Philip Kilby

Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.

The systems integration problem

Abstract The systems integration problem, defined as coupling GIS and other systems, is analysed by the use of two models based on database and federated database reference models. A three-schema model of a system enables the classification of incompatibilities between systems in terms of differences in external, conceptual and internal schemas. A systems reference model identifies transformation, constructor and accessor operations as the basic mechanisms to overcome these differences. The possible architectures of integrated systems are defined in terms of the presence of these operations and their general strengths and weaknesses are assessed.

A Comparison of Traditional and Constraint-based HeuristicMethods on Vehicle Routing Problems with Side Constraints

The vehicle routing problem (VRP) is a variantof the familiar travelling salesperson problem (TSP). In theVRP we are to perform a number of visits, using a number of vehiclesof limited capacity, while typically minimizing the distancetravelled. VRPs can be complicated by imposing time windows ordeadlines on visits, sequencing constraints between visits, andso on. In this paper, we use a constraint-based toolkit for solvingvehicle routing problems to study the effect of different heuristictechniques. We investigate the performance of a number of constructionand improvement techniques, and show that as the size of thesolution space is decreased through addition of side constraints,certain conventional techniques fail while constraint directedtechniques continue to perform acceptably. This suggests thatconstraint programming techniques are particularly suited toVRPs with side constraints.

An automated itinerary planning system for holiday travel

This article describes a prototype travel recommender system called the Electronic Travel Planner (ETP), which prepares travel itineraries for tourists. The system is driven by models of a traveler’s preferences and requirements, and makes reference to databases containing information pertaining to tourism and travel products. Its main tasks are to select destinations for the traveler to visit, to decide which tours or attractions are to be taken, and to compose a detailed itinerary linking up the chosen components. These tasks entail difficult optimization problems, which the prototype addresses by means of an heuristic problem-solving framework. Computational tests confirm the effectiveness of the methods used, and suggest that an automated approach will be feasible in full-scale travel planning applications.

CP Methods for Scheduling and Routing with Time-Dependent Task Costs

A particularly difficult class of scheduling and routing problems involves an objective that is a sum of time-varying action costs, which increases the size and complexity of the problem. Solve-and-improve approaches, which find an initial solution for a simplified model and improve it using a cost function, and Mixed Integer Programming (MIP) are often used for solving such problems. However, Constraint Programming (CP), particularly with Lazy Clause Generation (LCG), has been found to be faster than MIP for some scheduling problems with time-varying action costs. In this paper, we compare CP and LCG against a solve-and-improve approach for two recently introduced problems in maritime logistics with time-varying action costs: the Liner Shipping Fleet Repositioning Problem (LSFRP) and the Bulk Port Cargo Throughput Optimisation Problem (BPCTOP). We present a novel CP model for the LSFRP, which is faster than all previous methods and outperforms a simplified automated planning model without time-varying costs. We show that a LCG solver is faster for solving the BPCTOP than a standard finite domain CP solver with a simplified model. We find that CP and LCG are effective methods for solving scheduling problems, and are worth investigating for other scheduling and routing problems that are currently being solved using MIP or solve-and-improve approaches.

Static and Dynamic Order Scheduling for Recreational Rental Vehicles at Tourism Holdings Limited

Tourism Holdings Limited (THL), with 14 locations in Australia and New Zealand, operates a fleet of approximately 4,000 recreational rental vehicles of many types. It allocates vehicles to bookings centrally. If demand for a particular vehicle type at a location exceeds supply, THL may substitute vehicles of similar types or relocate vehicles from other locations to the location that needs the vehicles. The static problem that THL faces daily is to determine a vehicle schedule that minimizes the tangible and intangible costs of such substitutions and relocations. The dynamic problem is to determine---sometimes as the customer waits---whether a vehicle will be available to cover a potential booking and to incorporate that booking into the schedule. The Commonwealth Scientific and Industrial Research Organisation (CSIRO) has researched, developed, and supplied software, VASS and D-VASS, to solve the static and dynamic aspects of THLs schedule creation and maintenance. This paper describes the THL problem, the systems that CSIRO implemented, and how THL embedded these systems into its operations.

Scheduling patrol boats and crews for the Royal Australian Navy

The Royal Australian Navys Patrol Boat Force carries out essential tasks in the surveillance, policing and defence of Australias coastal waters. To help the Navy make efficient use of a new generation of boats, the authors have developed optimization procedures to schedule the activities of the boats and their crews. The procedures—embodied in a software system called CBM (‘Crews, Boats, Missions’)—use simulated annealing and specialized heuristic techniques within a multi-stage problem-solving framework. Tests show that CBM is reliable in terms of solution quality, and flexible with respect to the range of scheduling conditions applied. CBM has proved valuable to the Navy as an investigatory tool, and it is planned that it should be adapted for operational use, as part of a decision support system to aid in the ongoing management of patrol boat operations.

Dynamic scheduling of recreational rental vehicles with revenue management extensions

AbstractThe rental fleet scheduling problem (RFSP) arises in vehicle-rental operations that offer a wide variety of vehicle types to customers, and allow a rented vehicle to ‘migrate’ to a setdown depot other than the pickup depot. When there is a shortage of vehicles of a particular type at a depot, vehicles may be relocated to that depot, or vehicles of similar types may be substituted. The RFSP involves assigning vehicles to rentals so as to minimise the costs of these operations, and arises in both static and online contexts. The authors have adapted a well-known assignment algorithm for application in the online context. In addition, a network-flow algorithm with more comprehensive coverage of problem conditions is used to investigate the determination of rental pricing using revenue management principles. The paper concludes with an outline of the algorithms’ use in supporting the operations of a large recreational vehicle rental company.

dMap: A Low-Cost Distributed Mapping Concept for Future Road Asset Management

Road assets including road signs and utility poles are among the objects that are closely monitored by government bodies and transportation authorities in many countries. This paper presents a new approach to collect and analyse the information needed for road asset management and other digital cartography applications. Instead of using dedicated surveying vehicles, skilled drivers and high quality sensors that are common for traditional data collection, it envisions an infra-structure in which the data collection is done through cheap sensors that mainstream consumer cars can host in the near future. In order to investigate the new design, a prototype sensor named dSensor has been developed, each to be mounted on public transport vehicles, to collect information from the road scene. Each dSensor has three cameras, wireless modem, Global Positioning Systems (GPS), accelerometer, gyroscope, magnetometer and a laptop. A collection of vehicles equipped with dSensors and a server constitute the distributed mapping system called dMap for road asset management. The dMap design supports many features of an ideal road asset find and replace management system and in comparison to similar solutions or concepts for road asset management, the dMap is cost effective with high quality information particularly on matters such as update rate.

Benders Decomposition for the Design of a Hub and Shuttle Public Transit System

The BusPlus project aims at improving the off-peak hours public transit service in Canberra, Australia. To address the difficulty of covering a large geographic area, proposes a hub and shuttle model consisting of a combination of a few high-frequency bus routes between key hubs and a large number of shuttles that bring passengers from their origin to the closest hub and take them from their last bus stop to their destination. This paper focuses on the design of the bus network and proposes an efficient solving method to this multimodal network design problem based on the Benders decomposition method. Starting from a mixed-integer programming (MIP) formulation of the problem, the paper presents a Benders decomposition approach using dedicated solution techniques for solving independent subproblems, Pareto-optimal cuts, cut bundling, and core point update. Computational results on real-world data from Canberra’s public transit system justify the design choices and show that the approach outperforms the MIP...