A bi-criteria approach to the truck-multidrone routing problem

In the rapidly expanding field of e-commerce logistics, the optimisation of last-mile delivery solutions is paramount. This paper introduces a novel methodology that addresses this challenge by generating approximate Pareto fronts in a hybrid truck-drone delivery system. Specifically, we examine a generalized single truck multidrone problem that allows multi-visit flight missions and rendezvous points distinct from launch locations. Our goal is providing decision-makers with a portfolio of optimal routing solutions that balance service time and environmental impact, criteria that are increasingly shaping decision-making in this domain. To achieve this, we introduce a bivector coding scheme inspired by flow-shop scheduling problems and implement a Simulated Annealing algorithm. This algorithm features an advanced stopping mechanism, negating the need for manual adjustments by utilizing a distinctive blend of a domination rate and a Kalman filter. Importantly, our framework employs an iterated greedy search algorithm to evolve from initial solutions towards identifying non-dominated solutions sets, which are then ranked using a hypervolume coefficient. To validate our methodology, we conduct a sensitivity analysis on two different size instances using a full factorial design of experiments. Our analysis reveals crucial insights into the impact of the number of drones, their autonomy, and their flight speed settings. From it, we conclude that it is a robust and adaptable framework for its practical application for obtaining Pareto fronts solutions among which picking the ultimate routing to be implemented.