Classical Vehicle Routing Problem Research Articles

On the Use of Learnheuristics in Vehicle Routing Optimization Problems with Dynamic Inputs

Freight transportation is becoming an increasingly critical activity for enterprises in a global world. Moreover, the distribution activities have a non-negligible impact on the environment, as well as on the citizens’ welfare. The classical vehicle routing problem (VRP) aims at designing routes that minimize the cost of serving customers using a given set of capacitated vehicles. Some VRP variants consider traveling times, either in the objective function (e.g., including the goal of minimizing total traveling time or designing balanced routes) or as constraints (e.g., the setting of time windows or a maximum time per route). Typically, the traveling time between two customers or between one customer and the depot is assumed to be both known in advance and static. However, in real life, there are plenty of factors (predictable or not) that may affect these traveling times, e.g., traffic jams, accidents, road works, or even the weather. In this work, we analyze the VRP with dynamic traveling times. Our work assumes not only that these inputs are dynamic in nature, but also that they are a function of the structure of the emerging routing plan. In other words, these traveling times need to be dynamically re-evaluated as the solution is being constructed. In order to solve this dynamic optimization problem, a learnheuristic-based approach is proposed. Our approach integrates statistical learning techniques within a metaheuristic framework. A number of computational experiments are carried out in order to illustrate our approach and discuss its effectiveness.

A self-adaptive evolutionary algorithm for dynamic vehicle routing problems with traffic congestion

The Dynamic Vehicle Routing Problem (DVRP) is a complex variation of classical Vehicle Routing Problem (VRP). The aim of DVRP is to find a set of routes to serve multiple customers at minimal total travelling cost while the travelling time between point to point may vary during the process because of factors like traffic congestion. To effectively handle DVRP, a good algorithm should be able to adjust itself to the changes and continuously search for the best solution under dynamic environments. Because of this dynamic nature of DVRP, evolutionary algorithms (EAs) appear highly appropriate for DVRP as they search in a parallel manner with a population of solutions. Solutions scattered over the search space can better capture the dynamic changes. Solutions for new changes are not built from scratch as they can inherit problem-specific knowledge from parent solutions. However, the performance of EA is highly dependent on the utilised configuration. To address this issue, we propose a self-adaptive EA for DVRP. The proposed EA evolves a set of configurations including parameter values, operator types, combination of operators and order of operator invocation. The configurations are then encoded into DVRP solutions. So the search can use different configuration during a search process to effectively handle the dynamic changes and guide the search process towards promising areas. Two well known routing problems with traffic congestion, vehicle routing and the travelling salesman, were used to evaluate the performance of the proposed EA. The results demonstrate that under same conditions on both problems the proposed self-adaptive EA is better than standard EA and other algorithms from literature.

The Mobile Charging Vehicle Routing Problem with Time Windows and Recharging Services.

For the environmental friendliness of the technology on battery electric vehicles, there is growing attention on it. However, the market share of battery electric vehicles remains low due to the range anxiety. As a remedy, the mobile charging services could offer charging service at any time or locations requested. For profitability of the services, the operator should route the charging vehicles in a more efficient manner. For this consideration, we formulate the mobile charging vehicle routing problem as a mixed integer linear program based on the classical vehicle routing problem with time windows. To demonstrate the model, test instances are designed and computational results are presented. In order to examine the change of the number of mobile charging vehicles and travel distance, sensitivity analyses, such as battery capacity and recharging rate, are performed. The results show that larger battery capacity, quicker charging rate, or higher service efficiency could decrease the number of mobile charging vehicles and total traveled distances, respectively.

A simheuristic approach for the two-dimensional vehicle routing problem with stochastic travel times

The two-dimensional vehicle routing problem (2L-VRP) is a realistic extension of the classical vehicle routing problem in which customers’ demands are composed by sets of non-stackable items. Examples can be found in real-life applications such as the transportation of furniture or industrial machinery. Often, it is necessary to consider stochastic travel times due to traffic conditions or customers availability. However, there is a lack of works discussing stochastic versions of the 2L-VRP. This paper offers a model of the 2L-VRP with stochastic travel times that also includes penalty costs generated by overtime. To solve this stochastic and non-smooth version of the 2L-VRP, a hybrid simheuristic algorithm is proposed. Our approach combines Monte Carlo simulation, an iterated local search framework, and biased-randomised routing and packing heuristics. Our algorithm is tested on an extensive benchmark, which extends the deterministic one for the 2L-VRP with unrestricted and non-oriented loading.

A constraint relaxation-based algorithm for the load-dependent vehicle routing problem with time windows

We introduce the load-dependent vehicle routing problem with time windows (LDVRPTW) in this paper. Transportation costs in this new problem, unlike those in the classical vehicle routing problem with time windows (VRPTW), are calculated based on not only the travel distances but also the vehicular loads on travel arcs. To solve this challenging NP-hard problem, we design a new constraint relaxation-based algorithm. In the proposed algorithm, a new constraint relaxation is introduced, i.e., some clients are not visited by a real vehicle and instead are entrusted to an additional virtual vehicle. Based on this relaxation, we present an effective execution scheme of local search procedures. The proposed algorithm is tested on benchmark instances of several special cases of the LDVRPTW, including the VRPTW. Numerical results for different variant problems demonstrate that the algorithm consistently yields impressive results: in particular, for one special variant, namely the fuel consumption rate considered vehicle routing problem (FCR-VRP), the algorithm improves the best-known solutions found by existing state-of-the-art methods.

A Game Theoretic Approach for the Real-Life Multiple-Criterion Vehicle Routing Problem With Multiple Time Windows

This paper presents a new framework for the optimization of real-life multiple-objective vehicle routing problems with multiple time windows. This framework uses a hybrid variable neighborhood tabu search heuristic that chooses Pareto nondominated solutions from the search space of solutions that satisfy a set of Nash equilibrium conditions for a multiple-agent game theory model. Even though the framework is general and can tackle different classes of vehicle routing problems, it is herein tested on three objectives: minimizing the total travel cost (expressed in time units), maximizing the minimal customers’ utility, and maximizing the minimal drivers’ utility. The results on real-life instances provided by a Canadian transportation company highlight the benefits of the multiple-criteria model; an important motivation to the transportation industry for its real-life implementation.

Tabu search algorithm for the distance-constrained vehicle routing problem with split deliveries by order.

The vehicle routing problem (VRP) has a wide range of applications in the field of logistics distribution. In order to reduce the cost of logistics distribution, the distance-constrained and capacitated VRP with split deliveries by order (DCVRPSDO) was studied. We show that the customer demand, which can’t be split in the classical VRP model, can only be discrete split deliveries by order. A model of double objective programming is constructed by taking the minimum number of vehicles used and minimum vehicle traveling cost as the first and the second objective, respectively. This approach contains a series of constraints, such as single depot, single vehicle type, distance-constrained and load capacity limit, split delivery by order, etc. DCVRPSDO is a new type of VRP. A new tabu search algorithm is designed to solve the problem and the examples testing show the efficiency of the proposed algorithm. This paper focuses on constructing a double objective mathematical programming model for DCVRPSDO and designing an adaptive tabu search algorithm (ATSA) with good performance to solving the problem. The performance of the ATSA is improved by adding some strategies into the search process, including: (a) a strategy of discrete split deliveries by order is used to split the customer demand; (b) a multi-neighborhood structure is designed to enhance the ability of global optimization; (c) two levels of evaluation objectives are set to select the current solution and the best solution; (d) a discriminating strategy of that the best solution must be feasible and the current solution can accept some infeasible solution, helps to balance the performance of the solution and the diversity of the neighborhood solution; (e) an adaptive penalty mechanism will help the candidate solution be closer to the neighborhood of feasible solution; (f) a strategy of tabu releasing is used to transfer the current solution into a new neighborhood of the better solution.

Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems

This paper considers a family of Vehicle Routing Problem (VRP) variants that generalize the classical Capacitated VRP by taking into account the possibility that vehicles differ by capacity, costs, depot allocation, or even by the subset of customers that they can visit. This work proposes a Branch-Cut-and-Price algorithm that adapts advanced features found in the best performing exact algorithms for homogeneous fleet VRPs. The original contributions include: (i) the use of Extended Capacity Cuts, defined over a pseudo-polynomially large extended formulation, together with Rank-1 Cuts, defined over the Set Partitioning Formulation; (ii) the concept of vehicle-type dependent memory for Rank-1 Cuts; and (iii) a new family of lifted Extended Capacity Cuts that takes advantage of the vehicle-type dependent route enumeration. The algorithm was extensively tested in instances of the literature and was shown to be significantly better than previous exact algorithms, finding optimal solutions for many instances with up to 200 customers and also for some larger instances. A new set of benchmark instances is also proposed.

Evaluating the impact of optimization algorithms for patient transits dispatching using discrete event simulation

The on-time completion of patient transits can be identified as a bottleneck for the efficiency of health care services in major New Zealand hospitals. Delayed transits of patients between wards and treatment or diagnostic facilities lead to increasing waiting times at clinics and inefficient resource utilization (e.g. surgery teams) as appointment times are not met. Patient transits are carried out by orderlies, but in some cases require the assistance of a nurse. Ad-hoc dispatching of staff members, nurses and orderlies, to transits has been identified as one major source for delays currently observed in the system. To address this issue we present automated, optimized dispatching algorithms for staff members performing those transits. To develop these algorithms, a network formulation of the problem is introduced that is strongly related to classical vehicle routing problem with semi-soft time windows. However, the need to synchronize the routes of staff members of different types (nurses and orderlies) adds a whole new layer of complexity to the problem, as routes cannot be assessed independently. We present a set of algorithms with varying complexity, ranging from simple heuristics to the use of critical path methods to combine mixed integer formulations for the separated orderly and nurse problems. To address a transit service’s stochasticity, volatility and the resulting need for constant re-optimization, we embed the optimization algorithms in a discrete event simulation to evaluate their performance under realistic circumstances.

A hybrid of ant colony and firefly algorithms (HAFA) for solving vehicle routing problems

Vehicle routing problem is a classical NP-hard optimization problem. In the present study, we developed a hybrid algorithm namely HAFA, which incorporates certain aspects of firefly optimization (FA) and ant colony system (ACS) algorithms for solving a class of vehicle routing problems. ACS provides the basic framework to our proposed algorithm and FA has been used to search for the unexplored solution space. Furthermore, pheromone shaking process has been used in ACS to escape from local optima by avoiding pheromone stagnation on the exploited regions. The performance of proposed algorithm is compared with some of other existing meta-heuristic approaches by testing on certain standard benchmark datasets. Results shows that the proposed approach is able to find near optimal solutions with faster convergence rate as compared to other existing meta-heuristics. Furthermore, the consistency of our algorithm in finding the optimal solutions has been shown by comparing the standard deviations with other algorithms. Finally, the results demonstrate the superiority of proposed approach over other existing FA based approaches for solving such type of discrete optimization problems.

Heuristic approaches for waste containers location problem and waste collection routes optimisation in an urban area

A generalisation of the traditional waste collection vehicle routing problem with time windows (WCVRPTW) is studied in this paper. In case of the number of waste containers is limited, some collection sites requires to be visited for multiple times per day instead of one. Therefore a waste containers management study is required to economise the collection cost. We propose an approach that combines the two problems: containers location (WCLP) and the vehicle routes optimisation. Two algorithms to solve this problem are used. The first is memetic algorithm (MA) to solve the WCLP in order to get the best containers distribution. The second is an iterated local search (ILS) algorithm to solve WCVRPTW with homogenous vehicles and taking into consideration WCLP as constraint. These algorithms are evaluated on classical vehicle routing problem (VRP) instances. The experiment results prove the impact of this combining on collection routes cost in the cited case.

A novel genetic algorithm for the maximum coverage problem in the three-level supply chain network

The maximum coverage problem is one of the most functional location issues. Nowadays, organisations are seeking to increase profits and one of the competitive advantages for organisations is efficient and effective designing of supply chain network. On the other hand, given the importance of distribution planning among the levels of supply chain, vehicle routing problem needs to be explored which leads to a significant reduction in costs of supply chain network. The purpose of this research is designing a supply chain network that includes the supply, distribution centres and retailers. It should be noted that the coverage radius is defined for all distribution centres and distribution centres gives any services to retailers that is within the actual coverage. Also, this service is done on routing. Since that the classical vehicle routing problem is NP-hard, to solve the problem in small and medium sizes, we used the GAMS software. Next, genetic algorithms and simulated annealing is used to solve the problem in large size. Finally, the results have been evaluated.

Multi-type ant system algorithm for the time dependent vehicle routing problem with time windows

The time dependent vehicle routing problem with time windows (TDVRPTW) is considered. A multi-type ant system (MTAS) algorithm hybridized with the ant colony system (ACS) and the max-min ant system (MMAS) algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection (NNS) mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm's good performance with all these strategies on classic vehicle routing problem with time windows (VRPTW) benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.

Multi-objective optimization using genetic algorithm based clustering for multi- depot heterogeneous fleet vehicle routing problem with time windows

Efficient routing and scheduling of vehicles has significant economic implications for both the public and private sectors. For this purpose, we propose in this study a decision support system which aims to optimise the classical capacitated vehicle routing problem by considering the existence of different vehicle types (with distinct capacities and costs) and multiple available depots, that we call the multi-depot heterogeneous vehicle routing problem with time window (MDHVRPTW) by respecting a set of criteria including: schedules requests from clients, the heterogeneous capacity of vehicles...., and we solve this problem by proposing a new scheme based on the application of the bio-inspired genetic algorithm heuristics and by embedding a clustering algorithm within a VRPTW optimisation frame work, that we will specify later. Computational experiments with the benchmark test instances confirm that our approach produces acceptable quality solutions compared with the best previous results in similar problems in terms of generated solutions and processing time. Experimental results prove that our proposed genetic algorithm is effective in solving the MDHVRPTW problem and hence has a great potential.

Determining the vehicles routes by considering its different types and capacity (heterogeneous) to minimize the total distribution cost

Packaged sugar is one of the products in sugar cane manufacture, PT Madubaru Yogyakarta. Currently, the company deals with a high distribution cost because there is no plan to determine the vehicle route, vehicle type, and capacity for distributing the product. In this research, the optimum route of the distributing vehicles is developed. The company has three different types and capacity of vehicles: L300, HD, and PS. A problem in determining the distribution route here is called as Vehicle Routing Problem (VRP). The basic form of classic VRP says that all vehicles owned by a company have the same capacity (homogenous), meanwhile not all companies have the vehicles with same capacity. The heterogeneous variant is used to minimize the fixed cost of vehicles and distribution variant cost using Sequential Insertion Algorithm. This research has three purposes; are minimizing the number of vehicles used (NV), Total time of Completion tour (TCT) and Distribution Total Cost (TCD). The results based on a test calculation of a shipment date (August 19, 2016) of the company show three alternative solutions to distribute the packaged sugar to 12 consumers. The third alternative solution is the optimal solution and chosen as the decision result of the packaged sugar shipment. Based on the calculation results, it is needed 2 vehicles type HD with capacity 7,000 kg and type PS with capacity 3,500 kg, with total time of completion tour (TCT) is 828.49 minutes or 13.81 hours, and distribution total cost is IDR. 959,011.

A general variable neighborhood search for solving the multi-objective open vehicle routing problem

The multi-objective open vehicle routing problem (MO-OVRP) is a variant of the classic vehicle routing problem in which routes are not required to return to the depot after completing their service and where more than one objective is optimized. This work is intended to solve a more realistic and general version of the problem by considering three different objective functions. MO-OVRP seeks solutions that minimize the total number of routes, the total travel cost, and the longest route. For this purpose, we present a general variable neighborhood search algorithm to approximate the efficient set. The performance of the proposal is supported by an extensive computational experimentation which includes the comparison with the well-known multi-objective genetic algorithm NSGA-II.

An arc interdiction vehicle routing problem with information asymmetry

Abstract In some cases, due to security, sensitivity or high value, it is possible that shipments are interrupted by some adversary decision makers. The vehicle routing problem (VRP) for these kinds of shipments is some more complicated in comparison with classical VRPs, and it has been considered recently by researchers. In reality, two decision makers may have different perceptions or asymmetric information about the network. We study vehicle routing network interdiction problem with information asymmetry and investigate the benefits and risks of considering this assumption. By taking the average of benefits and risks over some network instances, it is observed that when more budgets is assigned to interdiction and the distributor estimates the interdictor's parameters with less accuracy, Network Interdiction Vehicle Routing Problem (NIVRP) with information asymmetry is able to formulate the real cases, more effectively.

A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet

We consider a family of rich vehicle routing problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments.

Field services design and management of natural gas distribution networks: a class of vehicle routing problem with time windows approach

Service operations management of metropolitan gas networks at operational level implies the optimisation of decisions related to logistic activities, taking into account multi-objectives and operational constraints. This paper proposes a metaheuristic approach for the operational planning of the daily logistic activities based on vehicle routing with time window model. Experimental results for a real planning case in a gas distribution network demonstrate the approach effectiveness.

The Vehicle Routing Problem with Release and Due Dates

A novel extension of the classical vehicle routing and scheduling problems is introduced that integrates aspects of machine scheduling into vehicle routing. Associated with each customer order is a release date that defines the earliest time that the order is available to leave the depot for delivery and a due date that indicates the time by which the order should ideally be delivered to the customer. The objective is to minimize a convex combination of the operational costs and customer service level, represented by the total distance traveled and the total weighted tardiness of delivery, respectively. A path-relinking algorithm (PRA) is proposed to address the problem, and a variety of benchmark instances are generated to evaluate its performance. The PRA exploits the efficiency and aggressive improvement of neighborhood search but relies on a new path-relinking procedure and advanced population management strategies to navigate the search space effectively. To provide a comparator algorithm to the PRA, we embed the neighborhood search into a standard iterated local search algorithm (ILS). Extensive computational experiments on the benchmark instances show that the newly defined features have a significant and varied impact on the problem, and the performance of the PRA dominates that of the ILS algorithm. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0756 .