  This paper introduces an enhanced meta-heuristic (ML-ACO) that combines
machine learning (ML) and ant colony optimization (ACO) to solve combinatorial
optimization problems. To illustrate the underlying mechanism of our ML-ACO
algorithm, we start by describing a test problem, the orienteering problem. In
this problem, the objective is to find a route that visits a subset of vertices
in a graph within a time budget to maximize the collected score. In the first
phase of our ML-ACO algorithm, an ML model is trained using a set of small
problem instances where the optimal solution is known. Specifically,
classification models are used to classify an edge as being part of the optimal
route, or not, using problem-specific features and statistical measures. The
trained model is then used to predict the probability that an edge in the graph
of a test problem instance belongs to the corresponding optimal route. In the
second phase, we incorporate the predicted probabilities into the ACO component
of our algorithm, i.e., using the probability values as heuristic weights or to
warm start the pheromone matrix. Here, the probability values bias sampling
towards favoring those predicted high-quality edges when constructing feasible
routes. We have tested multiple classification models including graph neural
networks, logistic regression and support vector machines, and the experimental
results show that our solution prediction approach consistently boosts the
performance of ACO. Further, we empirically show that our ML model trained on
small synthetic instances generalizes well to large synthetic and real-world
instances. Our approach integrating ML with a meta-heuristic is generic and can
be applied to a wide range of optimization problems.
