An adaptive local search algorithm for vehicle routing problem with simultaneous and mixed pickups and deliveries

The Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) is an extension to the classical Vehicle Routing Problem (VRP), where customers may both receive and send goods simultaneously. The Vehicle Routing Problem with Mixed Pickup and Delivery (VRPMPD) differs from the VRPSPD in that the customers may have either pickup or delivery demand. However, the solution approaches proposed for the VRPSPD can be directly applied to the VRPMPD. In this study, an adaptive local search solution approach is developed for both the VRPSPD and the VRPMPD, which hybridizes a Simulated Annealing inspired algorithm with Variable Neighborhood Descent. The algorithm uses an adaptive threshold function that makes the algorithm self-tuning. The proposed approach is tested on well-known VRPSPD and VRPMPD benchmark instances derived from the literature. The computational results indicate that the proposed algorithm is effective in solving the problems in reasonable computation time.     

Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery

The vehicle routing problem with simultaneous pick-up and delivery is the problem of optimally integrating goods distribution and waste collection, when no precedence constraints are imposed on the order in which the operations must be performed. The purpose of this paper is to present heuristic algorithms to solve this problem approximately in a small amount of computing time. We present and compare constructive algorithms, local search algorithms and tabu search algorithms, reporting on our computational experience with all of them. In particular we address the issue of applying the tabu search paradigm to algorithms based on complex and variable neighborhoods. For this purpose we combine arc-exchange-based and node-exchange-based neighborhoods, employing different and interacting tabu lists. All the algorithms presented in this paper are applicable to problems in which each customer may have either a pick-up demand or a delivery demand as well as to problems in which each customer may require both kinds of operation.     

A genetic algorithm for the simultaneous delivery and pickup problems with time window

This paper concerns a Simultaneous Delivery and Pickup Problem with Time Windows (SDPPTW). A mixed binary integer programming model was developed for the problem and was validated. Due to its NP nature, a co-evolution genetic algorithm with variants of the cheapest insertion method was proposed to speed up the solution procedure. Since there were no existing benchmarks, this study generated some test problems which revised from the well-known Solomon’s benchmark for Vehicle Routing Problem with Time Windows (VRPTW). From the comparison with the results of Cplex software and the basic genetic algorithm, the proposed algorithm showed that it can provide better solutions within a comparatively shorter period of time.     

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 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.     

An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup

In this paper we use an ant colony system (ACS) algorithm to solve the vehicle routing problem with simultaneous delivery and pickup (VRPSDP) which is a combinatorial optimization problem. ACS is an algorithmic approach inspired by the foraging behavior of real ants. Artificial ants are used to construct a solution for the problem by using the pheromone information from previously generated solutions. The proposed ACS algorithm uses a construction rule as well as two multi-route local search schemes. The algorithm can also solve the vehicle routing problem with backhaul and mixed load (VRPBM). An extensive numerical experiment is performed on benchmark problem instances available in literature. It is found that ACS gives good results compared to the existing algorithms.     

考虑具有不同交付选择的物流配送路径问题研究

为了满足城市配送中顾客对交付方式及特定时间的个性化需求,引入顾客偏好概念刻画送货上门与自提服务的交付需求,以总运营成本最小化为优化目标建立了具有不同交付选择的车辆路径优化模型。考虑到模型的复杂性引入多种算子,设计并改进自适应大邻域搜索算法对模型进行求解。最后结合重庆市南岸区某配送案例进行实例分析,验证了该模型与算法的有效性。     

Vessel routing with pickups and deliveries: An application to the supply of offshore oil platforms

This paper presents a new routing problem, the Vessel Routing Problem with Selective Pickups and Deliveries (VRPSPD), an extension of existing pickup and delivery problems that arises in the planning of logistics operations in the offshore oil and gas industry. The VRPSPD is a single-vessel model that can lead to significant economic improvements to the current planning scheme without having a very large impact on the operations. In addition, we formulate a Multi-Vessel Routing Problem with Pickups and Deliveries (mVRPPD) that leads to even larger economical gains, but also entails more important changes in the current planning and operations. To quantify and justify the benefits of the VRPSPD and mVRPPD, an industry case based on real data was constructed and solved for 300 days. The VRPSPD is solvable with a commercial solver for most real-size instances. However, for the mVRPPD on the largest instances, it was necessary to develop a state-of-the-art adaptive large neighborhood heuristic search to reduce computational time.     

The Pickup and Delivery Problem with Cross-Docking

Usual models that deal with the integration of vehicle routing and cross-docking operations impose that every vehicle must stop at the dock even if the vehicle collects and delivers the same set of goods. In order to allow vehicles to avoid the stop at the dock and thus, reduce transportation costs, we introduce the Pickup and Delivery Problem with Cross-Docking (PDPCD). An Integer Programming formulation and a Branch-and-price algorithm for the problem are discussed. Our computational results indicate that optimal or near optimal solutions for PDPCD indeed allow total costs to be significantly reduced. Due to improvements in the resolution of the pricing problems, the Branch-and-price algorithm for PDPCD works better than similar algorithms for other models in the literature.     

Reverse logistics network design for product reuse,remanufacturing, recycling and refurbishing under uncertainty

With the improvement of the quality of life in human society, the need to use more natural resources is felt more than ever. In this regard, much research has been done on restoring depreciated and consumed products to the supply chain; many factors, including the quality of returned products, can significantly impact how the reverse logistics network will be used. The two-stage stochastic mixed-integer programming model proposed in this paper considers various processes of recovering recyclable products, including reuse, refurbishing, remanufacturing, recycling, and selling spare parts. Also, considering uncertainty on quality and quantity of returned products, product variety, and bill of material are model features. Due to the computational complexity of large-scale problems, such problems require considerable time to solve. To tackle this issue, a hybrid algorithm constructed by a genetic algorithm and branch and cut algorithm (with CPLEX solver) has been introduced, which can significantly reduce the solution time. Finally, the algorithm is applied to a real-world problem to design a reverse logistics network for a small-size laboratory equipment manufacturer.     

The single vehicle routing problem with deliveries and selective pickups

The single vehicle routing problem with deliveries and selective pickups (SVRPDSP) is defined on a graph in which pickup and delivery demands are associated with customer vertices. The difference between this problem and the single vehicle routing problem with pickups and deliveries (SVRPPD) lies in the fact that it is no longer necessary to satisfy all pickup demands. In the SVRPDSP a pickup revenue is associated with each vertex, and the pickup demand at that vertex will be collected only if it is profitable to do so. The net cost of a route is equal to the sum of routing costs, minus the total collected revenue. The aim is to design a vehicle route of minimum net cost, visiting each customer, performing all deliveries, and a subset of the pickups. A mixed integer linear programming formulation is proposed for the SVRPDSP. Classical construction and improvement heuristics, as well as a tabu search heuristic (TS), are developed and tested on a number of instances derived from VRPLIB. Computational results show that the solutions produced by the proposed heuristics are near-optimal. There is also some evidence that the best solutions identified by the heuristics are frequently non-Hamiltonian and may contain one or two customers visited twice.     

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.     

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

This paper proposes a formulation of the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) and a particle swarm optimization (PSO) algorithm for solving it. The formulation is a generalization of three existing VRPSPD formulations. The main PSO algorithm is developed based on GLNPSO, a PSO algorithm with multiple social structures. A random key-based solution representation and decoding method is proposed for implementing PSO for VRPSPD. The solution representation for VRPSPD with n customers and m   vehicles is a (n+2m)$(n+2m)$-dimensional particle. The decoding method starts by transforming the particle to a priority list of customers to enter the route and a priority matrix of vehicles to serve each customer. The vehicle routes are constructed based on the customer priority list and vehicle priority matrix. The proposed algorithm is tested using three benchmark data sets available from the literature. The computational result shows that the proposed method is competitive with other published results for solving VRPSPD. Some new best known solutions of the benchmark problem are also found by the proposed method.     

A tabu search heuristic for the single vehicle pickup and delivery problem with time windows

The single vehicle pickup and delivery problem with time windows is a generalization of the traveling salesman problem. In such a problem, a number of transportation requests have to be satisfied by one vehicle, each request having constraints to respect: a pickup at its origin and a delivery at its destination, and a time window at each location. The capacity of the vehicle has to be respected. The aim is to minimize the total distance traveled by the vehicle. A number of exact and approximate solution methods exists in the literature, but to the authors knowledge none of them make use of metaheuristics, still promising with other vehicle routing problems. In this paper we present tabu search and probabilistic tabu search. Results obtained on classical traveling salesman problems and a class of randomly generated instances indicate that our approach often produces optimal solutions in a relatively short execution time.     

Large-scale pickup and delivery work area design

This paper presents a new approach to rationalizing the design of work areas for drivers who pickup and deliver hundreds of packages a day. Taking into account the random nature of demand, visit frequency, and service time, the objective is to partition the customers into the minimum number of convex, continuous clusters such that each can be serviced by a single vehicle within the time available in a day. An additional requirement is that the aspect ratio of a work area must satisfy certain geometric conditions. The problem is formulated as a generic capacitated clustering problem with side constraints and solved with a combination of aggregation to achieve analytic tractability, column generation to determine good clusters, regeneration to diversify the exploration of the feasible region, and heuristic variable fixing to find good feasible solutions. A novel set of geometric constraints allows for the implicit generation of clusters, and several valid inequalities are introduced to strengthen the pricing subproblem formulation. In addition, ideas from tabu search are adopted to limit the number of subproblems that are solved at each iteration. This greatly improved the efficiency of the column generation algorithm without sacrificing quality. The methodology was tested with data provided by a leading carrier. Six data sets were examined, ranging in size from roughly 6000 to 45,000 customers. The results showed that much more compact work areas could be obtained than currently exist, and that the number of drivers could be reduced by an average of 7.6%. This translates into millions of dollars in annual saving when all service areas across the U.S. are taken into account.     

The pickup and delivery problem: Faces and branch-and-cut algorithm

This paper formulates the pickup and delivery problem, also known as the dial-a-ride problem, as an integer program. Its polyhedral structure is explored and four classes of valid inequalities developed. The results of a branch-and-cut algorithm based on these constraints are presented.     

Reverse logistics network design for a biogas plant: An approach based on MILP optimization and Analytical Hierarchical Process (AHP)

Among sustainable energy production processes, methanation (anaerobic co-digestion) has a high potential to valorize organic residual waste by exploiting its energetic capacities in the form of biogas. Nevertheless, at the early stage of the project, decisions must be made concerning the network used to supply biomass to the anaerobic co-digestion facility. However, these decisions involve complex hierarchical processes, taking into account the best compromise to be found among diverse factors and actors (economic, social, environmental, etc.). In this article a systematic approach integrating Mixed Integer Linear Programming (MILP) optimization and Analytical Hierarchical Process is proposed. It will allow project managers to evaluate possible scenarios for the implementation of an anaerobic co-digestion logistics network in order to facilitate the integration of the preferences of the stakeholders involved in the project. The approach proposed is then illustrated by the design of a municipal biogas facility in Nancy, France.     

具有同时集送货需求车辆路径问题的混沌量子进化算法研究

针对量子进化算法中旋转角取值的离散性使其解空间的搜索具有跳跃性,提出了基于混沌理论的精英均值计算旋转角算法,并将其应用于具有同时集送货需求车辆路径问题的求解.在理论上分析了解的强可行和弱可行条件的基础上,使用启发式算子对解进行改进.通过仿真实验与其他算法进行了比较,仿真结果表明所提出算法是求解此类问题的有效方法.     

多目标同时取送货车辆路径问题的改进蚁群算法

为使同时取送货车辆路径问题(vehicle routing problem with simultaneous pickup and delivery, VRPSPD)的运输成本和各路径间最大长度差最小化,建立同时考虑车辆容量和距离约束的VRPSPD双目标模型,通过软件测试验证了模型准确性.针对问题的特点构造一个嵌入禁忌表、且具有贪婪转移准则的多目标蚁群算法,对蚂蚁产生的解执行多目标迭代局部搜索程序,以在多个邻域上优化该解或产生新的Pareto解.采用响应曲面法拟合算法参数对目标值影响的数学关系,确定最优参数组合.用该算法求得文献中12组Solomon算例的Pareto解集,并以绝对偏向最小化总成本的解与文献中仅最小化总成本的几种算法的计算结果进行比较,结果表明算法可求得权衡各目标且使单一目标近似最优的Pareto解.     

复杂PDPTW问题的插入启发式算法

讨论了多车库、多货物类型且有最大工作时间约束的复杂有时间窗装卸货问题(PDPTW)，给出了解决此类问题的插入启发式算法、对复杂条件的特殊处理方法以及提高解的质量的处理技巧。算例表明此算法能快速有效地处理复杂PDPTW问题。