35 | 0.06 | 18 | 0.67 | 94.4 | 1.0 | 95.6 |

100x100.4z1 | 0.01 | 2 | 0.15 | 10 | 0.22 | 0.19 | 7 | 0.88 | 62.9 | 2.6 | 67.8 |

100x100.4z2 | 0.01 | 2 | 0.34 | 8 | 0.24 | 0.03 | 7 | 0.76 | 62.9 | 2.7 | 67.1 |

100x100.4z3 | 0.01 | 2 | 0.32 | 6 | 0.55 | 0.17 | 11 | 0.75 | 61.8 | 3.4 | 67.4 |

100x100.6z1 | 0.01 | 2 | 0.35 | 6 | 0.35 | 0.28 | 7 | 0.26 | 76.1 | 3.2 | 80.7 |

100x100.6z2 | 0.01 | 2 | 0.35 | 7 | 0.33 | 0.36 | 3 | 0.79 | 76.4 | 2.7 | 83.1 |

100x100.6z3 | 0.01 | 1 | 0.37 | 7 | 0.00 | 0.06 | 16 | 0.82 | 75.4 | 2.6 | 80.6 |

**Table 7.**Comparison between the coverage values obtained by the non-collaborative approaches (CACOC

_{0}and CACOC) and ABISS in case studies having unreachable zones (mean of 30 scenarios). The improvements achieved by ABISS with respect to CACOC

_{0}and CACOC are also reported. The second best configuration values are indicated by asterisks. The best results are in bold.

Case Study | Coverages (%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

CACOC_{0} | CACOC | ABISS | ||||||||

Total | UZ | Total | UZ | Total | Improvement vs. | UZ | Improvement vs. | |||

CACOC_{0} | CACOC | CACOC_{0} | CACOC | |||||||

50x50.2z1 | 76.4 | 50.5 | 80.4 | 58.1 | 84.6 | +10.7% | + 5.2% | 70.1 | +38.8% | + 20.7% |

50x50.4z1 | 89.9 | 70.9 | 93.0 | 83.9 | 94.4 | + 5.0% | + 1.5% | 88.8 | +25.2% | +5.8% |

100x100.4z1 | 51.2 | 12.9 | 59.8 | 36.6 | 62.9 | + 22.9% | + 5.2% | 39.6 | + 207.0% | + 8.2% |

100x100.4z2 | 47.8 | 38.3 | 56.6 | 57.2 | 62.9 | + 31.6% | + 11.1% | 67.1 | + 75.2% | + 17.3% |

100x100.4z3 | 50.4 | 24.6 | 57.2 | 36.7 | 61.8 | + 22.6% | + 8.0% | 51.5 | + 109.3% | + 40.3% |

100x100.6z1 | 64.0 | 25.7 | 71.9 | 41.0 | 76.1 | + 18.9% | + 5.8% | 55.4 | + 115.6% | + 35.1% |

100x100.6z2 | 62.2 | 48.5 | 70.1 | 71.8 | 76.4 | + 22.8% | + 9.0% | 77.3 | + 59.4% | + 7.7% |

100x100.6z3 | 63.7 | 39.6 | 75.4 | 67.4 | * 75.3 | + 18.2% | −0.1% | * 65.8 | + 66.2% | −2.4% |

Mean: | 63.2 | 38.9 | 70.6 | 56.6 | 74.3 | 17.6% | 5.3% | 64.5 | 65.8% | 13.9% |

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## Share and Cite

**MDPI and ACS Style**

Stolfi, D.H.; Brust, M.R.; Danoy, G.; Bouvry, P.
Emerging Inter-Swarm Collaboration for Surveillance Using Pheromones and Evolutionary Techniques. *Sensors* **2020**, *20*, 2566.
https://doi.org/10.3390/s20092566

**AMA Style**

Stolfi DH, Brust MR, Danoy G, Bouvry P.
Emerging Inter-Swarm Collaboration for Surveillance Using Pheromones and Evolutionary Techniques. *Sensors*. 2020; 20(9):2566.
https://doi.org/10.3390/s20092566

**Chicago/Turabian Style**

Stolfi, Daniel H., Matthias R. Brust, Grégoire Danoy, and Pascal Bouvry.
2020. "Emerging Inter-Swarm Collaboration for Surveillance Using Pheromones and Evolutionary Techniques" *Sensors* 20, no. 9: 2566.
https://doi.org/10.3390/s20092566