The drone arc routing problem (DARP) is one of the arc routing problems (ARPs) that has been studied by researchers recently. Unlike traditional ARPs, drones can travel directly between any two points in the graph. Due to the flexibility of drones, it is possible to use edges not defined in the graphs when deadheading the edges. This advantage of drones makes this problem more challenging than any other ARP. With this study, the energy capacities of drones are considered in a DARP. Thus, a novel DARP called the drone arc routing problem with deadheading demand (DARP-DD) is addressed in this study. Drone capacities are used both when servicing the edges and when deadheading the edges in the DARP-DD. A special case of the DARP-DD, called the multiple service drone arc routing problem with deadheading demand (MS-DARP-DD), is also discussed, where some critical required edges may need to be served more than once. To solve these challenging problems, a simulated annealing algorithm is used, and the components of the algorithm are designed. Additionally, novel neighbor search operators are developed in this study. The computational results show that the proposed algorithm and its components are effective and useful in solving the DARP-DD and MS-DARP-DD.

Many optimization problems are complex, challenging and take a significant amount of computational effort to solve. These problems have gained the attention of researchers and they have developed lots of metaheuristic algorithms to use for solving these problems. Most of the developed metaheuristic algorithms are based on some metaphors. For this reason, these algorithms have algorithm-specific parameters to reflect the nature of the inspired metaphor. This violates the algorithm's simplicity and brings extra workload to execute the algorithm. However, the optimization problems can also be solved with simple, useful, metaphor-less and algorithm-specific parameter-less metaheuristic algorithms. So, it is the essential motivation behind this study. We present a novel metaheuristic algorithm called Discrete Rao Algorithm (DRA) by updating some components of the generic Rao algorithm to solve the combinatorial optimization problems. To evaluate the performance of the DRA, we perform experiments on Traveling Salesman Problem (TSP) which is the well-known combinatorial optimization problem. The experiments are performed on different sized benchmark problems in the literature. The computational results show that the developed algorithm has obtained high quality solutions in a reasonable computation time and it is competitive with other algorithms in the literature for solving the TSP.