A hybrid genetic algorithm for the traveling salesman problem with drone

This paper addresses the traveling salesman problem with drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years reflecting the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms two existing methods in terms of solution quality and improves many best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to investigate their sensitivity to the performance of our method.