Heuristics for Arc Routing Problems and Their Applications

Arc Routing Problems (ARPs) are a type of routing problem that finds routes of minimum total cost covering the edges or arcs in a graph representing street or road networks. They find application in many essential services such as residential waste collection, winter gritting, and others. Being NP-hard, solutions are usually found using heuristic methods. This dissertation contributes to heuristics for ARP, with a focus on the Capacitated Arc Routing Problem (CARP) with additional constraints. In operations such as residential waste collection, vehicle breakdown disruptions occur frequently. A new variant Capacitated Arc Re-routing Problem for Vehicle Break-down (CARP-VB) is introduced to address the need to re-route using only remaining vehicles to avoid missing services. A new heuristic Probe is developed to solve CARP-VB. Experiments on benchmark instances show that Probe is better in reducing the makespan and hence effective in reducing delays and avoiding missing services. In addition to total cost, operators are also interested in solutions that are attractive, that is, routes that are contiguous, compact, and non-overlapping to manage the work. Operators may not adopt a solution that is not attractive even if it is optimum. They are also interested in solutions that are balanced in workload to meet equity requirements. A new multi-objective memetic algorithm, MA-ABC is developed, that optimizes three objectives: Attractiveness, makespan, and total cost. On testing with benchmark instances, MA-ABC was found to be effective in providing attractive and balanced route solutions without affecting the total cost. Changes in the problem specification such as demand and topology occurs frequently in business operations. Machine learning be applied to learn the distribution behind these changes and generate solutions quickly at time of inference. Splice is a machine learning framework for CARP that generates closer to optimum solutions quickly using a graph neural network and deep Q-learning. Splice can solve several variants of node and arc routing problems using the same architecture without any modification. Splice was trained and tested using randomly generated instances. Splice generated solutions faster that are also better in comparison to popular metaheuristics.