Multi-Agent Cross-Domain Collaborative Task Allocation Problem Based on Multi-Strategy Improved Dung Beetle Optimization Algorithm
Abstract
:1. Introduction
2. Cross-Domain Collaborative Task Allocation Model
2.1. Problem Description
- There was no redistribution problem in the load agent, and the matching relationship between the load and the target was no longer changed by the control allocation after the target allocation was completed. It was assumed that the target allocation and the control allocation were independent of each other, and the optimal solution of the target allocation was the premise in the control allocation;
- The number of load agents participating in the allocation exceeded the number of target agents or air relay control agents;
- Each load agent was independent of the others, and the corresponding damage probability was calculated in advance without considering its type selection problem;
- The air relay control agent had a unique type. In order to ensure the safety and reliability of the communication between it and the load agent, an attitude change was not allowed, and the flight was always level. In the calculation of the relay control agent’s detection ability, the detection performance of the radar transmitter, receiver, and antenna was the same and was only affected by the relative position of the sensor and the detection target;
- Each load agent could only be delivered by a single surface agent, so the target allocation problem was equivalent to the fire channel allocation problem of multiple surface agents to multiple target agents ;
- The possible time for the control handover of the load agent in the context of cross-domain cooperation was as follows: (a) When the load agent reached the set control handover distance, the air relay control agent obtained control of the load agent. (b) If the surface agent was seriously threatened or the control signal was disturbed, it was forced to transfer control to the air relay control agent. (c) When a new target appeared or according to a real-time situation judgment, control was handed over to the air relay control agent.
2.2. Encoder–Decoder Scheme
2.3. Mathematical Model of Target Allocation
2.3.1. Based on Comprehensive Optimizing Effectiveness
2.3.2. Based on the Greatest Distance Advantage
2.3.3. Based on Cluster Load Balancing
2.3.4. Mathematical Model Construction of Target Allocation
2.4. Mathematical Model of Control Allocation
2.4.1. The Advantages of Radar Detection Capability
2.4.2. The Advantage of Control Data Chain Connectivity
2.4.3. Mathematical Model Construction of Control Allocation
2.5. Establishment of Constrained Objective Functions for Cross-Domain Collaborative Task Allocation
3. Multi-Strategy Improved Dung Beetle Optimization Algorithm
3.1. Dung Beetle Optimization Algorithm
- 1.
- Population initialization: An initial dung beetle population of size is randomly generated, which is composed of four types of dung beetles, namely rolling beetles, new beetles, small beetles, and thieves. Each individual dung beetle in the population represents a target allocation or control allocation decision scheme, and the initial population is shown in Equation (17):
- 2.
- Ball-rolling behavior: The position update formula of the dung beetle’s rolling ball is shown in Equation (18), which guides the allocation plan to achieve optimization in the direction that deviates from the illumination, that is, the current global worst position.
- 3.
- Dancing behavior: When an individual dung beetle encounters an obstacle, it stops marching and uses dancing to reposition itself. The position update of the dancing behavior is shown in Equation (19):
- 4.
- Reproductive behavior: In order to optimize the spawning position of female dung beetles, the spawning boundary was set as shown in Equation (20):As the number of iterations increases, the spawning position will be dynamically updated, as shown in Equation (21):
- 5.
- Foraging behavior: The optimal foraging area for small dung beetles will be updated iteratively, as shown in Equation (22):The position of the small dung beetle is updated as shown in Equation (23):
- 6.
- Stealing behavior: When a thief dung beetle steals other dung beetles’ dung balls, its position is updated in the manner shown in Equation (24):
3.2. Algorithm Improvement Strategy for Cross-Domain Collaborative Task Allocation Problem
3.2.1. Fuch Chaotic Mapping and Opposition-Based Learning Strategy Fusion
3.2.2. Adaptive Rolling Dung Beetle Population Decreasing Strategy
3.2.3. Spiral Search Strategy for Spawning Position
3.2.4. Fusion of Convex Lens Imaging Opposition-Based Learning and Optimal Value Guidance Strategies
4. Experimental Verification and Results Analysis
4.1. Simulation of Environment Construction and Parameter Settings
- Basic parameter assumptions: The population size of dung beetles was set to n = 200, the number of iterations of the algorithm was set to T = 300, and the number of simulations was set to F = 100. In the control allocation, the number of radar accumulation pulses was set to = 5; the probability of radar false alarms was set to , which was corresponding number of false alarms .
- Load agent performance index scenario: The average flight speed of the load agent was set as km/h, and a random number in (0, 0.5) was randomly selected as the damage probability of each load agent to each target platform. With an increase in the scale of the task scene and the number of load agents, the regularity of the damage ability distribution of the load agents gradually increased and continued to approach a normal distribution. This is shown in Figure 5; Ncd is the total number of samples, which is obtained by multiplying the number of target agents and the number of load agents.
- Calculation of threat coefficient of target agent: The threat degree of the target agent was determined by many quantitative and qualitative factors, including quantitative indicators, such as the target’s speed, distance, and relative position, and qualitative indicators, such as the target’s threat type, defense capability, etc. In order to eliminate the dimension and magnitude differences between various factors, the quantitative factors of the quantitative and qualitative indicators were obtained by combining the analytic hierarchy process and the entropy weight method. Then, the factors that affected the threat degree were normalized to obtain the membership degree of each factor. The characteristic information of the four types of targets is shown in Table 3.
- 4.
- Task allocation situation scenario: The task allocation situation was determined by the relative position relationship of each agent platform. According to the performance index and historical experience statistics of the load agent, the water agent and the target agent were scattered in two rectangular areas, respectively. The vertex coordinates of the rectangle were (75, 0), (125, 0), (125, 25), (75, 25) and (0, 300), (200, 300), (200, 400), (0, 400). The aerial relay control agents were distributed in the irregular sector area; the vertex coordinates of the sector were (65.5672, 0), (−79.0625, 420.0352), (279.0625, 420.0352), (134.4328, 0); the center of the circle was (100, −100); the radius was 550; the coordinate position unit was km; and the angle was 38°. According to the simulation scene parameters and situation scenarios in Table 2, the situation graphs of three kinds of scale mission scenarios were randomly generated, as shown in Figure 6.
4.2. Comparative Analysis of Simulation Results
- Optimization performance: As can be seen from the data in Figure 7 and Figure 8 and Table 5, the solving performance of the MSIDBO algorithm for the control allocation model was close to that of MODBO, but the solving time was greatly shortened. Figure 12 shows that there were no significant differences between the two algorithms. In other task scenarios, the performance of the MSIDBO algorithm was significantly better than that of other algorithms, which indicates that the MSIDBO algorithm has significant advantages when solving cross-domain collaborative task allocation problems. For small-, medium-, and large-scale task scenarios, the optimization performance of the MSIDBO algorithm was 28.9–55.8%, 22.7–77%, and 14.6–62.4% higher than that of classical algorithms such as PSO, and 3.5–31.4%, 8.5–76.1%, and 2.1–62.1% higher than that of the original DBO algorithm and other existing improved forms, among which the index of the MODBO algorithm was not counted in the control allocation.
- Running time: It can be seen from Figure 7, Figure 8, Figure 9 and Figure 10 that, with an increase in the problem scale, the time for each algorithm to fall into the local optimal solution increased, and the number of iterations required to jump out of the local optimal solution increased continuously. The average running time of MSIDBO was close to that of DBO, PSO, SSA, and GWO and much lower than that of MODBO, MSADBO, IDBO, and other improved dung beetle algorithms, which indicates that MSIDBO has high computational efficiency.
- Convergence: It can be seen from Figure 7, Figure 8, Figure 9 and Figure 10 that the initial function value of the MSIDBO algorithm was large; it converged rapidly in the early iterations and the convergence index dropped sharply. This indicates that the solution space of the initial allocation scheme generated by the algorithm was uniform and had strong diversity, and the introduced fusion Fuch chaotic mapping and reverse learning strategy had obvious effects. In the middle iteration, the time to fall into the local optimal solution was less than that of other algorithms, indicating that the algorithm can quickly jump out of the local optimal solution and balance the contradiction between a global search and a local search.
- Computational Resource Utilization: The MSIDBO algorithm needs to replace the beetle population that exceeds the constraint boundary when updating the position in each iteration, and the fitness function is called frequently, which occupies a large amount of system computing resources and increases the iteration time cost. In practical tasks, the replacement set of dung beetle individuals should be generated in advance, and the replacement should be called in order.
- Parameter Tuning Challenges: In the adaptive rolling dung beetle population reduction strategy, we have innovatively designed the proportion of rolling dung beetles to decrease as the number of iterations increases. Consequently, the proportion of the other three types of dung beetles also varies. To determine the upper and lower bounds of the variations in the number of rolling dung beetles and other dung beetles, extensive experiments were needed to compare the algorithm’s performance with different parameters and .
5. Conclusions and Prospects
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Methods | Full Name of the Algorithm | Year | Authors |
---|---|---|---|
MSIDBO | Multi-Strategy Improved Dung Beetle Optimization Algorithm | 2024 | This paper |
MODBO | Multi-Option Dung Beetle Optimization Algorithm | 2024 | This paper 1 |
MSADBO | Improved Sine Algorithm Dung Beetle Optimization Algorithm | 2023 | Pan et al. [32] |
IDBO | Improved Dung Beetle Optimization Algorithm | 2024 | Li et al. [33] |
DBO | Dung Beetle Optimization Algorithm | 2023 | Xue et al. [25] |
PSO | Particle Swarm Optimization Algorithm | 1995 | Kennedy et al. [34] |
SSA | Sparrow Search Algorithm | 2020 | Xue et al. [35] |
GWO | Gray Wolf Optimization Algorithm | 2014 | Mirjalili et al. [36] |
Mission Scenario | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Number of surface agents, a | 2 | 4 | 8 | |||||||||
Air relay control agent number, b | 4 | 8 | 16 | |||||||||
Number of target agents, c | 8 | 16 | 24 | |||||||||
Number of target agents (of each type) | 1 | 2 | 1 | 4 | 4 | 2 | 3 | 7 | 6 | 3 | 4 | 11 |
Number of load agents, d | 50 | 100 | 200 |
Target Type | Type of Threat | Defensive Capabilities | Equipment Wear and Tear | Speed | Radius of Detection | Heading Deviation Angle | Value Weights |
---|---|---|---|---|---|---|---|
Low | Weak | Maintained | Slow speed | Medium | 25 | ||
Low | Present | Reliable | Slow speed | Near | 50 | ||
High | Strong | Reliable | High speed | Far | 100 | ||
Medium | Strong | Reliable | Medium speed | Far | 75 |
Methods | Simulation Parameters |
---|---|
MSIDBO | |
MODBO | |
MSADBO | |
IDBO | |
DBO | |
PSO | |
SSA | |
GWO |
Mission Scenario | Algorithm | Target Allocation | Task Allocation | ||||
---|---|---|---|---|---|---|---|
Average Run Time (in Milliseconds) | Global Optimum Value | Performance Comparison 2 | Average Run Time (in Milliseconds) | Global Optimum Value | Performance Comparison | ||
Mission 1 | MSIDBO | 44.03 | 0.2123 | 0.0% | 70.94 | 0.0973 | 0.0% |
MODBO | 74.35 | 0.2200 | 3.5% | 120.66 | 0.0976 | 0.4% | |
MSADBO | 76.19 | 0.2479 | 14.4% | 161.46 | 0.1137 | 14.4% | |
IDBO | 111.87 | 0.2893 | 26.6% | 181.73 | 0.1043 | 6.7% | |
DBO | 37.86 1 | 0.3093 | 31.4% | 61.79 | 0.1072 | 9.3% | |
PSO | 37.88 | 0.2987 | 28.9% | 59.02 | 0.2202 | 55.8% | |
SSA | 41.34 | 0.3234 | 34.4% | 67.04 | 0.1788 | 45.6% | |
GWO | 38.73 | 0.3152 | 32.7% | 61.39 | 0.1385 | 29.8% | |
Mission 2 | MSIDBO | 100.45 | 0.0504 | 0.0% | 373.38 | 0.0526 | 0.0% |
MODBO | 181.96 | 0.0698 | 27.8% | 371.84 | 0.0521 | −1.0% | |
MSADBO | 187.06 | 0.1439 | 65.0% | 371.61 | 0.0726 | 27.5% | |
IDBO | 272.44 | 0.2070 | 75.7% | 453.01 | 0.0575 | 8.5% | |
DBO | 94.63 | 0.2112 | 76.1% | 190.40 | 0.0771 | 31.8% | |
PSO | 92.80 | 0.2171 | 76.8% | 186.54 | 0.0681 | 22.7% | |
SSA | 101.33 | 0.2191 | 77.0% | 206.49 | 0.0979 | 46.3% | |
GWO | 94.58 | 0.2133 | 76.4% | 187.58 | 0.0939 | 43.9% | |
Mission 3 | MSIDBO | 240.60 | 0.6051 | 0.0% | 622.11 | 0.0336 | 0.0% |
MODBO | 451.76 | 0.6182 | 2.1% | 1017.60 | 0.0338 | 0.5% | |
MSADBO | 476.14 | 0.6513 | 7.1% | 1021.23 | 0.0686 | 51.1% | |
IDBO | 653.71 | 0.6984 | 13.4% | 1503.46 | 0.0873 | 61.5% | |
DBO | 221.76 | 0.7112 | 14.9% | 519.08 | 0.0887 | 62.1% | |
PSO | 224.37 | 0.7113 | 14.9% | 509.11 | 0.0851 | 60.5% | |
SSA | 246.66 | 0.7173 | 15.6% | 561.93 | 0.0892 | 62.4% | |
GWO | 228.83 | 0.7084 | 14.6% | 512.85 | 0.0888 | 62.2% |
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Zhou, Y.; Lu, F.; Xu, J.; Wu, L. Multi-Agent Cross-Domain Collaborative Task Allocation Problem Based on Multi-Strategy Improved Dung Beetle Optimization Algorithm. Appl. Sci. 2024, 14, 7175. https://doi.org/10.3390/app14167175
Zhou Y, Lu F, Xu J, Wu L. Multi-Agent Cross-Domain Collaborative Task Allocation Problem Based on Multi-Strategy Improved Dung Beetle Optimization Algorithm. Applied Sciences. 2024; 14(16):7175. https://doi.org/10.3390/app14167175
Chicago/Turabian StyleZhou, Yuxiang, Faxing Lu, Junfei Xu, and Ling Wu. 2024. "Multi-Agent Cross-Domain Collaborative Task Allocation Problem Based on Multi-Strategy Improved Dung Beetle Optimization Algorithm" Applied Sciences 14, no. 16: 7175. https://doi.org/10.3390/app14167175