In the context of frequent public emergencies, emergency logistics distribution is particularly critical, and because of the unique advantages of unmanned aerial vehicles (UAVs), the model of coordinated delivery of vehicles and UAVs is gradually becoming an essential form of emergency logistics distribution. However, the omission of start-up costs prevents the cost of UAV battery replacement and the sorting, assembly and verification of packages from being factored into the total cost. Furthermore, most existing models focus on route optimization and delivery cost, which cannot fully reflect the customer’s desire for service satisfaction under emergency conditions. It is necessary to convert the unsatisfactory degree of time window into a penalty cost rather than a model constraint. Additionally, there is a lack of analysis on the mutual waiting cost between vehicles and UAVs when one of them is performing delivery tasks. Considering the effects of the time window, customer demand, maximum load capacity, and duration of distribution benefits, we propose a collaborative delivery path optimization model for vehicles and UAVs to minimize the total distribution cost. A genetic algorithm is used to obtain the model solution under the constraints of distribution subloops, distribution order, and take-off and landing nodes. To assess the efficacy of the vehicle and UAV collaborative delivery path optimization model, this paper employs a county-level district in Xi’an city as a pilot area for an emergency delivery. Compared with the vehicle-alone delivery model, the UAV-alone delivery model and vehicle-UAV collaborative delivery model, this model can significantly reduce the utilization of distribution vehicles while also significantly lowering the start-up cost, waiting cost and penalty cost. Thus, the model can effectively improve delivery timeliness and customer satisfaction. The total cost of this model is 39.2% less than that of the vehicle-alone delivery model and 16.5% less than that of the UAV-alone delivery model. Although its delivery cost is slightly higher than the vehicle-UAV collaborative delivery model, the reduction in the start-up cost and penalty cost decrease the overall cost of distribution by 11.8%. This suggests that to cut costs of all sizes and conserve half of the resources used by vehicles, employing the vehicle-UAV collaborative delivery model for emergency distribution is preferable. Moreover, the model integrating the start-up cost, penalty cost, waiting cost, etc., can more effectively express the requirements of timeliness for UAV delivery under emergency conditions.

Because of their flexibility, controllability and convenience, Automated Guided Vehicles (AGV) have gradually gained popularity in intelligent manufacturing because to their adaptability, controllability, and simplicity. We examine the relationship between AGV scheduling tasks, charging thresholds, and power consumption, in order to address the issue of how AGV charging affects the scheduling of flexible manufacturing units with multiple AGVs. Aiming to promote AGVs load balance and reduce AGV charging times while meeting customer demands, we establish a scheduling model with the objective of minimizing the maximum completion time based on process sequence limitations, processing time restrictions, and workpiece transportation constraints. In accordance with the model’s characteristics, we code the machine, workpiece, and AGV independently, solve the model using a genetic algorithm, adjust the crossover mutation operator, and incorporate an elite retention strategy to the population initialization process to improve genetic diversity. Calculation examples are used to examine the marginal utility of the number of AGVs and electricity and validate the efficiency and viability of the scheduling model. The results show that the AVGs are effectively scheduled to complete transportation tasks and reduce the charging wait time. The multi-AGV flexible manufacturing cell scheduling can also help decision makers to seek AGVs load balance by simulation, reduce the charging times, and decrease the final completion time of manufacturing unit. In addition, AGV utilization can be maximized when the fleet size of AGV is 20%-40% of the number of workpieces.

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.