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.     

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 parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups

A well-known variant of the vehicle routing problem involves backhauls, where vehicles deliver goods from a depot to linehaul customers and pick up goods from backhaul customers to the depot. The vehicle routing problem with divisible deliveries and pickups (VRPDDP) allows vehicles to visit each client once or twice for deliveries or pickups. In this study, a very efficient parallel approach based on variable neighborhood search (VNS) is proposed to solve VRPDDP. In this approach, asynchronous cooperation with a centralized information exchange strategy is used for parallelization of the VNS approach, called cooperative VNS (CVNS). All available problem sets of VRPDDP have been successfully solved with the CVNS, and the best solutions available in the literature have been significantly improved.     

A two-phase metaheuristic for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem, which aims to minimize the total arrival time at customers, is a relatively new variant of vehicle routing problem. It can be used to model many real-world applications, e.g., the important application arisen from the humanitarian aid after a natural disaster. In this paper, an approach, called two-phase metaheuristic, is proposed to deal with this problem. This algorithm starts from a solution. At each iteration, two interdependent phases use different perturbation and local search operators for solution improvement. The effectiveness of the proposed algorithm is empirically investigated. The comparison results show that the proposed algorithm is promising. Moreover, for nine benchmark instances, the two-phase metaheuristic can find better solutions than those reported in the previous literature.     

带时间窗的同时集散货物路线问题研究

研究了业务繁忙环境下带时间窗的同时集散货物路线问题．以车辆数、运输距离和完成运输任务的总 时间最小为目标建立了多目标模型,提出用基于路线集合划分的分解迭代算法求解该问题．该算法首先用两种策略 将问题的解分解为几个子集合,用记录更新法分别求解每个子集合,将子集合求得的最好路线反馈回来形成新的当 前解,再分解迭代,逐渐改善解的质量．最后数据实验表明该算法能有效解决带时间窗的单向车辆路线问题和集散 一体化的双向车辆路线问题．     

A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service

The vehicle routing problem with simultaneous pick-up and delivery (VRP_SPD) is a variant of the classical vehicle routing problem (VRP) where clients require simultaneous pick-up and delivery service. Deliveries are supplied from a single depot at the beginning of the vehicle's service, while pick-up loads are taken to the same depot at the conclusion of the service. One important characteristic of this problem is that a vehicle's load in any given route is a mix of pick-up and delivery loads.     

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.     

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 probability matrix based particle swarm optimization for the capacitated vehicle routing problem

Particle swam optimization (PSO) is a relatively new metaheuristic that has recently drawn much attention from researchers in various optimization areas. However, application of PSO for the capacitated vehicle routing problem (CVRP) is very limited. This paper proposes a simple PSO approach for solving the CVRP. The proposed PSO approach uses a probability matrix as the main device for particle encoding and decoding. While existing research used the PSO solely for assignment of customers to routes and used other algorithms to sequence customers within the routes, the proposed approach applies the PSO approach to both simultaneously. The computational results show the effectiveness of the proposed PSO approach compared to the previous approaches.     

Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a relatively new version of the classical capacitated vehicle routing problem, and it is equivalent to a traveling repairman problem with capacity constraints and a homogeneous vehicle fleet, which aims to minimize the total arrival time at customers. Many real‐world applications can be modeled by this problem, such as the important application resulting from the humanitarian aid following a natural disaster. In this paper, two heuristics are proposed. The first one is a constructive heuristic to generate an initial solution and the second is the skewed variable neighborhood search (SVNS) heuristic. The SVNS algorithm starts with the initial solution. At each iteration, the perturbation phase and the local search phase are used to improve the solution of the CCVRP, and the distance function in acceptance criteria phase is used to improve the exploration of faraway valleys. This algorithm is applied to a set of benchmarks, and the comparison results show that the proposed algorithms provide better solutions than those reported in the previous literature on memetic algorithms and adaptive large neighborhood search heuristics.     

用于求解混合车辆路径问题的混合进化算法

文中研究了具有NP难度的混合车辆路径问题(Mixed Capacitated General Routing Problem,MCGRP),其是在基本车辆路径问题(Vehicle Routing Problem,VRP)的基础上通过添加限载容量约束及弧上的用户需求而衍生的。给定一列车辆数不限的车队,使车辆从站点出发向用户提供服务,服务完用户需求后仍返回站点;规定每辆车的总载重不能超过其载重量,且每个需求只能被一辆车服务且仅服务一次。MCGRP旨在求解每辆车的服务路线,使得在满足以上约束条件的情况下所有车辆的旅行消耗之和最小。混合车辆路径问题具有较高的理论价值和实际应用价值,针对该问题提出了一种高效的混合进化算法。该算法采用基于5种邻域算符的变邻域禁忌搜索来提高解的质量,并通过一种基于路径的交叉算符来继承解的优异性,从而有效地加速算法的收敛。在一组共计23个经典算例上的实验结果表明,该混合进化算法在求解混合车辆路径问题时是非常高效的。     

A hybrid large-neighborhood search algorithm for the cumulative capacitated vehicle routing problem with time-window constraints

This paper introduces a special vehicle routing problem, i.e. the cumulative capacitated vehicle routing problem with time-window constraints (Cum-CVRPTW). The problem can be defined as designing least-cost delivery routes from a depot to a set of geographically-scattered customers, subject to the constraint that each customer has to be served within a time window; accordingly, the objective costs are computed as the sum of arrival times at all the customers. The Cum-CVRPTW finds practical utility in many situations, e.g. the provision of humanitarian aids in the context of natural disasters. The Cum-CVRPTW can be viewed as a combination of two NP-hard problems, i.e. the vehicle routing problem with time windows and the cumulative vehicle routing problem. To effectively address this problem, an effective algorithm is designed, which is based on the frameworks of Large Neighborhood Search Algorithm and hybridizes with Genetic Algorithm. The proposed algorithm adopts a constraint-relaxation scheme to extend the search space, enabling the iterative exploration of both the feasible and infeasible neighborhood solutions of an incumbent solution. Furthermore, some speed-up techniques are designed to reduce the computational complexity. To elucidate its effectiveness, the proposed algorithm is examined on the benchmark instances from the literature. The resultant numerical findings show that the algorithm is able to improve and obtain some best-known solutions found by existing state-of-the-art methods.     

Heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem in a carrier

In this paper, we present heuristic algorithms for a three-dimensional loading capacitated vehicle routing problem arising in a real-world situation. In this problem, customers make requests of goods, which are packed in a sortment of boxes. The objective is to find minimum cost delivery routes for a set of identical vehicles that, departing from a depot, visit all customers only once and return to the depot. Apart of the usual 3D container loading constraints which ensure that the boxes are packed completely inside the vehicles and that the boxes do not overlap each other in each vehicle, the problem also takes into account constraints related to the vertical stability of the cargo and multi-drop situations. The algorithms are based on the combination of classical heuristics from both vehicle routing and container loading literatures, as well as two metaheuristic strategies, and their use in more elaborate procedures. Although these approaches cannot assure optimal solutions for the respective problems, they are relatively simple, fast enough to solve real instances, flexible enough to include other practical considerations, and normally assure relatively good solutions in acceptable computational times in practice. The approaches are also sufficiently generic to be embedded with algorithms other than those considered in this study, as well as they can be easily adapted to consider other practical constraints, such as the load bearing strength of the boxes, time windows and pickups and deliveries. Computational tests were performed with these methods considering instances based on the vehicle routing literature and actual customers’ orders, as well as instances based on a real-world situation of a Brazilian carrier. The results show that the heuristics are able to produce relatively good solutions for real instances with hundreds of customers and thousands of boxes.     

The capacitated vehicle routing problem with stochastic demands and time windows

The capacitated vehicle routing problem with stochastic demands and time windows is an extension of the capacitated vehicle routing problem with stochastic demands, in which demands are stochastic and a time window is imposed on each vertex. A vertex failure occurring when the realized demand exceeds the vehicle capacity may trigger a chain reaction of failures on the remaining vertices in the same route, as a result of time windows. This paper models this problem as a stochastic program with recourse, and proposes an adaptive large neighborhood search heuristic for its solution. Modified Solomon benchmark instances are used in the experiments. Computational results clearly show the superiority of the proposed heuristic over an alternative solution approach.     

A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery

Vehicle routing problem (VRP) is an important and well-known combinatorial optimization problem encountered in many transport logistics and distribution systems. The VRP has several variants depending on tasks performed and on some restrictions, such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. In this paper, we consider vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The VRPSPD deals with optimally integrating goods distribution and collection when there are no precedence restrictions on the order in which the operations must be performed. Since the VRPSPD is an NP-hard problem, we present a heuristic solution approach based on particle swarm optimization (PSO) in which a local search is performed by variable neighborhood descent algorithm (VND). Moreover, it implements an annealing-like strategy to preserve the swarm diversity. The effectiveness of the proposed PSO is investigated by an experiment conducted on benchmark problem instances available in the literature. The computational results indicate that the proposed algorithm competes with the heuristic approaches in the literature and improves several best known solutions.     

Active guided evolution strategies for large-scale vehicle routing problems with time windows

We present a new and effective metaheuristic algorithm, active guided evolution strategies, for the vehicle routing problem with time windows. The algorithm combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. More precisely, guided local search is used to regulate a composite local search in the first stage and the neighborhood of the evolution strategies algorithm in the second stage. The vehicle routing problem with time windows is a classical problem in operations research, where the objective is to design least cost routes for a fleet of identical capacitated vehicles to service geographically scattered customers within pre-specified time windows. The presented algorithm is specifically designed for large-scale problems. The computational experiments were carried out on an extended set of 302 benchmark problems. The results demonstrate that the suggested method is highly competitive, providing the best-known solutions to 86% of all test instances within reasonable computing times. The power of the algorithm is confirmed by the results obtained on 23 capacitated vehicle routing problems from the literature.     

A fast two-level variable neighborhood search for the clustered vehicle routing problem

In this paper, we present an improved two-level heuristic to solve the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the classical capacitated vehicle routing problem (CVRP) in which customers are grouped into predefined clusters, and all customers in a cluster must be served consecutively by the same vehicle. This paper contributes to the literature in the following ways: (i) new upper bounds are presented for multiple benchmark instances, (ii) good heuristic solutions are provided in much smaller computing times than existing approaches, (iii) the CluVRP is reduced to its cluster level without assuming Euclidean coordinates or distances, and (iv) a new variant of the CluVRP, the CluVRP with weak cluster constraints, is introduced. In this variant, clusters are allocated to vehicles in their entirety, but all corresponding customers can be visited by the vehicle in any order.The proposed heuristic solves the CluVRP by combining two variable neighborhood search algorithms, that explore the solution space at the cluster level and the individual customer level respectively. The algorithm is tested on different benchmark instances from the literature with up to 484 nodes, obtaining high quality solutions while requiring only a limited calculation time.     

行驶时间和服务时间随机的集配货一体的分批配送车辆路径优化

将铁路物流中心集配货路径问题抽象为行驶时间和服务时间随机的集送货一体的分批配送车辆路径问题进行优化.根据问题特点建立带修正的随机规划模型,对迭代局部搜索算法进行改进,设计允许分批配送的初始解构造算法、局部搜索算法和扰动机制.算例测试证实:分批配送在中等规模和大规模算例中能发挥较好的作用,大部分中等规模和大规模算例都比不允许分批配送时所得到的解更优,部分中等规模和大规模算例车辆数有所减少;配送点数随着算例规模的扩大而增加,但是配送点数占顾客点数的比例却逐步降低;随机因素随机性增加将导致目标函数增大,对分批配送点数的影响不大.     

A heuristic method for the vehicle routing problem with mixed deliveries and pickups

The vehicle routing problem with deliveries and pickups is a challenging extension to the vehicle routing problem that lately attracted growing attention in the literature. This paper investigates the relationship between two versions of this problem, called “mixed” and “simultaneous”. In particular, we wish to know whether a solution algorithm designed for the simultaneous case can solve the mixed case. To this end, we implement a metaheuristic based on reactive tabu search. The results suggest that this approach can yield good results.     

An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a variation of the classical capacitated vehicle routing problem in which the objective is the minimization of the sum of arrival times at customers, instead of the total routing cost. This paper presents an adaptive large neighborhood search heuristic for the CCVRP. This algorithm is applied to a set of benchmark instances and compared with two recently published memetic algorithms.