Routing and scheduling of vehicles and crews: The state of the art

This is the second half of a two-part survey on arc routing problems. The first part appeared in the March-April 1995 issue of this journal. Here, the rural postman problem RPP is reviewed. The paper is organized as follows: applications, the undirected RPP, the directed RPP, the stacker crane problem, and the capacitated arc routing problem.

Arc Routing Problems, Part II: The Rural Postman Problem

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.

Routing problems: A bibliography

The Capacitated Arc Routing Problem arises in several contexts where streets or roads must be traversed for maintenance purposes or for the delivery of services. A tabu search is proposed for this difficult problem. On benchmark instances, it outperforms all known heuristics and often produces a proven optimum.

A Tabu Search Heuristic for the Capacitated Arc Routing Problem

The Capacitated Arc Routing Problem or CARP arises in applications like waste collection or winter gritting Metaheuristics are tools of choice for solving large instances of this NP-hard problem The paper presents basic components that can be combined into powerful memetic algorithms (MAs) for solving an extended version of the CARP (ECARP) The best resulting MA outperforms all known heuristics on three sets of benchmark files containing in total 81 instances with up to 140 nodes and 190 edges In particular, one open instance is broken by reaching a tight lower bound designed by Belenguer and Benavent, 26 best-known solutions are improved, and all other best-known solutions are retrieved

/pdf/competitive-memetic-algorithms-for-arc-routing-problems-2bkcwcbvyz.pdf

Competitive Memetic Algorithms for Arc Routing Problems

Computational experiments with algorithms for a class of routing problems

Miles-in-Trail (MIT) restrictions are one of the most commonly used traffic management initiatives. They are most often used to manage arrival flows into airports. Traffic managers often use MIT restrictions to protect a destination airport, particularly when capacity has been reduced due to weather or during periods of high volume. They also use MIT restrictions to smooth out flows to support merging streams. Currently, traffic managers must rely largely on experience to determine if a proposed MIT restriction will have the intended effect on traffic demand, as no tool is available to specifically assess the impact of proposed MIT restrictions. The inability to assess the impact of such a widely used traffic management initiative can sometimes result in inefficient restrictions that increase impacts on flights as well as controller effort. The MITRE Corporation's CAASD has developed a prototype MIT Impact Assessment (MIA) capability which allows traffic managers to evaluate the impact of proposed MIT restrictions on resources and flights before implementing them. This paper proposes an operational concept for arrival MIT restrictions using the MIA capability. This paper also provides an analysis to identify the type of situations when the proposed MIA capability can be used in the future to employ less restrictive MIT restrictions and to determine the impact of MIT restrictions on flying times.

/pdf/the-miles-in-trail-impact-assessment-capability-19it99il7x.pdf

The Miles-in-Trail Impact Assessment Capability

When airspace is partially or completely blocked by severe weather, a major challenge for airspace managers and users is the creation and selection of viable alternate routing for air traffic. Research is underway for an automate d capability to help to meet this challenge. An important component of such a capability is the quantification of the attributes of operationally-acceptable routes. In this paper we describe two such quantifications, for route lateral deviation, and for flow preference.

/pdf/quantifying-desirable-air-route-attributes-for-a-reroute-5ahktudi8j.pdf

Quantifying Desirable Air Route Attributes for a Reroute Generation Capability

Decision Support for Complex Traffic Flow Management Actions: Integrated Impact Assessment

A network queuing model of the National Airspace System has been developed to support research into a strategic air traffic flow management capability. One of the challenges in the execution of the model is the size of the network – the computing resources required when modeling the entire United States are immense. As a way to reduce the network size, we investigate route clustering, i.e., grouping similar routes to reduce the number of paths between two airports. Clustering routes comes at a cost: as the number of clusters falls, the with-in cluster variability rises, and the solution quality is diminished. A trade-off curve for solution quality vs. cluster variability is developed for a sample problem involving seven major airports. I. Introduction/Background A prototype capability for strategic air traffic flow management is undergoing research and development. The capability, called Flow Contingency Management (FCM), will supply automated decision support for what currently is a mostly manual process. 1 It is recognized that strategic decisions made with a 2- to 24-hour time horizon will likely improve air traffic flows in the National Airspace System (NAS) by averting large-scale traffic congestion due to weather. The Next-Generation Air Transportation System (NextGen) mid-term concept reflects the need for this type of capability. Basic functionality has been developed for the prototype, including the representation of weather and traffic forecasts, and the integration of the two forecasts for predictions of significant impact. At the operative look-ahead times, there is significant uncertainty in the forecasts of both weather and traffic and, therefore, it is not appropriate to represent traffic at the level of individual flights. Rather, an aggregate model has been developed whereby traffic is represented as flows (an undifferentiated count of flights progressing in quarter-hour steps) in a queuing network. An initial formulation of such a model uses historical aircraft routings, one-day-prior filed flight routes, and “dayof” filed and predicted counts as input to a regression model to create the demand on a network of routes between airports. In the network, routes are represented by sequences of airspace sectors, 5 demand is expressed as the fraction per route of total flow between airports, and airports are represented as source and sink nodes. The queuing network model operates by associating air traffic demand with a sequence of sectors, and advancing time in quarterhour increments. Sectors have a finite capacity, and flights may queue before transiting a sector, if demand would exceed capacity. In prior work, it was found that clustering airports reduced the network size and complexity, as well as the model’s run-time. 2 In this paper, we explore another means of reducing network size: route clustering, i.e., grouping of similar routes between airports. Assessing similarity of routes requires a similarity/difference measure and we propose the use of a specialized algorithm called “edit distance,” appropriate for lexical string representation, i.e., the sequence of sectors in a route. The paper is organized as follows. The next section describes the clustering algorithm: edit distance, similarity/difference assessment, and selection of a clustering method. Subsequent sections examine initial results, selection of a similarity threshold, and trading-off regression model error and resultant network size. A final section summarizes findings and suggests a next step in the analysis.

/pdf/air-route-clustering-for-a-queuing-network-model-of-the-2s7mzzckfi.pdf

James DeArmon

Papers

Computational experiments with algorithms for a class of routing problems

The Miles-in-Trail Impact Assessment Capability

Quantifying Desirable Air Route Attributes for a Reroute Generation Capability

Decision Support for Complex Traffic Flow Management Actions: Integrated Impact Assessment

Air Route Clustering for a Queuing Network Model of the National Airspace System