TDRP-DS definition We define the truck–drone routing problem with drone swaps (TDRP-DS). The drone swap mode involves a drone launching from a truck with the possibility of being retrieved by any other truck. The customers along the truck routes, termed drone launch/retrieval locations (LRLs), are used as bases from which the trucks can launch or retrieve drones. The TDRP-DS objective is to minimize the variable costs of trucks and drones in use. Solving the TDRP-DS necessitates finding the cost-minimizing cooperative routes given the network and demand of customers with delivery deadline. There is one depot and several customers. Each customer has a delivery deadline that corresponds to the latest service-starting time. The customers are classified into two types: truck customer (denoted as TC) and drone customer (denoted as UC). Each TC can only be serviced by a truck, and each UC can only be serviced by a drone. TCs that are serviced by trucks act simultaneously as LRLs. Each truck can concurrently carry at most h2 drones. When a truck–drone combination departs from the depot, the truck carries a predetermined number (h1) of drones. All trucks (carrying drones) in use depart from the depot at the same time. Trucks are permitted to wait for retrieved drones at LRLs. A route traveled by one drone can cover exactly one UC. Drones are not allowed to launch directly from the depot; however, drones can fly directly to the depot after the assigned delivery. The capacity, variable cost, and average velocity of each truck are the same. Each drone has a fixed maximum flying time for each launch and a constant velocity. The capacity, and variable cost of each drone are the same. i) Referring to the benchmark instances with 100 customers from Solomon (1987), i.e., C101, R101, and RC101, we designed TDRP-DS instances. The depots in the chosen benchmark instances still functioned as depots in the TDRP-DS instances. Let n denote the number of customers included in the TDRP-DS network. The n customers were classified into TCs and. The coordinates of the selected nodes were referenced to calculate the traveling/flying distance of the truck or drone on the arcs, and the Manhattan distances between the nodes were scaled down. The earliest service-starting time of customer time windows and the depot time window were ignored. The latest service-starting time of customer time windows was scaled down to function as the delivery deadline. Each TDRP-DS instance was denoted (C/R/RC)“n”- , where n = 15–30. ii) In small-scale instances, the node coordinates were randomly generated. Each small-scale instance was denoted as R“n”- , where n = 6–12, and is 0.1, 0.2, or 0.3. The demand of a TC or UC was a random number in the range (0, QK/2) or (0, QU/2), respectively. The delivery deadlines were randomly generated. Other parameters had the same values as those for the medium-scale instances.