A particle swarm optimization algorithm for open vehicle routing problem

This paper presents a real-value version of particle swarm optimization (PSO) for solving the open vehicle routing problem (OVRP) that is a well-known combinatorial optimization problem. In OVRP a vehicle does not return to the depot after servicing the last customer on a route. A particular decoding method is proposed for implementing PSO for OVRP. In the decoding method, a vector of the customer’s position is constructed in descending order. Then each customer is assigned to a route with taking into account feasibility conditions. Finally one-point move has been applied on constructed routes that seem promising to result in a better solution. Experimental evaluations on benchmark data sets demonstrate the competitiveness of the proposed algorithm.     

An ILP improvement procedure for the Open Vehicle Routing Problem

We address the Open Vehicle Routing Problem (OVRP), a variant of the “classical” (capacitated and distance constrained) Vehicle Routing Problem (VRP) in which the vehicles are not required to return to the depot after completing their service. We present a heuristic improvement procedure for OVRP based on Integer Linear Programming (ILP) techniques. Given an initial feasible solution to be possibly improved, the method follows a destruct-and-repair paradigm, where the given solution is randomly destroyed (i.e., customers are removed in a random way) and repaired by solving an ILP model, in the attempt of finding a new improved feasible solution. The overall procedure can be considered as a general framework which could be extended to cover other variants of Vehicle Routing Problems. We report computational results on benchmark instances from the literature. In several cases, the proposed algorithm is able to find the new best known solution for the considered instances.     

A New Multi-objective Competitive Open Vehicle Routing Problem Solved by Particle Swarm Optimization

This paper presents a new variant of an open vehicle routing problem (OVRP), in which competition exists between distributors. In the OVRP with competitive time windows (OVRPCTW), the reaching time to customers affects the sales amount. Therefore, distributors intend to service customers earlier than rivals, to obtain the maximum sales. Moreover, a part of a driver??s benefit is related to the amount of sales; thus, the balance of goods carried in each vehicle is important in view of the limited vehicle capacities. In this paper, a new, multi-objective mathematical model of the homogeneous and competitive OVRP is presented, to minimize the travel cost of routes and to maximize the obtained sales while concurrently balancing the goods distributed among vehicles. This model is solved by the use of a multi-objective particle swarm optimization (MOPSO) algorithm, and the related results are compared with the results of NSGA-II, which is a well-known multi-objective evolutionary algorithm. A comparison of our results with three performance metrics confirms that the proposed MOPSO is an efficient algorithm for solving the competitive OVRP with a reasonable computational time and cost.     

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。     

基于第三方物流的家具配送开放式车辆路径问题

为了降低家具配送成本,提高物流效率,基于第三方物流配送模式,构建了以总行驶距离最短和车辆数最少为最优目标的开放式车辆路径问题(open vehicle routing problem,OVRP)数学模型,并设计了一个改进的两阶段禁忌搜索算法进行求解,第1阶段求解包含所有客户的TSP(traveling salesman problem)路径来作为第2阶段划分OVRP路径的基础.设计了一个随机动态禁忌表,并将"邻域算子编号"和"邻域交换点对"同时作为禁忌对象,避免了过度禁忌的情况.另外,对5个邻域算子进行了测试,表明采用由点交换、分序点插入、点逆序和前点前向插入这4个算子组成的多邻域结构体效果最佳.经算例测试和文献对比,验证了设计算法的有效性,采用第三方物流配送比自营物流配送更节省成本.     

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.     

有数量限制的开放式车辆路径加速算法

设计有数量限制的开放式车辆路径加速禁忌搜索算法,将所有点(包括客户和仓库)做Delaunay三角剖分后,限制问题的解的大多数边与Delaunay三角剖分的边重合。实验结果表明,该算法在保证寻求到相对较优解的前提下,执行速度得到大幅度的提升,解与上界关联紧密,可以应用到其他启发式搜索问题的求解中。     

Open vehicle routing problem with demand uncertainty and its robust strategies

We investigate the open vehicle routing problem with uncertain demands, where the vehicles do not necessarily return to their original locations after delivering goods to customers. We firstly describe the customer’s demand as specific bounded uncertainty sets with expected demand value and nominal value, and propose the robust optimization model that aim at minimizing transportation costs and unsatisfied demands in the specific bounded uncertainty sets. We propose four robust strategies to cope with the uncertain demand and an improved differential evolution algorithm (IDE) to solve the robust optimization model. Then we analyze the performance of four different robust strategies by considering the extra costs and unmet demand. Finally, the computational experiments indicate that the robust optimization greatly avoid unmet demand while incurring a small extra cost and the optimal return strategy is the best strategy by balancing the trade-off the cost and unmet demand among different robust strategies.     

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.     

A new and efficient ant-based heuristic method for solving the traveling salesman problem

Abstract: In this paper, we present an efficient metaheuristic approach for solving the problem of the traveling salesman. We introduce the multiple ant clans concept from parallel genetic algorithms to search solution space using different islands to avoid local minima in order to obtain a global minimum for solving the traveling salesman problem. Our simulation results indicate that the proposed novel traveling salesman problem method (called the ACOMAC algorithm) performs better than a promising approach named the ant colony system. This investigation is concerned with a real life logistics system design which optimizes the performance of a logistics system subject to a required service level in the vehicle routing problem. In this work, we also concentrate on developing a vehicle routing model by improving the ant colony system and using the multiple ant clans concept. The simulation results reveal that the proposed method is very effective and potentially useful in solving vehicle routing problems.     

需求可拆分的开放式车辆路径问题研究

传统的开放式车辆路径问题假设客户的需求不可拆分、车辆类型相同,但在实际的物流配送中,车辆类型不完全相同,对需求的拆分能充分利用车辆的装载能力,降低运输成本。为此,提出需求可拆分的不同种车辆的开放式车辆路径问题,给出整数规划的数学模型,利用禁忌搜索算法对该问题求解,改进算法中初始解和邻域结构的产生过程。通过实验验证模型的有效性,并将结果与传统的开放式车辆路径问题进行比较,表明该算法可有效减少运输成本。     

A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem

This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the demands of customers are fulfilled by a fleet of fixed number of vehicles with various capacities and related costs. Moreover, the vehicles start at the depot and terminate at one of the customers. This problem is an important variant of the classical vehicle routing problem and can cover more practical situations in transportation and logistics. We propose a multistart adaptive memory programming metaheuristic with modified tabu search algorithm to solve this new vehicle routing problem. The algorithmic efficiency and effectiveness are experimentally evaluated on a set of generated instances.     

Metaheuristics for the waste collection vehicle routing problem with time windows,driver rest period and multiple disposal facilities

In this problem there is a set of waste disposal facilities, a set of customers at which waste is collected and an unlimited number of homogeneous vehicles based at a single depot. Empty vehicles leave the depot and collect waste from customers, emptying themselves at the waste disposal facilities as and when necessary. Vehicles return to the depot empty. We take into consideration time windows associated with customers, disposal facilities and the depot. We also have a driver rest period. The problem is solved heuristically. A neighbour set is defined for each customer as the set of customers that are close, but with compatible time windows. A procedure that attempts to fully utilise a vehicle is used to obtain an initial solution, with this initial solution being improved using an interchange procedure. We present two metaheuristic algorithms using tabu search and variable neighbourhood search that are based around the neighbour sets. We also present a metaheuristic based on variable neighbourhood tabu search, where the variable neighbourhood is searched via tabu search. Computational results are presented for publicly available waste collection problems involving up to 2092 customers and 19 waste disposal facilities, which indicate that our algorithms produce better quality solutions than previous work presented in the literature.     

A simulated annealing heuristic for the open location-routing problem

This paper introduces the open location-routing problem (OLRP) that is a variant of the capacitated location-routing problem (CLRP). OLRP is motivated from the rise in contracting with third-party logistic (TPL) companies and is different from CLRP in that vehicles do not return to the distribution center after servicing all customers. The goal of OLRP is to minimize the total cost, consisting of facility operation costs, vehicle fixed costs, and traveling costs. We propose a simulated annealing (SA)-based heuristic for solving OLRP, which is tested on OLRP instances that have been adopted from three sets of well-known CLRP benchmark instances with up to 318 customers and 4 potential depots. The computational results indicate that the proposed heuristic efficiently solves OLRP.     

Location arc routing problem with inventory constraints

Dust suppression of hauling roads in open pit mines is done by periodically spraying water from a water truck. The objective of this paper is to present and compare two methods for locating water depots along the road network so that penalty costs for the lack of humidity in roads and routing costs are minimized. Because the demands are located on the arcs of the network and the arcs require service more than once in a time horizon, this problem belongs to the periodic capacitated arc routing domain. We compare two methods for finding the initial depot location. We then use an exchange algorithm to modify the initial location and an adaptive large neighborhood search algorithm to modify the initial routing of vehicles. This method is the first one used for depot location in periodic arc routing problems.     

A generalized exchange heuristic for the capacitated vehicle routing problem

We consider the problem of dispatching the minimum number of vehicles from a central depot to make deliveries to a set of clients with known demands. The objective is to minimize the total distance travelled, subject to vehicle capacity requirements. We present a new heuristic algorithm for solving this problem. The algorithm is based on generalized edge-exchange search procedures, and relaxation of the capacity requirements. Computational results, based upon standard test problems with up to 249 customers, indicate that our heuristic compares favourably with known heuristics in terms of solution quality.     

A two-phase hybrid heuristic algorithm for the capacitated location-routing problem

In this paper, we propose a two-phase hybrid heuristic algorithm to solve the capacitated location-routing problem (CLRP). The CLRP combines depot location and routing decisions. We are given on input a set of identical vehicles (each having a capacity and a fixed cost), a set of depots with restricted capacities and opening costs, and a set of customers with deterministic demands. The problem consists of determining the depots to be opened, the customers and the vehicles to be assigned to each open depot, and the routes to be performed to fulfill the demand of the customers. The objective is to minimize the sum of the costs of the open depots, of the fixed cost associated with the used vehicles, and of the variable traveling costs related to the performed routes. In the proposed hybrid heuristic algorithm, after a Construction phase (first phase), a modified granular tabu search, with different diversification strategies, is applied during the Improvement phase (second phase). In addition, a random perturbation procedure is considered to avoid that the algorithm remains in a local optimum for a given number of iterations. Computational experiments on benchmark instances from the literature show that the proposed algorithm is able to produce, within short computing time, several solutions obtained by the previously published methods and new best known solutions.     

Variable neighborhood search for location routing

In this paper we propose various neighborhood search heuristics (VNS) for solving the location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. The objective is to find depot locations and to design least cost routes for vehicles. We integrate a variable neighborhood descent as the local search in the general variable neighborhood heuristic framework to solve this problem. We propose five neighborhood structures which are either of routing or location type and use them in both shaking and local search steps. The proposed three VNS methods are tested on benchmark instances and successfully compared with other two state-of-the-art heuristics.