Modern methods for the Canadian Traveller Problem

Abstract

The Canadian Traveller Problem (CTP) is a stochastic shortest path problem in which edge availability is uncertain and revealed only during traversal, requiring adaptive decision-making under incomplete information.

This thesis proposes a unified framework for modelling and solving the CTP in an online stochastic setting. The framework distinguishes two optimisation paradigms: an \emph{offline} framework, in which candidate paths are evaluated through a Monte Carlo (MC) estimator before any traversal, and an \emph{online} framework, in which paths are constructed through realised walks with edge states sampled on arrival. Simulated Annealing (SA), Particle Swarm Optimization (PSO), and Self-Organizing Migrating Algorithm (SOMA) are implemented in the offline framework; Ant Colony Optimization (ACO) operates in the online framework. To ensure comparability across frameworks, all solvers are assessed with a common evaluation-time estimator $\hat{C}_{\text{eval}}$ based on $N_{\text{eval}} = 100$ Monte Carlo samples.

Systematic experiments on three graph topologies, four uncertainty levels, and sizes up to $n = 100$ reveal that graph topology is a stronger predictor of solver behaviour than algorithm class. On topologies admitting a single source-to-destination path (simple path, balanced tree), every non-failing solver produces identical or near-identical cost. Algorithmic differences become measurable only on parallel paths graphs, where Optimistic Dijkstra, SA, and ACO achieve comparable quality, PSO shows a small gap attributable to its repair mechanism, and SOMA lags more substantially. These findings hold across all tested uncertainty levels.} \EnglishKeywords{Canadian Traveller Problem; stochastic optimization; shortest path; metaheuristics; Monte Carlo simulation; Ant Colony Optimization; Simulated Annealing; Particle Swarm Optimization; Self-Organizing Migrating Algorithm.