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Ma et al. Intell Robot 2023;3(4):581-95 I http://dx.doi.org/10.20517/ir.2023.33 Page 7 of 15

and initializing the weights of ant colony pheromones and the heterogeneous neural network of graphs. Next,
we proceed with GHNN learning: utilizing training datasets to train GHNNs. Tasks and agents serve as nodes
in the graph, with edges representing the strength of the relationship between tasks and agents.

Duringthetrainingprocess, theGHNNwilllearnthesimilarityandmatchingdegreebetweentasksandagents.
We then proceed with the initialization of the improved ACO algorithm: for each agent, we randomly initialize
an ant and initialize the pheromone concentration matrix.

Algorithm 1 Improvement of ant colony optimization algorithms in graph-based heterogeneous neural net-
work
1: Initialize the pheromone concentration matrix
2: Initialize the status of tasks and proxy nodes
3: for each iteration, do
4: for each ant, do
5: Select the next task or proxy node based on the current state and phenome concentration
6: Update the path and task allocation of ants
7: Calculate the economic benefits or rescue efficiency of the current path as the fitness value of
ants
8: end for
9: Update pheromone concentration matrix
10: for each path , do
11: for each ant , do
12: Calculate delta_Pheromone( , ) = /fitness( , )
13: Update Pheromone( , ) = (1 - evaporation_rate) * Pheromone( , ) +
∑
(delta_Pheromone( , ))
14: end for
15: end for
16: end for

3.2. Improvement of ant colony optimization algorithms based on graph heterogeneous neural net-
work
The method proposed in this paper includes three main steps: GHNN learning, task allocation using ACO
algorithms, and collaboration enhancement. Firstly, we use GHNNs to learn meaningful representations of
the relationships between tasks and agents in the system topology. Neural networks capture the similarity,
correlation, and collaboration potential between tasks and agents, providing valuable heuristic information for
ACO algorithms. Secondly, we integrate the learned graph representation into ACO algorithms as pheromone
information. This rich pheromone guides the decision-making process of ants and improves the efficiency and
effectiveness of task allocation. Finally, we utilize graph neural networks to promote collaborative decision-
making among intelligent agents, learning their communication and cooperation strategies.

GHNNs are a type of neural network used to process heterogeneous graph data. In heterogeneous graphs,
nodes can have different attributes and types, and edges can also have different relationships. GHNNs trans-
form the information in a graph into low-dimensional vectors by learning the representations of nodes and
edges, thereby better dealing with complex graph structures and heterogeneous information. They typically
consist of multiple subnetworks, each responsible for handling a type of node or edge. Each subnetwork can
use different neural network structures, such as graph convolutional neural network (GCN), graph attention
network (GAT), etc., to adapt to different types of nodes and edges. The subnetwork learns the representation