Spatial coverage in routing and path planning problems

Routing and path planning problems that involve spatial coverage have received increasing attention in recent years in different application areas. Spatial coverage refers to the possibility of considering nodes that are not directly served by a vehicle as visited for the purpose of the objective function or constraints. Despite similarities between the underlying problems, solution approaches have been developed in different disciplines independently, leading to different terminologies and solution techniques. This paper proposes a unified view of the approaches: Based on a formal introduction of the concept of spatial coverage in vehicle routing, it presents a classification scheme for core problem features and summarizes problem variants and solution concepts developed in the domains of operations research and robotics. The connections between these related problem classes offer insights into common underlying structures and open possibilities for developing new applications and algorithms

Approximation algorithms for regret minimization in vehicle routing problems

In this thesis, we present new approximation algorithms as well as hardness of approximation results for NP-hard vehicle routing problems related to public transportation. We consider two different problem classes that also occur frequently in areas such as logistics, robotics, or distribution systems. For the first problem class, the goal is to visit as many locations in a network as possible subject to timing or cost constraints. For the second problem class, a given set of locations is to be visited using a minimum-cost set of routes under some constraints. Due to the relevance of both problem classes for public transportation, a secondary objective must be taken into account beyond a low operation cost: namely, it is crucial to design routes that optimize customer satisfaction in order to encourage customers to use the service. Our measure of choice is the regret of a customer, that is the time comparison of the chosen route with the shortest path to a destination. From the first problem class, we investigate variants and extensions of the Orienteering problem that asks to find a short walk maximizing the profit obtained from visiting distinct locations. We give approximation algorithms for variants in which the walk has to respect constraints on the regret of the visited vertices. Additionally, we describe a framework to extend approximation algorithms for Orienteering problems to consider also a second budget constraint, namely node demands, that have to be satisfied in order to collect the profit. We obtain polynomial time approximation schemes for the Capacitated Orienteering problem on trees and Euclidean metrics. Furthermore, we study variants of the School Bus problem (SBP). In SBP, a given set of locations is to be connected to a destination node with both low operation cost and a low maximum regret. We note that the Orienteering problem can be seen as the pricing problem for SBP and it often appears as subroutine in algorithms for SBP. For tree-shaped networks, we describe algorithms with a small constant approximation factor and complement them by showing hardness of approximation results. We give an overview of the known results in arbitrary networks and we prove that a general variant cannot be approximated unless P = NP. Finally, we describe an integer programming approach to solve School Bus problems in practice and present an improved bus schedule for a private school in the lake Geneva region

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

Optimization Approaches for Mobility and Service Sharing

Mobility and service sharing is undergoing a fast rise in popularity and industrial growth in recent years. For example, in patient-centered medical home care, services are delivered to patients at home, who share a group of medical staff riding together in a vehicle that also carries shared medical devices; companies such as Amazon and Meijer have been investing tremendous human effort and money in grocery delivery to customers who share the use of delivery vehicles and staff. In such mobility and service sharing systems, decision-makers need to make a wide range of system design and operational decisions, including locating service facilities, matching supplies with demand for shared mobility services, dispatching vehicles and staff, and scheduling appointments. The complexity of the linking decisions and constraints, as well as the dimensionality of the problems in the real world, pose challenges in finding optimal strategies efficiently. In this work, we apply techniques from Operations Research to investigate the optimal and practical solution approaches to improve the quality of service, cost-effectiveness, and operational efficiency of mobility and service sharing in a variety of applications. We deploy stochastic programming, integer programming, and approximation algorithms to address the issues in decision-making for seeking fast and reliable solutions for planning and operations problems. This dissertation contains four main chapters. In Chapter 2, we consider a class of vehicle routing problems (VRPs) where the objective is to minimize the longest route taken by any vehicle as opposed to the total distance of all routes. In such a setting, the traditional decomposition approach fails to solve the problem effectively. We investigate the hardness result of the problem and develop an approximation algorithm that achieves the best approximation ratio. In Chapter 3, we focus on developing an efficient computational algorithm for the elementary shortest path problem with resource constraints, which is solved as the pricing subproblem of the column generation-based approach for many VRP variants. Inspired by the color-coding approach, we develop a randomized algorithm that can be easily implemented in parallel. We also extend the state-of-the-art pulse algorithm for elementary shortest path problem with a new bounding scheme on the load of the route. In Chapter 4, we consider a carsharing fleet location design problem with mixed vehicle types and a restriction on CO2 emission. We use a minimum-cost flow model on a spatial-temporal network and provide insights on fleet location, car-type design, and their environmental impacts. In Chapter 5, we focus on the design and operations of an integrated car-and-ride sharing system for heterogeneous users/travelers with an application of satisfying transportation needs in underserved communities. The system aims to provide self-sustained community-based shared transportation. We address the uncertain travel and service time in operations via a stochastic integer programming model and propose decomposition algorithms to solve it efficiently. Overall, our contributions are threefold: (i) providing mathematical models of various complex mobility and service sharing systems, (ii) deriving efficient solution algorithms to solve the proposed models, (iii) evaluating the solution approaches via extensive numerical experiments. The models and solution algorithms that we develop in this work can be used by practitioners to solve a variety of mobility and service sharing problems in different business contexts, and thus can generate significant societal and economic impacts.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155115/1/miaoyu_1.pd

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering