Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots

Dial-a-ride problems are concerned with the design of efficient vehicle routes for transporting individual persons from specific origin to specific destination locations. In real-life this operational planning problem is often complicated by several factors. Users may have special requirements (e.g. to be transported in a wheelchair) while service providers operate a heterogeneous fleet of vehicles from multiple depots in their service area. In this paper, a general dial-a-ride problem in which these three real-life aspects may simultaneously be taken into account is introduced: the Multi-Depot Heterogeneous Dial-A-Ride Problem (MD-H-DARP). Both a three- and two-index formulation are discussed. A branch-and-cut algorithm for the standard dial-a-ride problem is adapted to exactly solve small problem instances of the MD-H-DARP. To be able to solve larger problem instances, a new deterministic annealing meta-heuristic is proposed. Extensive numerical experiments are presented on different sets of benchmark instances for the homogeneous and the heterogeneous single depot dial-a-ride problem. Instances for the MD-H-DARP are introduced as well. The branch-and-cut algorithm provides considerably better results than an existing algorithm which uses a less compact formulation. All seven previously unsolved benchmark instances for the heterogeneous dial-a-ride problem could be solved to optimality within a matter of seconds. While computation times of the exact algorithm increase drastically with problem size, the proposed meta-heuristic algorithm provides near-optimal solutions within limited computation time for all instances. Several best known solutions for unsolved instances are improved and the algorithm clearly outperforms current state-of-the-art heuristics for the homogeneous and heterogeneous dial-a-ride problem, both in terms of solution quality and computation time.     

Partial recharge strategies for the electric vehicle routing problem with time windows

The Electric Vehicle Routing Problem with Time Windows (EVRPTW) is an extension to the well-known Vehicle Routing Problem with Time Windows (VRPTW) where the fleet consists of electric vehicles (EVs). Since EVs have limited driving range due to their battery capacities they may need to visit recharging stations while servicing the customers along their route. The recharging may take place at any battery level and after the recharging the battery is assumed to be full. In this paper, we relax the full recharge restriction and allow partial recharging (EVRPTW-PR), which is more practical in the real world due to shorter recharging duration. We formulate this problem as a 0–1 mixed integer linear program and develop an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it efficiently. We apply several removal and insertion mechanisms by selecting them dynamically and adaptively based on their past performances, including new mechanisms specifically designed for EVRPTW and EVRPTW-PR. These new mechanisms include the removal of the stations independently or along with the preceding or succeeding customers and the insertion of the stations with determining the charge amount based on the recharging decisions. We test the performance of ALNS by using benchmark instances from the recent literature. The computational results show that the proposed method is effective in finding high quality solutions and the partial recharging option may significantly improve the routing decisions.     

Solving the Fleet Size and Mix Vehicle Routing Problem with Time Windows via Adaptive Memory Programming

This paper presents a novel Adaptive Memory Programming (AMP) solution approach for the Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW). The FSMVRPTW seeks to design a set of depot returning vehicle routes to service a set of customers with known demands, for a heterogeneous fleet of vehicles with different capacities and fixed costs. Each customer is serviced only once by exactly one vehicle, within fixed time intervals that represent the earliest and latest times during the day that service can take place. The objective is to minimize the total transportation costs, or similarly to determine the optimal fleet composition and dimension following least cost vehicle routes. The proposed method utilizes the basic concept of an AMP solution framework equipped with a probabilistic semi-parallel construction heuristic, a novel solution re-construction mechanism, an innovative Iterated Tabu Search algorithm tuned for intensification local search and frequency-based long term memory structures. Computational experiments on well-known benchmark data sets illustrate the efficiency and effectiveness of the proposed method. Compared to the current state-of-the-art, the proposed method improves the best reported cumulative and mean results over most problem instances with reasonable computational requirements.     

The fleet size and mix pollution-routing problem

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO₂ emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one.     

带时间窗的混和车辆路径问题的优化算法研究

文章针对带时间窗约束的混合车辆路径问题的特点,建立了带时间窗的混合车辆路径问题的数学模型,并设计了变邻域禁忌搜索算法对该问题进行求解。通过标准算例测试及与现有文献计算结果的比较,验证了该算法的有效性。     

A real-life Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet: Formulation and Adaptive Large Neighborhood Search based Matheuristic

In this paper, a new rich Vehicle Routing Problem that could arise in a real life context is introduced and formalized: the Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet. The goal of the problem is to minimize the total delivery cost. A heterogeneous fleet composed of vehicles with different capacity, characteristics (i.e. refrigerated vehicles) and hourly costs is considered. A limit on the maximum route duration is imposed. Unlike what happens in classical multi-depot VRP, not every customer may/will be served by all the vehicles or from all the depots. The planning horizon, as in most real life applications, consists of multiple periods, and the period in which each route is performed is a variable of the problem. The set of periods, within the time horizon, in which the delivery may be carried out is known for each customer. A Mixed Integer Programming (MIP) formulation for MDMPVRPHF is presented in this paper, and an Adaptive Large Neighborhood Search (ALNS) based Matheuristic approach is proposed, in which different destroy operators are defined. Computational results, pertaining to realistic instances, which show the effectiveness of the proposed method, are provided.     

Application specific instance generator and a memetic algorithm for capacitated arc routing problems

Capacitated arc routing problem (CARP) is a well known combinatorial problem that requires identifying minimum total distance traveled by a fleet of vehicles in order to serve a set of roads without violating the vehicles’ capacity constraints. A number of optimization algorithms have been proposed over the years to solve basic CARPs and their performance have been analyzed using selected benchmark suites available in literature. From an application point of view, there is a need to assess the performance of algorithms on specific class of instances that resemble realistic applications, e.g., inspection of electric power lines, garbage collection, winter gritting etc. In this paper we introduce a benchmark generator that controls the size and complexity of the underlying road network resembling a target application. It allows generation of road networks with multiple lanes, one-way/two-way roads and varying degree of connectedness. Furthermore, an algorithm capable of solving real life CARP instances efficiently within a fixed computational budget of evaluations is introduced. The proposed algorithm, referred to as MA-CARP, is a memetic algorithm embedded with a similarity based parent selection scheme inspired by multiple sequence alignment, hybrid crossovers and a modified neighborhood search to improve its rate of convergence. The mechanism of test instance generation is presented for three typical scenarios, namely, inspection of electric power lines, garbage collection and winter gritting. The code for the generator is available from http://seit.unsw.adfa.edu.au/research/sites/mdo/Research-Data/InstanceGenerator.rar. The performance of the algorithm is compared with a state-of-the-art algorithm for three generated benchmarks. The results obtained using the proposed algorithm are better for all the above instances clearly highlighting its potential for solving CARP problems.     

The impact of depot location,fleet composition and routing on emissions in city logistics

This paper investigates the combined impact of depot location, fleet composition and routing decisions on vehicle emissions in city logistics. We consider a city in which goods need to be delivered from a depot to customers located in nested zones characterized by different speed limits. The objective is to minimize the total depot, vehicle and routing cost, where the latter can be defined with respect to the cost of fuel consumption and CO₂ emissions. A new powerful adaptive large neighborhood search metaheuristic is developed and successfully applied to a large pool of new benchmark instances. Extensive analyses are performed to empirically assess the effect of various problem parameters, such as depot cost and location, customer distribution and heterogeneous vehicles on key performance indicators, including fuel consumption, emissions and operational costs. Several managerial insights are presented.     

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.     

A scenario-based planning for the pickup and delivery problem with time windows,scheduled lines and stochastic demands

The Pickup and Delivery Problem with Time Windows, Scheduled Lines and Stochastic Demands (PDPTW-SLSD) concerns scheduling a set of vehicles to serve a set of requests, whose expected demands are known in distribution when planning, but are only revealed with certainty upon the vehicles’ arrival. In addition, a part of the transportation plan can be carried out on limited-capacity scheduled public transportation line services. This paper proposes a scenario-based sample average approximation approach for the PDPTW-SLSD. An adaptive large neighborhood search heuristic embedded into sample average approximation method is used to generate good-quality solutions. Computational results on instances with up to 40 requests (i.e., 80 locations) reveal that the integrated transportation networks can lead to operational cost savings of up to 16% compared with classical pickup and delivery systems.     

The time-dependent pollution-routing problem

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.     

A disjunctive convex programming approach to the pollution-routing problem

The pollution-routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of values. In this paper, we keep speed as a continuous decision variable within an interval and propose new formulations for the PRP. In particular, we build two mixed-integer convex optimization models for the PRP, by employing tools from disjunctive convex programming. These are the first arc-based formulations for the PRP with continuous speed. We also derive several families of valid inequalities to further strengthen both models. We test the proposed formulations on benchmark instances. Some instances are solved to optimality for the first time.     

Free-floating bike sharing: Solving real-life large-scale static rebalancing problems

Free-floating bike sharing (FFBS) is an innovative bike sharing model. FFBS saves on start-up cost, in comparison to station-based bike sharing (SBBS), by avoiding construction of expensive docking stations and kiosk machines. FFBS prevents bike theft and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. However, like SBBS, the success of FFBS depends on the efficiency of its rebalancing operations to serve the maximal demand as possible.Bicycle rebalancing refers to the reestablishment of the number of bikes at sites to desired quantities by using a fleet of vehicles transporting the bicycles. Static rebalancing for SBBS is a challenging combinatorial optimization problem. FFBS takes it a step further, with an increase in the scale of the problem. This article is the first effort in a series of studies of FFBS planning and management, tackling static rebalancing with single and multiple vehicles. We present a Novel Mixed Integer Linear Program for solving the Static Complete Rebalancing Problem. The proposed formulation, can not only handle single as well as multiple vehicles, but also allows for multiple visits to a node by the same vehicle. We present a hybrid nested large neighborhood search with variable neighborhood descent algorithm, which is both effective and efficient in solving static complete rebalancing problems for large-scale bike sharing programs.Computational experiments were carried out on the 1 Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP) instances used previously in the literature and on three new sets of instances, two (one real-life and one general) based on Share-A-Bull Bikes (SABB) FFBS program recently launched at the Tampa campus of University of South Florida and the other based on Divvy SBBS in Chicago. Computational experiments on the 1-PDTSP instances demonstrate that the proposed algorithm outperforms a tabu search algorithm and is highly competitive with exact algorithms previously reported in the literature for solving static rebalancing problems in SBSS. Computational experiments on the SABB and Divvy instances, demonstrate that the proposed algorithm is able to deal with the increase in scale of the static rebalancing problem pertaining to both FFBS and SBBS, while deriving high-quality solutions in a reasonable amount of CPU time.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

The load-dependent vehicle routing problem and its pick-up and delivery extension

The present paper examines a Vehicle Routing Problem (VRP) of major practical importance which is referred to as the Load-Dependent VRP (LDVRP). LDVRP is applicable for transportation activities where the weight of the transported cargo accounts for a significant part of the vehicle gross weight. Contrary to the basic VRP which calls for the minimization of the distance travelled, the LDVRP objective is aimed at minimizing the total product of the distance travelled and the gross weight carried along this distance. Thus, it is capable of producing sensible routing plans which take into account the variation of the cargo weight along the vehicle trips. The LDVRP objective is closely related to the total energy requirements of the vehicle fleet, making it a credible alternative when the environmental aspects of transportation activities are examined and optimized. A novel LDVRP extension which considers simultaneous pick-up and delivery service is introduced, formulated and solved for the first time. To deal with large-scale instances of the examined problems, we propose a local-search algorithm. Towards an efficient implementation, the local-search algorithm employs a computational scheme which calculates the complex weighted-distance objective changes in constant time. Solution results are presented for both problems on a variety of well-known test cases demonstrating the effectiveness of the proposed solution approach. The structure of the obtained LDVRP and VRP solutions is compared in pursuit of interesting conclusions on the relative suitability of the two routing models, when the decision maker must deal with the weighted distance objective. In addition, results of a branch-and-cut procedure for small-scale instances of the LDVRP with simultaneous pick-ups and deliveries are reported. Finally, extensive computational experiments have been performed to explore the managerial implications of three key problem characteristics, namely the deviation of customer demands, the cargo to tare weight ratio, as well as the size of the available vehicle fleet.     

Developing green fleet management strategies: Repair/retrofit/replacement decisions under environmental regulation

The considerable cost of maintaining large fleets has generated interest in cost minimization strategies. With many related decisions, numerous constraints, and significant sources of uncertainty (e.g. vehicle breakdowns), fleet managers face complex dynamic optimization problems. Existing methodologies frequently make simplifying assumptions or fail to converge quickly for large problems. This paper presents an approximate dynamic programming approach for making vehicle purchase, resale, and retrofit decisions in a fleet setting with stochastic vehicle breakdowns. Value iteration is informed by dual variables from linear programs, as well as other bounds on vehicle shadow prices. Sample problems are based on a government fleet seeking to comply with emissions regulation. The model predicts the expected cost of compliance, the rules the fleet manager will use in deciding how to comply, and the regulation’s impact on the value of vehicles in the fleet. Stricter regulation lowers the value of some vehicle categories while raising the value of others. Such insights can help guide regulators, as well as the fleet managers they oversee. The methodologies developed could be applied more broadly to general multi-asset replacement problems, many of which have similar structures.     

Fleet scheduling and dispatching for demand-responsive passenger services

This paper describes a software system designed to manage the deployment of a fleet of demand-responsive passenger vehicles such as taxis or variably routed buses. Multiple modes of operation are supported both for the fleet and for individual vehicles. Booking requests can be immediate (i.e. with zero notice) or in advance of travel. An initial implementation is chosen for each incoming request, subject to time-window and other constraints, and with an objective of minimising additional travel time or maximising a surrogate for future fleet capacity. This incremental insertion scheme is supplemented by post-insert improvement procedures, a periodically executed steepest-descent improvement procedure applied to the fleet as a whole, and a “rank-homing” heuristic incorporating information about future patterns of demand. A simple objective for trip-insertion and other scheduling operations is based on localised minimisation of travel time, while an alternative incorporating occupancy ratios has a more strategic orientation. Apart from its scheduling functions, the system includes automated vehicle dispatching procedures designed to achieve a favourable combination of customer service and efficiency of vehicle deployment. Provision is made for a variety of contingencies, including travel slower or faster than expected, unexpected vehicle locations, vehicle breakdowns and trip cancellations. Simulation tests indicate that the improvement procedures yield substantial efficiencies over more naı̈ve scheduling methods and that the system will be effective in real-time applications.     

Short range transit planning in Cairo

This paper describes an approach to short‐range planning that was developed to analyze and suggest improvements to the existing transit system serving metropolitan Cairo. The methodology is based on a corridor‐by‐corridor analysis which not only brings the scale of analysis down to a level which is necessary to address operational issues, but also results in a technology transfer strategy which allows the local planners to apply and test planning techniques in one corridor while more advanced techniques are developed for another. Procedures using the results of a system‐wide on‐board transit survey are developed to allocate the bus fleet to the existing bus network, identify new express services, and identify new direct services. Because the effectiveness of procedures used in short‐range transit planning depends on the existence of accurate data, and given the resources required for a large‐scale survey, the development of planning procedures based on a continuing monitoring program is also recommended. This paper concludes that although techniques using on‐board surveys are limited in their applicability, the corridor‐based approach to planning is sound.

     

Optimal scheduling of a taxi fleet with mixed electric and gasoline vehicles to service advance reservations

This study addresses the problem of scheduling a fleet of taxis that are appointed to solely service customers with advance reservations. In contrast to previous studies that have dealt with the planning and operations of a taxi fleet with only electric vehicles (EVs), we consider that most taxi companies may have to operate with fleets comprised of both gasoline vehicles (GVs) and plug-in EVs during the transition from GV to (complete) EV taxi fleets. This paper presents an innovative multi-layer taxi-flow time-space network which effectively describes the movements of the taxis in the dimensions of space and time. An optimization model is then developed based on the time-space network to determine an optimal schedule for the taxi fleet. The objective is to minimize the total operating cost of the fleet, with a set of operating constraints for the EVs and GVs included in the model. Given that the model is formulated as an integer multi-commodity network flow problem, which is characterized as NP-hard, we propose two simple but effective decomposition-based heuristics to efficiently solve the problem with practical sizes. Test instances generated based on the data provided by a Taiwan taxi company are solved to evaluate the solution algorithms. The results show that the gaps between the objective values of the heuristic solutions and those of the optimal solutions are less than 3%, and the heuristics require much less time to obtain the good quality solutions. As a result, it is shown that the model, coupled with the algorithms, can be an effective planning tool to assist the company in routing and scheduling its fleet to service reservation customers.     

Robo-Taxi service fleet sizing: assessing the impact of user trust and willingness-to-use

The first commercial fleets of Robo-Taxis will be on the road soon. Today important efforts are made to anticipate future Robo-Taxi services. Fleet size is one of the key parameters considered in the planning phase of service design and configuration. Based on multi-agent approaches, the fleet size can be explored using dynamic demand response simulations. Time and cost are the most common variables considered in such simulation approaches. However, personal taste variation can affect the demand and consequently the required fleet size. In this paper, we explore the impact of user trust and willingness-to-use on the Robo-Taxi fleet size. This research is based upon simulating the transportation system of the Rouen-Normandie metropolitan area in France using MATSim, a multi-agent activity-based simulator. A local survey is made in order to explore the variation of user trust and their willingness-to-use future Robo-Taxis according to the sociodemographic attributes. Integrating survey data in the model shows the significant importance of traveler trust and willingness-to-use varying the Robo-Taxi use and the required fleet size.