Online traveling salesman problems with rejection options

In this article, we consider online versions of the traveling salesman problem on metric spaces for which requests to visit points are not mandatory. Associated with each request is a penalty (if rejected). Requests are revealed over time (at their release dates) to a server who must decide which requests to accept and serve in order to minimize a linear combination of the time to serve all accepted requests and the total penalties of all rejected requests. In the basic online version of the problem, a request can be accepted any time after its release date. In the real-time online version, a request must be accepted or rejected at the time of its release date. For the basic version, we provide a best possible 2-competitive online algorithm for the problem on a general metric space. For the real-time version, we first consider special metric spaces: on the nonnegative real line, we provide a best possible 2.5-competitive polynomial time online algorithm; on the real line, we prove a Ω(√ln n) lower bound of 2.64 on any competitive ratios and give a 3-competitive online algorithm. We then consider the case of a general metric space and prove a inline image lower bound on the competitive ratio of any online algorithms. Finally, among the restricted class of online algorithms with prior knowledge about the total number of requests n, we propose an asymptotically best possible O(√ln n)-competitive algorithm.United States. Office of Naval Research (Grant N00014-09-1-0326)United States. Office of Naval Research (Grant N00014-12-1-0033)United States. Air Force Office of Scientific Research (Grant FA9550-10-1-0437

Strategies for Handling Temporal Uncertainty in Pickup and Delivery Problems with Time Windows

In many real-life routing problems there is more uncertainty with respect to the required timing of the service than with respect to the service locations. We focus on a pickup and delivery problem with time windows in which the pickup and drop-off locations of the service requests are fully known in advance, but the time at which these jobs will require service is only fully revealed during operations. We develop a sample-scenario routing strategy to accommodate a variety of potential time real- izations while designing and updating the routes. Our experiments on a breadth of instances show that advance time related information, if used intelligently, can yield benefits. Furthermore, we show that it is beneficial to tailor the consensus function that is used in the sample-scenario approach to the specifics of the problem setting. By doing so, our strategy performs well on instances with both short time windows and limited advance confirmation

ROBUST ENERGY-AWARE UNMANNED AERIAL VEHICLE ROUTING USING ENSEMBLE WEATHER FORECASTS

The Marine Corps seeks to develop energy-aware unmanned aerial vehicle (UAV) routing for last-mile logistics resupply. UAVs have limited range and time on station to execute their assigned mission. To optimize the delivery of supplies to dispersed units, users must optimally utilize the internal energy onboard the UAV while considering external factors such as weather and priorities of resupply requests. Energy-aware UAV routing will increase Marine Corps logistics capabilities during expeditionary advanced base operations (EABO). The current EABO construct places forces within the threat rings of adversary weapon systems. Use of UAVs can allow dispersed forces to operate in the adversary’s threat rings without the stoppage of logistical support. This thesis builds upon the two-layer framework developed in previous theses by Jatho (2020) and Haller (2021) to include ensemble weather forecasts and partial delivery of supplies. The first layer, which solves the boundary value problem to obtain optimal trajectories between all nodes in the network, is solved for each member of the ensemble forecast. The second layer consists of a stochastic vehicle routing problem using the cost matrix from the first layer. This thesis also introduces the notion of partial delivery of supplies in the second layer to allow demand nodes to request multiple packages of supplies that can be delivered by multiple UAVs. Finally, this thesis analyzes various case studies and corresponding results.ONR, NRL, Arlington, VA 22203Captain, United States Marine CorpsApproved for public release. Distribution is unlimited

Dynamic vehicle routing problems: Three decades and counting

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

Online Traveling Salesman Problems with Service Flexibility

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem. We are concerned here with online versions of this problem defi ned on metric spaces. One novel aspect in the paper is the introduction of a sound theoretical model to incorporate "yes-no" decisions on which requests to serve, together with an online strategy to visit the accepted requests. In order to do so, we assume that there is a penalty for not serving a request. Requests for visit of points in the metric space are revealed over time to a server, initially at a given origin, who must decide in an online fashion which requests to serve in order to minimize the time to serve all accepted requests plus the sum of the penalties associated with the rejected requests. We first look at the special case of the non-negative real line. After providing a polynomial time algorithm for the online version of the problem, we propose and prove the optimality of a 2-competitive polynomial time online algorithm based on re-optimization approaches. We also consider the impact of advanced information (lookahead) on this optimal competitive ratio. We then consider the generalizations of these results to the case of the real line. We show that the previous algorithm can be extended to an optimal 2-competitive online algorithm. Finally we consider the case of a general metric space and propose an original c-competitive online algorithm, where .... We also give a polynomial-time (1:5p + 1)-competitive online algorithm which uses a polynomial-time -approximation for the online problem.United States. Office of Naval Research (ONR grant N00014-09-1-0326

Online optimization problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 149-153).In this thesis, we study online optimization problems in routing and allocation applications. Online problems are problems where information is revealed incrementally, and decisions must be made before all information is available. We design and analyze algorithms for a variety of online problems, including traveling salesman problems with rejection options, generalized assignment problems, stochastic matching problems, and resource allocation problems. We use worst case competitive ratios to analyze the performance of proposed algorithms. We begin our study with online traveling salesman problems with rejection options where acceptance/rejection decisions are not required to be explicitly made. We propose an online algorithm in arbitrary metric spaces, and show that it is the best possible. We then consider problems where acceptance/rejection decisions must be made at the time when requests arrive. For dierent metric spaces, we propose dierent online algorithms, some of which are asymptotically optimal. We then consider generalized online assignment problems with budget constraints and resource constraints. We first prove that all online algorithms are arbitrarily bad for general cases. Then, under some assumptions, we propose, analyze, and empirically compare two online algorithms, a greedy algorithm and a primal dual algorithm. We study online stochastic matching problems. Instances with a fixed number of arrivals are studied first. A novel algorithm based on discretization is proposed and analyzed for unweighted problems. The same algorithm is modified to accommodate vertex-weighted cases. Finally, we consider cases where arrivals follow a Poisson Process. Finally, we consider online resource allocation problems. We first consider the problems with free but fixed inventory under certain assumptions, and present near optimal algorithms. We then relax some unrealistic assumptions. Finally, we generalize the technique to problems with flexible inventory with non-decreasing marginal costs.by Xin Lu.Ph.D

Online Optimization with Lookahead

The main contributions of this thesis consist of the development of a systematic groundwork for comprehensive performance evaluation of algorithms in online optimization with lookahead and the subsequent validation of the presented approaches in theoretical analysis and computational experiments