# Research on Multiple AUVs Task Allocation with Energy Constraints in Underwater Search Environment

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Mutiple AUVs Task Allocation Problem

#### 2.2. Task Allocation Algorithms

#### 2.3. SCIP Solver

## 3. Methodology

#### 3.1. Problem Formulation and Modeling

#### 3.2. Algorithms and Frameworks

- Input Parameters

- $X={\left\{{x}_{i}\right\}}_{i=0}^{n}$: Set of task nodes, where ${x}_{0}$ is the starting point, and the remaining nodes are target points.
- $V={\left\{{v}_{i}\right\}}_{i=1}^{m}$: Set of AUVs.
- ${P}_{u}\left[j\right]$: Energy required to complete task j.
- ${A}_{u}\left[v\right]$: Energy capacity of AUV v.
- $dist[i,j]$: Distance between node i and node j.
- $MaxPathLength\left[v\right]$: Maximum path length for AUV v.

- Output

#### Algorithm Steps

**Initialize Remaining Energy**: Initialize the remaining energy variable for all AUVs.**Calculate Node Distances**: Calculate the Euclidean distance between each pair of nodes and compute the energy required to reach each target point based on the energy consumption model.**Set Constraints**:**No Immediate Return Constraint**: Ensure that an AUV does not immediately return to the same node after completing a task.**One AUV per Task Constraint**: Ensure that each target point is serviced by exactly one AUV.**Path Continuity Constraint**: Ensure path continuity for each AUV between consecutive nodes.**Energy Limit Constraint**: Ensure that the total energy consumed by each AUV does not exceed its energy capacity after completing all assigned tasks.**Path Length Limit Constraint**: Ensure that the total travel distance for each AUV does not exceed its maximum path length.

**Optimize Solution**: Call the optimizer to solve the above constraint model and obtain the optimal path for each AUV.

Algorithm 1: SCIP-based MRTA-CVRP algorithm |

#### 3.3. Analysis of the Optimality and Existence of Solutions

#### 3.3.1. Optimality of Solutions

#### 3.3.2. Existence of Solutions

## 4. Results and Discussion

#### 4.1. Simulation Setup and Results

#### 4.2. Comparative Analysis of Our Algorithm and PSO Algorithm

#### 4.2.1. Introduction to PSO Algorithm

#### 4.2.2. Performance Comparison

#### 4.2.3. Computational Time Comparison

#### 4.2.4. Machine Configuration

#### 4.2.5. Summary

#### 4.3. Practical Implications

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AUV | Autonomous Underwater Vehicle |

CVRP | Capacitated Vehicle Routing Problem |

SCIP | Solving Constraint Integer Programs |

MRTA | Multiple Robots Task Allocation |

MILP | Mixed-Integer Linear Programs |

CIP | Constraint Integer Programming |

PSO | Particle Swarm Optimization |

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

SCIP Status | problem is solved [optimal solution found] |

Solving Time (s) | 1.00 |

Solving Nodes | 1 (total of 2 nodes in 2 runs) |

Primal Bound | +9.68047032967033 × 10^{3} (6 solutions) |

Dual Bound | +9.68047032967033 × 10^{3} |

Gap | 0.00% |

Objective value | 9680.47032967033 |

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

SCIP Status | problem is solved [infeasible] |

Solving Time (s) | 0.00 |

Solving Nodes | 0 |

Primal Bound | +1.00000000000000 × 10^{20} (0 solutions) |

Dual Bound | +1.00000000000000 × 10^{20} |

Gap | 0.00% |

Objective value | infeasible |

Experiment No. | a | b | c | d | e | f |
---|---|---|---|---|---|---|

SCIP Solver (s) | 10,040.6 | 11,220.9 | 9680.5 | 0 | 22,480.7 | 21,783.9 |

PSO (s) | 12,007.5 | 11,258.8 | 10,308.7 | inf | 24,776.6 | 26,993.1 |

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

Processor | Core i7-10750H @ 2.60 GHz |

Memory | 16 GB RAM |

Operating System | Windows 10 64-bit |

Solver Version | 8.0.4 |

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## Share and Cite

**MDPI and ACS Style**

Wang, H.; Li, Y.; Li, S.; Xu, G.
Research on Multiple AUVs Task Allocation with Energy Constraints in Underwater Search Environment. *Electronics* **2024**, *13*, 3852.
https://doi.org/10.3390/electronics13193852

**AMA Style**

Wang H, Li Y, Li S, Xu G.
Research on Multiple AUVs Task Allocation with Energy Constraints in Underwater Search Environment. *Electronics*. 2024; 13(19):3852.
https://doi.org/10.3390/electronics13193852

**Chicago/Turabian Style**

Wang, Hailin, Yiping Li, Shuo Li, and Gaopeng Xu.
2024. "Research on Multiple AUVs Task Allocation with Energy Constraints in Underwater Search Environment" *Electronics* 13, no. 19: 3852.
https://doi.org/10.3390/electronics13193852