Heuristic Initialisation based on Graph Structures for Shortest Path Search on Multi-objective Multigraphs

This paper investigates heuristic initialisation for shortest path search on multi-objective multigraphs using genetic algorithms. An initialised solution comprises a node path and an edge path. The state-of-the-art initialisation method encodes node paths into random-key node priority sequences and assigns random values to represent the indices of traversed parallel edges, where the node priority is a combination of hop count and a random value. However, this method has three limitations. (i) Hop counts are computed using Dijkstra’s algorithm, incurring non-negligible computational cost. (ii) The upper bound of the random values added to hop counts is defined by a hyperparameter, requiring tedious parameter tuning. (iii) Heuristic information about edges is ignored, despite its potential to improve solution quality. To address these issues, this paper first eliminates the randomisation hyperparameter and constrains randomness to the range [0, 1). Second, a heuristic edge initialisation method is proposed. Finally, to reduce the computational burden of Dijkstra’s algorithm, a learning-based node priority generation method is devised using neural networks trained on node embeddings. Experiments on benchmark multi-objective multigraphs show that (i) combining hop counts with randomness in [0, 1) and heuristic edge initialisation outperforms the state-of-the-art method, and (ii) with limited training data, the learning-based node priorities surpass entirely random node priorities and are comparable to state-of-the-art performance, highlighting their potential in large-scale and dynamic scenarios.