A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem

In the heterogeneous fleet vehicle routing problem (HVRP), several different types of vehicles can be used to service the customers. The types of vehicles differ with respect to capacity, fixed cost, and variable cost. We assume that the number of vehicles of each type is fixed and equal to a constant. We must decide how to make the best use of the fixed fleet of heterogeneous vehicles.     

The fleet size and mix vehicle routing problem

In this paper, we address the problem of routing a fleet of vehicles from a central depot to customers with known demand. Routes originate and terminate at the central depot and obey vehicle capacity restrictions. Typically, researchers assume that all vehicles are identical. In this work, we relax the homogeneous fleet assumption. The objective is to determine optimal fleet size and mix by minimizing a total cost function which includes fixed cost and variable cost components. We describe several efficient heuristic solution procedures as well as techniques for generating a lower bound and an underestimate of the optimal solution. Finally, we present some encouraging computational results and suggestions for further study.     

An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem

One of the most important problems in combinatorial optimization is the well-known vehicle routing problem (VRP), which calls for the determination of the optimal routes to be performed by a fleet of vehicles to serve a given set of customers. Recently, there has been an increasing interest towards extensions of VRP arising from real-world applications. In this paper we consider a variant in which time windows for service at the customers are given, and vehicles may perform more than one route within a working shift. We call the resulting problem the minimum multiple trip VRP (MMTVRP), where a “multiple trip” is a sequence of routes corresponding to a working shift for a vehicle. The problem objective is to minimize the overall number of the multiple trips (hence the size of the required fleet), breaking ties in favor of the minimum routing cost.     

An enhanced ant colony optimization (EACO) applied to capacitated vehicle routing problem

In this paper, an enhanced ant colony optimization (EACO) is proposed for capacitated vehicle routing problem. The capacitated vehicle routing problem is to service customers with known demands by a homogeneous fleet of fixed capacity vehicles starting from a depot. It plays a major role in the field of logistics and belongs to NP-hard problems. Therefore, it is difficult to solve the capacitated vehicle routing problem directly when solutions increase exponentially with the number of serviced customers. The framework of this paper is to develop an enhanced ant colony optimization for the capacitated vehicle routing problem. It takes the advantages of simulated annealing and ant colony optimization for solving the capacitated vehicle routing problem. In the proposed algorithm, simulated annealing provides a good initial solution for ant colony optimization. Furthermore, an information gain based ant colony optimization is used to ameliorate the search performance. Computational results show that the proposed algorithm is superior to original ant colony optimization and simulated annealing separately reported on fourteen small-scale instances and twenty large-scale instances.     

A multilevel approach for modelling vehicle routing problem with uncertain travelling time

Vehicle routing problem is concerned with finding optimal collection or delivery routes in a transportation network, beginning and ending at a central depot, for a fleet of vehicles to serve a set of customers under some constraints. Assuming the travel times between two customers are uncertain variables, this paper proposes an uncertain multilevel programming model for a vehicle routing problem, of which the leader’s object is to minimize the total waiting times of the customers, and the followers’ objects are to minimize the waiting times of the vehicles for the beginning moments of the customers’ time windows. The uncertain multilevel programming model is transformed into a determinacy programming model, and an intelligent algorithm is designed for solving the crisp model.     

A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries

The vehicle routing problem with simultaneous pick-up and deliveries, which considers simultaneous distribution and collection of goods to/from customers, is an extension of the capacitated vehicle routing problem. There are various real cases, where fleet of vehicles originated in a depot serves customers with pick-up and deliveries from/to their locations. Increasing importance of reverse logistics activities make it necessary to determine efficient and effective vehicle routes for simultaneous pick-up and delivery activities. The vehicle routing problem with simultaneous pick-up and deliveries is also NP-hard as a capacitated vehicle routing problem and this study proposes a genetic algorithm based approach to this problem. Computational example is presented with parameter settings in order to illustrate the proposed approach. Moreover, performance of the proposed approach is evaluated by solving several test problems.     

A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem

In the heterogeneous fixed fleet vehicle routing problem there are different types of vehicles and a given number of vehicles of each type. The resolution of this problem consists of assigning the customers to the existing vehicles and, in relation to each vehicle, defining the order of visiting each customer for the delivery or collection of goods. The objective is to minimize the total costs, satisfying customers’ requirements and visiting each customer exactly once. In this paper a tabu search algorithm is proposed and tested on several benchmark problems. The computational experiments show that the proposed algorithm produces high quality solutions within an acceptable computation time. Four new best solutions are reported for a set of test problems used in the literature.     

A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited availability of vehicles. The main objective is to minimize the fixed vehicle cost and the distribution cost, where the latter can be defined with respect to en-route time (T) or distance (D). The proposed unified algorithm is able to solve the four variants of heterogeneous fleet routing problem, called FT, FD, HT and HD, where the last variant is new. The HEA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle the heterogeneous fleet dimension. Extensive computational experiments on benchmark instances have shown that the HEA is highly effective on FT, FD and HT. In particular, out of the 360 instances we obtained 75 new best solutions and matched 102 within reasonable computational times. New benchmark results on HD are also presented.     

Two memetic algorithms for heterogeneous fleet vehicle routing problems

The vehicle routing problem (VRP) plays an important role in the distribution step of supply chains. From a depot with identical vehicles of limited capacity, it consists in determining a set of vehicle trips of minimum total length, to satisfy the demands of a set of customers. In general, the number of vehicles used is a decision variable. The heterogeneous fleet VRP (HFVRP or HVRP) is a natural generalization with several vehicle types, each type being defined by a capacity, a fixed cost, a cost per distance unit and a number of vehicles available. The vehicle fleet mix problem (VFMP) is a variant with an unlimited number of vehicles per type. This paper presents two memetic algorithms (genetic algorithms hybridized with a local search) able to solve both the VFMP and the HVRP. They are based on chromosomes encoded as giant tours, without trip delimiters, and on an optimal evaluation procedure which splits these tours into feasible trips and assigns vehicles to them. The second algorithm uses a distance measure in solution space to diversify the search. Numerical tests on standard VFMP and HFVRP instances show that the two methods, especially the one with distance measure, compete with published metaheuristics and improve several best-known solutions.     

An efficient variable neighborhood search heuristic for very large scale vehicle routing problems

In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.     

A heuristic based on multi-exchange techniques for a regional fleet assignment location-routing problem

We deal with a distribution network design problem that involves location, fleet assignment and routing decisions. Specifically, the distribution network under investigation is characterized by one central depot, a set of customers split into regions, and a heterogeneous fleet of vehicles. The goal is to locate one regional depot in each region, to assign some vehicles to each region, and to design the vehicles routes, each starting and ending at the central depot, in such a way that the regional depot is visited once by all vehicles assigned to the corresponding region, the vehicle capacities are not exceeded, the customer demands are satisfied and the overall distribution cost is minimized. The study has been motivated by a real life application related to a company operating in the North of Italy.     

Artificial intelligence heuristics in solving vehicle routing problems with time window constraints

This paper describes the authors’ research on various heuristics in solving vehicle routing problem with time window constraints (VRPTW) to near optimal solutions. VRPTW is NP-hard problem and best solved to near optimum by heuristics. In the vehicle routing problem, a set of geographically dispersed customers with known demands and predefined time windows are to be served by a fleet of vehicles with limited capacity. The optimized routines for each vehicle are scheduled as to achieve the minimal total cost without violating the capacity and time window constraints. In this paper, we explore different hybridizations of artificial intelligence based techniques including simulated annealing, tabu search and genetic algorithm for better performance in VRPTW. All the implemented hybrid heuristics are applied to solve the Solomon's 56 VRPTW with 100-customer instances, and yield 23 solutions competitive to the best solutions published in literature according to the authors’ best knowledge.     

改进迭代局部搜索算法在MMTVRP中的应用

为了解决运送不相容货物的带时间窗的多行程车辆路径问题,需要制定一个明确的路径规划来服务一组客户,以满足客户运送不相容的大宗货物的需求。车辆在工作日期间允许执行多个行程,目的就是最大限度地减少使用车辆的数量。通过创建巨网结构并采用辅助分割过程和改进的迭代局部搜索算法获得解决方案,在多个相关约束条件限制下,车辆实现了以最少的数量、最短的行程在规定的时间窗内送达货物,并从车队不同规模的角度分别介绍了采用多行程方式送货的优势。最后通过典型的带时间窗的车辆路径问题的实例分析表明,该算法在某些情况下可以使车队规模减半,从而最大程度上减少了运行成本。     

The green vehicle routing problem: A heuristic based exact solution approach

This paper develops a simulated annealing heuristic based exact solution approach to solve the green vehicle routing problem (G-VRP) which extends the classical vehicle routing problem by considering a limited driving range of vehicles in conjunction with limited refueling infrastructure. The problem particularly arises for companies and agencies that employ a fleet of alternative energy powered vehicles on transportation systems for urban areas or for goods distribution. Exact algorithm is based on the branch-and-cut algorithm which combines several valid inequalities derived from the literature to improve lower bounds and introduces a heuristic algorithm based on simulated annealing to obtain upper bounds. Solution approach is evaluated in terms of the number of test instances solved to optimality, bound quality and computation time to reach the best solution of the various test problems. Computational results show that 22 of 40 instances with 20 customers can be solved optimally within reasonable computation time.     

A GRASP×ELS approach for the capacitated location-routing problem

This paper addresses the capacitated location-routing problem (CLRP), raised by distribution networks involving depot location, fleet assignment and routing decisions. The CLRP is defined by a set of potential depot locations, with opening costs and limited capacities, a homogeneous fleet of vehicles, and a set of customers with known demands. The objective is to open a subset of depots, to assign customers to these depots and to design vehicle routes, in order to minimize both the cost of open depots and the total cost of the routes. The proposed solution method is a greedy randomized adaptive search procedure (GRASP), calling an evolutionary local search (ELS) and searching within two solution spaces: giant tours without trip delimiters and true CLRP solutions. Giant tours are evaluated via a splitting procedure that minimizes the total cost subject to vehicle capacity, fleet size and depot capacities. This framework is benchmarked on classical instances. Numerical experiments show that the approach outperforms all previously published methods and provides numerous new best solutions.     

A new approach on auxiliary vehicle assignment in capacitated location routing problem

The location routing problem (LRP) considers locating depots and vehicle routing decisions simultaneously. In classic LRP the number of customers in each route depends on the capacity of the vehicle. In this paper a capacitated LRP model with auxiliary vehicle assignment is presented in which the length of each route is not restricted by main vehicle capacity. Two kinds of vehicles are considered: main vehicles with higher capacity and fixed cost and auxiliary vehicles with lower capacity and fixed cost. The auxiliary vehicles can be added to the transportation system as an alternative strategy to cover the capacity limitations and they are just used to transfer goods from depots to vehicles and cannot serve the customers by themselves. To show the applicability of the proposed model, some numerical examples derived from the well-known instances are used. Moreover the model has been solved by some meta-heuristics for large sized instances. The results show the efficiency of the proposed model and the solution approach, considering the classic model and the exact solution approach, respectively.     

Vehicle routing with pick-up and delivery: tour-partitioning heuristics

Many applications of the classical vehicle routing problem involve pick-up and delivery services between the depot and peripheral locations (warehouses, stores, stations). This paper studies an important version of the vehicle routing problem with pick-up and delivery (the so-called delivery and backhaul problem): delivery in our case refers to transportation of goods from the depot to customers, and pick-up (backhaul) refers to shipment from customers to the depot. The objective is to find a set of vehicle routes that service customers such that vehicle capacity is not violated and the total distance traveled is minimized. Tour partitioning heuristics for solving the capacitated vehicle routing problem are based on breaking a basic tour into disjoint segments served by different vehicles. This idea is adapted for solving the delivery and backhaul problem. Two heuristics that focus on efficient utilization of vehicles’ capacities are introduced, analyzed and tested numerically.     

基于暂态混沌神经网络的多车调度混合优化算法

探讨车辆调度问题的解决方法．提出一种用于求解带容量约束的多车调度问题（CVRP）的混合优化算法．该算法分为路线划分、构造初始解和改进解3个阶段：第1阶段用模糊C均值聚类算法将所有客户按车容量要求装车;第2阶段用暂态混沌神经网络方法对每条路线排序;第3阶段用禁忌搜索法改进得到的解．最后采用标准问题进行仿真计算,通过与其他算法的比较,说明该算法是求解CVRP问题可行且高效的方法．     

Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations?

This paper discusses the vehicle routing problem with multiple driving ranges (VRPMDR), an extension of the classical routing problem where the total distance each vehicle can travel is limited and is not necessarily the same for all vehicles – heterogeneous fleet with respect to maximum route lengths. The VRPMDR finds applications in routing electric and hybrid-electric vehicles, which can only cover limited distances depending on the running time of their batteries. Also, these vehicles require from long charging times, which in practice makes it difficult to consider en route recharging. The paper formally introduces the problem, describes an integer programming formulation and a multi-round heuristic algorithm that iteratively constructs a solution for the problem. Using a set of benchmarks adapted from the literature, the algorithm is then employed to analyze how distance-based costs are increased when considering ‘greener’ fleet configurations – i.e., when using electric vehicles with different degrees of autonomy.