Solving the Multiple Traveling Salesman Problem by a Novel Meta-heuristic Algorithm

The multiple traveling salesman problem (MTSP) is a generalization of the famous traveling salesman problem (TSP), where more than one salesman is used in the solution. Although the MTSP is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. This paper presents an efficient and evolutionary optimization algorithm which has been developed through combining Modified Imperialist Competitive Algorithm and Lin-Kernigan Algorithm (MICA) in order to solve the MTSP.  In the proposed algorithm, an absorption function and several local search algorithms as a revolution operator are used. The performance of our algorithm was tested on several MTSP benchmark problems and the results confirmed that the MICA performs well and is quite competitive with other meta-heuristic algorithms

Approximation Algorithms and Heuristics for a Heterogeneous Traveling Salesman Problem

Unmanned Vehicles (UVs) are developed for several civil and military applications. For these applications, there is a need for multiple vehicles with different capabilities to visit and monitor a set of given targets. In such scenarios, routing problems arise naturally where there is a need to plan paths in order to optimally use resources and time. The focus of this thesis is to address a basic optimization problem that arises in this setting. We consider a routing problem where some targets have to be visited by specific vehicles. We approach this problem by dividing the routing into two sub problems: partitioning the targets while satisfying vehicle target constraints and sequencing. We solve the partitioning problem with the help of a minimum spanning tree algorithm. We use 3 different approaches to solve the sequencing problem; namely, the 2 approximation algorithm, Christofide's algorithm and the Lin - Kernighan Heuristic (LKH). The approximation algorithms were implemented in MATLAB. We also developed an integer programming (IP) model and a relaxed linear programming (LP) model in C with the help of Concert Technology for CPLEX, to obtain lower bounds. We compare the performance of the developed approximation algorithms with both the IP and the LP model and found that the heuristic performed very well and provided the better quality solutions as compared to the approximation algorithms. It was also found that the approximation algorithms gave better solutions than the apriori guarantees

Approximation Algorithms and Heuristics for a 2-depot, Heterogeneous Hamiltonian Path Problem

Various civil and military applications of UAVs, or ground robots, require a set of vehicles to monitor a group of targets. Routing problems naturally arise in this setting where the operators of the vehicles have to plan the paths suitably in order to optimize the use of resources available such as sensors, fuel etc. These vehicles may differ either in their structural (design and dynamics) or functional (sensing) capabilities. This thesis addresses an important routing problem involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves dividing the routing problem into two sub-problems: Partitioning and Sequencing. Partitioning the targets involves finding two distinct sets of targets, each corresponding to one of the vehicles. We then find a sequence in which these targets need to be visited in order to optimize the use of resources to the maximum possible extent. The sequencing problem can be solved either by Christofides algorithm or the Lin-Kernighan Heuristic (LKH). The problem of partitioning is tackled by solving a Linear Program (LP) obtained by relaxing some of the constraints of an Integer Programming (IP) model for the problem. We observe the performance of two LP models for the partitioning. The first LP model is obtained by relaxing only the integrality constraints whereas in the second model relaxes both integrality and degree constraints. The algorithms were implemented in a C++ environment with the help of Concert Technology for CPLEX, and Boost Graph Libraries. The performance of these algorithms was studied for 50 random instances of varying problem sizes. It was found that on an average, the algorithms based on the first LP model provided better (closer to the optimum) solutions as compared to those based on the second LP model. We also observed that for both the LP models, the average quality of solutions given by the heuristics were found to be better ( within 5% of the optimum) than the average quality of solutions obtained from the approximation algorithm (between 30 - 60% of the optimum depending on the problem size)

Algorithms for Multiple Vehicle Routing Problems

Surveillance and monitoring applications require a collection of heterogeneous vehicles to visit a set of targets. This dissertation considers three fundamental routing problems involving multiple vehicles that arise in these applications. The main objective of this dissertation is to develop novel approximation algorithms for these routing problems that find feasible solutions and also provide a bound on the quality of the solutions produced by the algorithms. The first routing problem considered is a multiple depot, multiple terminal, Hamiltonian Path problem. Given multiple vehicles starting at distinct depots, a set of targets and terminal locations, the objective of this problem is to find a vertex-disjoint path for each vehicle such that each target is visited once by a vehicle, the paths end at the terminals and the sum of the distances travelled by the vehicles is a minimum. A 2-approximation algorithm is presented for this routing problem when the costs are symmetric and satisfy the triangle inequality. For the case where all the vehicles start from the same depot, a 5/3-approximation algorithm is developed. The second routing problem addressed in this dissertation is a multiple depot, heterogeneous traveling salesman problem. The objective of this problem is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances travelled by the vehicles is minimized. A primal-dual algorithm with an approximation ratio of 2 is presented for this problem when the vehicles involved are ground vehicles that can move forwards and backwards with a constraint on their minimum turning radius. Finally, this dissertation addresses a multiple depot heterogeneous traveling salesman problem when the travel costs are asymmetric and satisfy the triangle inequality. An approximation algorithm and a heuristic is developed for this problem with simulation results that corroborate the performance of the proposed algorithms. All the main algorithms presented in the dissertation advance the state of art in the area of approximation algorithms for multiple vehicle routing problems. This dissertation has its value for providing approximation algorithms for the routing problems that involves multiple vehicles with additional constraints. Some algorithms have constant approximation factor, which is very useful in the application but difficult to find. In addition to the approximation algorithms, some heuristic algorithms were also proposed to improve solution qualities or computation time

Routing Vehicles with Motion, Resource and Mission Constraints: Algorithms and Bounds

Unmanned Aerial Vehicles (UAVs) are used for several military and civil applications such as reconnaissance, surveillance etc. The UAVs, due to their design and size limitations, have inherent kinematic constraints, communication constraints etc. This thesis considers the path planning problems for UAVs while satisfying a class of constraints. We consider a multiple depot UAV routing problem, where the vehicles have motion constraints due to bound on their yaw-rate. For a given set of targets, it is required that each target should be on the path of at least one of the vehicles. This problem is hard to solve and currently there are no algorithm that could find an optimal solution. We aim to find tight lower bounds for this problem via Lagrangian relaxation. The complicating constraints of the problem are relaxed, and the cost function is penalized whenever those constraints are violated. This reduces the original problem to a known problem - a standard multiple traveling salesmen problem (MTSP). Simulation results are presented to show that this method significantly improved the existing lower bounds. The second problem we consider is the routing of UAVs in GPS denied environments and with limited communication range. Two different architectures for navigation assisted by an array of Unattended Ground Sensors (UGSs) are considered. In the first case, when an UAV localizes itself by communicating with an UGS, the second UAV can orbit around the first UAV. Contact with UGS allows them to act as beacons for relative navigation eliminating the need for GPS. A randomized algorithm with approximation ratio of 9/2 and a transformation technique are developed to solve this problem. In the second architecture, when two UAVs are located at two different UGSs, the third UAV localizes by triangulation using range measurements from the first two UAVs. This three UAV case is solved using a graph transformation technique to pose it as an one-in-a-set TSP. The solutions produced by these algorithms were used to simulate the UAV routing on AMASE, a simulation tool for routing UAVs developed by the Air Force Research Laboratories

Estimating the efficacy of mass rescue operations in ocean areas with vehicle routing models and heuristics

Tese de doutoramento, Estatística e Investigação Operacional (Optimização), Universidade de Lisboa, Faculdade de Ciências, 2018Mass rescue operations (MRO) in maritime areas, particularly in ocean areas, are a major concern for the authorities responsible for conducting search and rescue (SAR) activities. A mass rescue operation can be defined as a search and rescue activity characterized by the need for immediate assistance to a large number of persons in distress, such that the capabilities normally available to search and rescue are inadequate. In this dissertation we deal with a mass rescue operation within ocean areas and we consider the problem of rescuing a set of survivors following a maritime incident (cruise ship, oil platform, ditched airplane) that are drifting in time. The recovery of survivors is performed by nearby ships and helicopters. We also consider the possibility of ships capable of refuelling helicopters while hovering which can extend the range to which survivors can be rescued. A linear binary integer formulation is presented along with an application that allows users to build instances of the problem. The formulation considers a discretization of time within a certain time step in order to assess the possibility of travelling along different locations. The problem considered in this work can be perceived as an extension of the generalized vehicle routing problem (GVRP) with a profit stance since we may not be able to recover all of the survivors. We also present a look ahead approach, based on the pilot method, to the problem along with some optimal results using state of the art Mixed-integer linear programming solvers. Finally, the efficacy of the solution from the GVRP is estimated for a set of scenarios that combine incident severity, location, traffic density for nearby ships and SAR assets availability and location. Using traffic density maps and the estimated MRO efficacy, one can produce a combined vulnerability map to ascertain the quality of response to each scenario.Marinha Portuguesa, Plano de Atividades de Formação Nacional (PAFN

Coordination Strategies for Human Supervisory Control of Robotic Teams

Autonomous mobile sensor teams are crucial to many civilian and military applications. These robotic teams often operate within a larger supervisory system, involving human operators who oversee the mission and analyze sensory data. Here, both the human and the robotic system sub-components, as well as interactions between them, must be carefully considered in designing effective mission coordination strategies. This dissertation explores a series of representative sub-problems relating to the analysis and coordination of both mobile sensors and human operators within supervisory systems. The content herein is presented in three parts: Part I focuses on coordinating operator behavior independently (operator-focused methods), Part II focuses on coordinating mobile-sensor behavior independently (sensor-focused methods), and Part III focuses on jointly coordinating both operator and mobile sensor behavior (joint methods). The content herein is primarily motivated by a particular application in which Unmanned Aerial Vehicles collect visual imagery to be analyzed by a remotely located operator, although many of the results apply to any system of similar architecture. Specifically, with regard to operator-focused methods, Chapter 2 illustrates how physiological sensing, namely eye tracking, may provide aid in modeling operator behavior and assessing the usability of user interfaces. The results of a pilot usability study in which human observers interact with a supervisory control interface are presented, and eye-tracking data is correlated with various usability metrics. Chapter 3 develops robust scheduling algorithms for determining the ordering in which operators should process sensory tasks to both boost performance and decrease variance. A scenario-based, Mixed-Integer Linear Program (MILP) framework is presented, and is assessed in a series of numerical studies. With regard to sensor-focused methods, Chapters 4 and 5 consider two types of supervisory surveillance missions:Chapter 4 develops a cloud-based coverage strategy for persistent surveillance of planar regions. The scheme operates in a dynamic environment, only requiring sporadic, unplanned data exchanges between a central cloud and the sensors in the field. The framework is shown to provide collision avoidance and, in certain cases, produce convergence to a Pareto-optimal coverage configuration. In chapter 5, a heuristic routing scheme is discussed to produce Dubins tours for persistent surveillance of discrete targets, each with associated visibility and dwell-time constraints. Under some assumptions, the problem is posed as a constrained optimization that seeks a minimum-length tour, while simultaneously constraining the time required to reach the first target. A sampling-based scheme is used to approximate solutions to the constrained optimization. This approach is also shown to have desirable resolution completeness properties.Finally, Chapter 6 explores joint methods for coordinating both operator and sensor behavior in the context of a discrete surveillance mission (similar to that of Chapter 5), in which UAVs collect imagery of static targets to be analyzed by the human operator.In particular, a method is proposed to simultaneously construct UAV routes and operator schedules, with the goal of maintaining the operator's task load within a high-performance regime and preventing unnecessary UAV loitering. The full routing/scheduling problem is posed as a mixed-integer (non-linear) program, which can be equivalently represented as a MILP through the addition of auxiliary variables. For scalability, a MILP-based receding-horizon method is proposed to incrementally construct suboptimal solutions to the full optimization problem, which can be extended using a scenario-based approach (similar to that of Chapter 3) to incorporate robustness to operator uncertainty