This study presents the Drone Swarms Routing Problem (DSRP), which consists of identifying the maximum number of victims in post-disaster areas. The post-disaster area is modeled in a complete graph, where each search location is represented by a vertex, and the edges are the shortest paths between destinations, with an associated weight, corresponding to the battery consumption to fly to a location. In addition, in the DSRP addressed here, a set of drones are deployed in a cooperative drone swarms approach to boost the search. In this context, a V-shaped formation is applied with leader replacements, which allows energy saving. We propose a computation model for the DSRP that considers each drone as an agent that selects the next search location to visit through a simple and efficient method, the Drone Swarm Heuristic. In order to evaluate the proposed model, scenarios based on the Beirut port explosion in 2020 are used. Numerical experiments are presented in the offline and online versions of the proposed method. The results from such scenarios showed the efficiency of the proposed approach, attesting not only the coverage capacity of the computational model but also the advantage of adopting the V-shaped formation flight with leader replacements.

We consider the multi-vehicle one-to-one pickup and delivery problem with split loads, a NP-hard problem linked with a variety of applications for bulk product transportation, bike-sharing systems and inventory re-balancing. This problem is notoriously difficult due to the interaction of two challenging vehicle routing attributes, "pickups and deliveries" and "split deliveries". This possibly leads to optimal solutions of a size that grows exponentially with the instance size, containing multiple visits per customer pair, even in the same route. To solve this problem, we propose an iterated local search metaheuristic as well as a branch-and-price algorithm. The core of the metaheuristic consists of a new large neighborhood search, which reduces the problem of finding the best insertion combination of a pickup and delivery pair into a route (with possible splits) to a resource-constrained shortest path and knapsack problem. Similarly, the branch-and-price algorithm uses sophisticated labeling techniques, route relaxations, pre-processing and branching rules for an efficient resolution. Our computational experiments on classical single-vehicle instances demonstrate the excellent performance of the metaheuristic, which produces new best known solutions for 92 out of 93 test instances, and outperforms all previous algorithms. Experimental results on new multi-vehicle instances with distance constraints are also reported. The branch-and-price algorithm produces optimal solutions for instances with up to 20 pickup-and-delivery pairs, and very accurate solutions are found by the metaheuristic.