Kaarthik Sundar

Algorithms for Routing an Unmanned Aerial Vehicle in the Presence of Refueling Depots

We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total fuel required by the UAV is a minimum. We develop an approximation algorithm for the problem, and propose fast construction and improvement heuristics to solve the same. Computational results show that solutions whose costs are on an average within 1.4% of the optimum can be obtained relatively fast for the problem involving five depots and 25 targets.

Heuristics for Routing Heterogeneous Unmanned Vehicles with Fuel Constraints

This paper addresses a multiple depot, multiple unmanned vehicle routing problem with fuel constraints. The objective of the problem is to find a tour for each vehicle such that all the specified targets are visited at least once by some vehicle, the tours satisfy the fuel constraints, and the total travel cost of the vehicles is a minimum. We consider a scenario where the vehicles are allowed to refuel by visiting any of the depots or fuel stations. This is a difficult optimization problem that involves partitioning the targets among the vehicles and finding a feasible tour for each vehicle. The focus of this paper is on developing fast variable neighborhood descent (VND) and variable neighborhood search (VNS) heuristics for finding good feasible solutions for large instances of the vehicle routing problem. Simulation results are presented to corroborate the performance of the proposed heuristics on a set of 23 large instances obtained from a standard library. These results show that the proposed VND heuristic, on an average, performed better than the proposed VNS heuristic for the tested instances.

Route planning algorithms for unmanned aerial vehicles with refueling constraints

Small UAVs are currently used in several monitoring applications to monitor a set of targets and collect relevant data. One of the main constraints that characterize a small UAV is the maximum amount of fuel the vehicle carry. In this article, we consider a single UAV routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total cost of the edges present in the path is a minimum. We first develop a mixed integer, linear programming formulation to solve the problem optimally. We also propose fast and efficient construction and improvement heuristics to solve the same. Computational results are also presented to corroborate the solution quality and the running times of all the algorithms.

Generalized multiple depot traveling salesmen problem-Polyhedral study and exact algorithm

The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least one target in each cluster is visited by some salesman. The GMDTSP is an NP-hard problem as it generalizes the MDTSP and has practical applications in design of ring networks, vehicle routing, flexible manufacturing scheduling and postal routing. We present an integer programming formulation for the GMDTSP and valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis of the convex hull of feasible solutions to the GMDTSP and derive facet-defining inequalities that strengthen the linear programming relaxation of the GMDTSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the problem. The performance of the algorithm is evaluated through extensive computational experiments on several benchmark instances.

An exact algorithm for a heterogeneous, multiple depot, multiple traveling salesman problem

Unmanned aerial vehicles are being used in several monitoring applications to collect data from a set of targets. These vehicles are heterogeneous in the sense that they can differ either in their motion constraints or sensing capabilities. Furthermore, not all vehicles may be able to visit a given target because vehicles may occasionally be equipped with disparate sensors due to the respective payload restrictions. This article addresses a problem where a group of heterogeneous vehicles located at distinct depots visit a set of targets. The targets are partitioned into disjoint subsets: targets to be visited by specific vehicles and targets that any of the vehicles can visit. The objective is to find an optimal tour for each vehicle starting at its respective depot such that each target is visited at least once by some vehicle, the vehicle-target constraints are satisfied and the sum of the costs of the tours for all the vehicles is minimized. We formulate the problem as a mixed-integer linear program and develop a branch-and-cut algorithm to compute an optimal solution to the problem. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.

Formulations and algorithms for the multiple depot, fuel-constrained, multiple vehicle routing problem

We consider a multiple depot, multiple vehicle routing problem with fuel constraints. We are given a set of targets, a set of depots and a set of homogeneous vehicles, one for each depot. The depots are also allowed to act as refueling stations. The vehicles are allowed to refuel at any depot, and our objective is to determine a route for each vehicle with a minimum total cost such that each target is visited at least once by some vehicle, and the vehicles never run out fuel as it traverses its route. We refer to this problem as the Multiple Depot, Fuel-Constrained, Multiple Vehicle Routing Problem (FCMVRP). This paper presents four new mixed integer linear programming formulations to compute an optimal solution for the problem. Extensive computational results for a large set of instances are also presented.

Multiple depot ring star problem: a polyhedral study and an exact algorithm

The multiple depot ring-star problem (MDRSP) is an important combinatorial optimization problem that arises in optical fiber network design and in applications that collect data using stationary sensing devices and autonomous vehicles. Given the locations of a set of customers and a set of depots, the goal is to (i) find a set of simple cycles such that each cycle (ring) passes through a subset of customers and exactly one depot, (ii) assign each non-visited customer to a visited customer or a depot, and (iii) minimize the sum of the routing costs, i.e., the cost of the cycles and the assignment costs. We present a mixed integer linear programming formulation for the MDRSP and propose valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis and derive facet-inducing results for the MDRSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the MDRSP. The performance of the branch-and-cut algorithm is evaluated through extensive computational experiments on several classes of test instances.

Path planning for cooperative routing of air-ground vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances.

Unit commitment with N-1 Security and wind uncertainty

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch. In particular, uncontrollable wind generation increases the risk of random component failures. To address these questions, we present an N-1 Security and Chance-Constrained Unit Commitment (SCCUC) that includes the modeling of generation reserves that respond to wind fluctuations and tertiary reserves to account for single component outages. The basic formulation is reformulated as a mixed-integer second-order cone problem to limit the probability of failure. We develop three different algorithms to solve the problem to optimality and present a detailed case study on the IEEE RTS-96 single area system. The case study assesses the economic impacts due to contingencies and various degrees of wind power penetration into the system and also corroborates the effectiveness of the algorithms.

Algorithms for Heterogeneous, Multiple Depot, Multiple Unmanned Vehicle Path Planning Problems

Unmanned vehicles, both aerial and ground, are being used in several monitoring applications to collect data from a set of targets. This article addresses a problem where a group of heterogeneous aerial or ground vehicles with different motion constraints located at distinct depots visit a set of targets. The vehicles also may be equipped with different sensors, and therefore, a target may not be visited by any vehicle. The objective is to find an optimal path for each vehicle starting and ending at its respective depot such that each target is visited at least once by some vehicle, the vehicle–target constraints are satisfied, and the sum of the length of the paths for all the vehicles is minimized. Two variants of this problem are formulated (one for ground vehicles and another for aerial vehicles) as mixed-integer linear programs and a branch-and-cut algorithm is developed to compute an optimal solution to each of the variants. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.