A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption

The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all of the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu-search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.Comment: 18 page

Algorithms for Stochastic Integer Programs Using Fenchel Cutting Planes

This dissertation develops theory and methodology based on Fenchel cutting planes for solving stochastic integer programs (SIPs) with binary or general integer variables in the second-stage. The methodology is applied to auto-carrier loading problem under uncertainty. The motivation is that many applications can be modeled as SIPs, but this class of problems is hard to solve. In this dissertation, the underlying parameter distributions are assumed to be discrete so that the original problem can be formulated as a deterministic equivalent mixed-integer program. The developed methods are evaluated based on computational experiments using both real and randomly generated instances from the literature. We begin with studying a methodology using Fenchel cutting planes for SIPs with binary variables and implement an algorithm to improve runtime performance. We then introduce the stochastic auto-carrier loading problem where we present a mathematical model for tactical decision making regarding the number and types of auto-carriers needed based on the uncertainty of availability of vehicles. This involves the auto-carrier loading problem for which actual dimensions of the vehicles, regulations on total height of the auto-carriers and maximum weight of the axles, and safety requirements are considered. The problem is modeled as a two-stage SIP, and computational experiments are performed using test instances based on real data. Next, we develop theory and a methodology for Fenchel cutting planes for mixed integer programs with special structure. Integer programs have to be solved to generate a Fenchel cutting plane and this poses a challenge. Therefore, we propose a new methodology for constructing a reduced set of integer points so that the generation of Fenchel cutting planes is computationally favorable. We then present the computational results based on randomly generated instances from the literature and discuss the limitations of the methodology. We finally extend the methodology to SIPs with general integer variables in the second-stage with special structure, and study different normalizations for Fenchel cut generation and report their computational performance

17-07 Phase-II: Community-Aware Charging Station Network Design for Electrified Vehicles in Urban Areas: \u3c/i\u3e Reducing Congestion, Emissions, Improving Accessibility, and Promoting Walking, Bicycling, and use of Public Transportation

A major challenge for achieving large-scale adoption of EVs is an accessible infrastructure for the communities. The societal benefits of large-scale adoption of EVs cannot be realized without adequate deployment of publicly accessible charging stations due to mutual dependence of EV sales and public infrastructure deployment. Such infrastructure deployment also presents a number of unique opportunities for promoting livability while helping to reduce the negative side-effects of transportation (e.g., congestion, emissions, and noise pollution). In this phase, we develop a modeling framework (MF) to consider various factors and their associated uncertainties for an optimal network design for electrified vehicles. The factors considered in the study include: state of charge, dwell time, Origin-Destination (OD) pair