My research focuses on mathematical optimization under uncertainty (robust optimization, data-driven optimization) for complex, large-scale problems (numerical optimization, large-scale optimization) where multiple agents compete against – and sometimes coordinate with – one another for limited resources over time (computational game theory, evolutionary game theory, dynamic optimization). Research domains include urban transporation/logistics, smart cities, supply chain management, hazards and disaster management, and healthcare operations management.

- Arc Routing Problems for Combined Drone-truck Fleets

This research contributes to national prosperity by advancing planning methods for combined drone/truck fleets to serve critical societal needs, such as energy transmission infrastructure monitoring, urban police patrolling, rural and suburban mail delivery, roadway pavement inspection, and traffic monitoring. Despite the significant opportunities offered by drones for remote operations, their limited flying time and small battery capacity hamper large-scale operations. Coordination between drones and roadway-dependent motor vehicles, such as trucks, can help resolve these issues by providing batteries and payload required for continued drone services. This project will provide a novel approach to cover large service areas using combined drone/truck fleets. This award highlights the societal applications characterized by combined ‘arc’ routing, for which existing routing methods cannot provide adequate decision-making tools. In particular, this project will validate the methods developed through a case study involving surveillance of electric power transmission lines, the backbone of the nation’s energy infrastructure. This project will train the future workforce in computational operations research and develop open-source software packages to support the further use of unmanned vehicles.

The project will advance our understanding of arc routing problems in combined drone/truck fleets by developing computational optimization models and algorithms. The combined drone/truck arc routing problem is fundamentally different and significantly more challenging than traditional arc routing problems because drones can fly directly from one point to another point in the network without following ground arcs. In addition, a drone may serve only part of an arc due to its limited capacity and footprint, or potentially multiple distinct routes covering the entire arc. The optimal routing of mobile hubs served by trucks must also be incorporated into this already challenging problem. Furthermore, a drone may launch from one truck and return to another truck if beneficial; therefore, synchronization between drones and trucks plays a significant role. This project will provide a novel mixed-integer linear programming formulation and adaptive heuristics based on decomposition, dynamic programming, partitioning, large neighborhood search, and machine learning for efficient operations of the combined fleets. The models and algorithms will be validated with actual data from power transmission line monitoring.


- Types of the mixed fleet problems

- Examples

- Pseudo Node Insertion Method

The advantage of a drone-truck mixed fleet operations in last-mile logistics can be summarized in two folds: 1) enabling faster pick-up/delivery of items and 2) expanding operation areas beyond the range that could be achieved by using only one type of vehicle. The drone-truck combined operation (DTCO) solutions are based on truck routes and locations, usually customer nodes, where drones depart from and return to trucks. Since synchronous rendezvous of both vehicles can be very rare, these solutions may contain waste time caused by waiting of one vehicle for the other. In this research, a pseudo node insertion method is proposed to make DTCO more efficient by resolving the drone-truck asynchronization issue. Pseudo nodes are created at the point where a drone and a truck can meet simultaneously. We present a detailed method to calculate the location of the pseudo node, and provide a detailed analysis for the travel completion time saving conditions. Furthermore, we explore a variety of scenarios to enhance the efficiency of DTCO by way of inserting pseudo nodes. An algorithm for the pseudo node insertion method is provided, and numerical examples are presented to discuss efficacy and efficiency of our proposed approach.

In the above figure, the DTCO solution is shown in (a), which can be improved by way of inserting pseudo nodes as shown in (b). The travel completion time is analyzed in (c) for both problems, where the red boxes show the waiting time. It is clear that the travel completion time is effectively reduced if the pseudo nodes are used.

- Survey of Optimization Methods for Drone-truck Combined Operations

We survey the state-of-the-art optimization approaches in the civil application of drone operations (DO) and drone-truck combined operations (DTCO) including construction/infrastructure, agriculture, transportation/logistics, security/disaster management, entertainment/media, etc. In particular, we review ongoing research on various optimization issues related to DO and DTCO including mathematical models, solution methods, synchronization between a drone and a truck, and barriers in implementing DO and DTCO. First, we introduce DO and DTCO and their applications, and explore some previous works including survey papers. In addition, we survey the state of the art of DO and DTCO studies and discuss the research gaps in the literature. Furthermore, the detailed review of DTCO models and solution methods are reviewed. Finally, future research directions are discussed. All the reviewed papers are summarized in an Excel file, which can be downloaded [here].

Research Grants