The multi-depot vehicle routing problem with heterogeneous vehicle fleet: Formulation and a variable neighborhood search implementation

The multi-depot fleet size and mix vehicle routing problem, also known as the multi-depot routing with heterogeneous vehicles, is investigated. A mathematical formulation is given and lower as well as upper bounds are produced using a three hour execution time of CPLEX. An efficient implementation of variable neighborhood search that incorporates new features in addition to the adaptation of several existing neighborhoods and local search operators is proposed. These features include a preprocessing scheme for identifying borderline customers, a mechanism that aggregates and disaggregates routes between depots, and a neighborhood reduction test that saves nearly 80% of the CPU time, especially on the large instances. The proposed algorithm is highly competitive as it produces 23 new best results when tested on the 26 data instances published in the literature.     

A population-based metaheuristic for the pickup and delivery problem with time windows and LIFO loading

In this paper, we solve the pickup and delivery problem with time windows and last-in-first-out (LIFO) loading. LIFO loading minimizes handling while unloading items from the vehicle: the items are loaded according to a linear stack structure, and an item can only be delivered if it is the one on top of the stack. Three exact branch-price-and-cut algorithms are available for this problem. These can solve instances with up to 75 requests within one hour. We propose a population-based metaheuristic capable of handling larger instances much faster. First, a set of initial solutions is generated with a greedy randomized adaptive search procedure. For each of these solutions, local search is applied in order to first decrease the total number of vehicles and then the total traveled distance. Two different strategies are used to create offspring. The first selects vehicle routes from the solution pool. The second selects two parents to create an offspring with a crossover operator. For both strategies, local search is then performed on the child solution. Finally, the offspring is added to the population and the best survivors are kept. The population is managed so as to maintain good quality solutions with respect to total cost and population diversity. Computational results on medium to large instances confirm the effectiveness of the proposed metaheuristic.     

A general variable neighborhood search for the swap-body vehicle routing problem

The Swap-Body Vehicle Routing Problem, a generalization of the well known Vehicle Routing Problem, can be stated as follows: the vehicle fleet consisting of trucks, semi-trailers, and swap bodies, is available at a single depot to serve a given set of customers. To serve a subset of customers, one may use either a truck carrying one swap body or a train (a truck with a semi-trailer attached to it) carrying two swap bodies. In both cases, a vehicle (a truck or a train) must perform a route starting and ending at the depot, so to satisfy demands of visited customers, maximal allowed route duration, allowed load on the used vehicle, and accessibility constraint of each customer. The accessibility constraint indicates whether a customer is allowed to be visited by a train or not. In addition, a set of swap locations is given where semi-trailers and swap bodies may be parked or swapped. The goal of the Swap-Body Vehicle Routing Problem is to minimize the total costs consisting of the fixed costs for using vehicles and costs for performing routes. In this paper, we propose two general variable neighborhood search heuristics to solve this problem. The quality of the proposed methods is evaluated on the instances provided by the organizers of VeRolog Solver Challenge 2014.     

A GRASP with evolutionary path relinking for the truck and trailer routing problem

In the truck and trailer routing problem (TTRP) a heterogeneous fleet composed of trucks and trailers has to serve a set of customers, some only accessible by truck and others accessible with a truck pulling a trailer. This problem is solved using a route-first, cluster-second procedure embedded within a hybrid metaheuristic based on a greedy randomized adaptive search procedure (GRASP), a variable neighborhood search (VNS) and a path relinking (PR). We test PR as a post-optimization procedure, as an intensification mechanism, and within evolutionary path relinking (EvPR). Numerical experiments show that all the variants of the proposed GRASP with path relinking outperform all previously published methods. Remarkably, GRASP with EvPR obtains average gaps to best-known solutions of less than 1% and provides several new best solutions.     

A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows

This paper presents a new hybrid variable neighborhood-tabu search heuristic for the Vehicle Routing Problem with Multiple Time windows. It also proposes a minimum backward time slack algorithm applicable to a multiple time windows environment. This algorithm records the minimum waiting time and the minimum delay during route generation and adjusts the arrival and departure times backward. The implementation of the proposed heuristic is compared to an ant colony heuristic on benchmark instances involving multiple time windows. Computational results on newly generated instances are provided.     

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.     

A hybrid metaheuristic approach for the capacitated p-median problem

The capacitated p-median problem (CPMP) seeks to obtain the optimal location of p medians considering distances and capacities for the services to be given by each median. This paper presents an efficient hybrid metaheuristic algorithm by combining a proposed cutting-plane neighborhood structure and a tabu search metaheuristic for the CPMP. In the proposed neighborhood structure to move from the current solution to a neighbor solution, an open median is selected and closed. Then, a linear programming (LP) model is generated by relaxing binary constraints and adding new constraints. The generated LP solution is improved using cutting-plane inequalities. The solution of this strong LP is considered as a new neighbor solution. In order to select an open median to be closed, several strategies are proposed. The neighborhood structure is combined with a tabu search algorithm in the proposed approach. The parameters of the proposed hybrid algorithm are tuned using design of experiments approach. The proposed algorithm is tested on several sets of benchmark instances. The statistical analysis shows efficiency and effectiveness of the hybrid algorithm in comparison with the best approach found in the literature.     

A multi-phase oscillated variable neighbourhood search algorithm for a real-world open vehicle routing problem

The aim of this study is to solve the newspaper delivery optimization problem for a media delivery company in Turkey by reducing the total cost of carriers. The problem is modelled as an open vehicle routing problem (OVRP), which is a variant of the vehicle routing problem. A variable neighbourhood search-based algorithm is proposed to solve a real-world OVRP. The proposed algorithm is tested with varieties of small and large-scale benchmark suites and a very large-scale real-world problem instance. The results of the proposed algorithm provide either the best known solution or a competitive solution for each of the benchmark instances. The algorithm also improves the real-world company’s solutions by more than 10%.     

Variable neighborhood search for the pharmacy duty scheduling problem

In this paper, we study on the Pharmacy Duty Scheduling (PDS) problem, where a subset of pharmacies should be on duty on national holidays, at weekends and at nights in order to be able to satisfy the emergency drug needs of the society. PDS problem is a multi-period p-median problem with special side constraints and it is an NP-Hard problem. We propose four Variable Neighborhood Search (VNS) heuristics. The first one is the basic version, BVNS. The latter two, Variable Neighborhood Decomposition Search (VNDS) and Variable Neighborhood Restricted Search (VNRS), aim to obtain better results in less computing time by decomposing or restricting the search space. The last one, Reduced VNS (RVNS), is for obtaining good initial solutions rapidly for BVNS, VNDS and VNRS. We test BVNS, VNRS and VNDS heuristics on randomly generated instances and report the computational test results. We also use VNS heuristics on real data for the pharmacies in central İzmir and obtain significant improvements.     

A cooperative parallel metaheuristic for the capacitated vehicle routing problem

This paper introduces a cooperative parallel metaheuristic for the capacitated vehicle routing problem. The proposed metaheuristic consists of multiple parallel tabu search threads that cooperate by asynchronously exchanging best-found solutions through a common solution pool. The solutions sent to the pool are clustered according to their similarities. The search history information identified from the solution clusters is applied to guide the intensification or diversification of the tabu search threads. Computational experiments on two sets of large-scale benchmark instance sets from the literature demonstrate that the suggested metaheuristic is highly competitive, providing new best solutions to ten of those well-studied instances.     

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.     

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.     

Efficient stochastic hybrid heuristics for the multi-depot vehicle routing problem

The paper addresses the problem of multi-depot vehicle routing in order to minimize the delivery time of vehicle objective. Three hybrid heuristics are presented to solve the multi-depot vehicle routing problem. Each hybrid heuristic combines elements from both constructive heuristic search and improvement techniques. The improvement techniques are deterministic, stochastic and simulated annealing (SA) methods. Experiments are run on a number of randomly generated test problems of varying depots and customer sizes. Our heuristics are shown to outperform one of the best-known existing heuristic. Statistical tests of significance are performed to substantiate the claims of improvement.     

需求可拆分车辆路径问题的禁忌搜索算法

为解决实际配送运输中的车辆路径问题（Vehicle Routing Problem,VRP）,通过改进传统的数学模型,解除每个客户需求只能由l辆车配送的约束,建立改进的可拆分车辆路径问题（Split Delivery VRP,SDVRP）数学模型,并利用禁忌搜索算法（Taboo Search Algorithm,TSA）进行求解．在TSA的设计中,根据SDVRP模型的特点对初始解、邻域搜索和解的评价等进行特殊处理．算例表明,该模型不仅可以解决VRP模型中不允许配送点需求量超出装载量的限制,而且通过相应配送点需求量的拆分和重新组合,可节省车辆数目、缩短路线长度、提高车辆装载率．     

A two phase variable neighborhood search for the multi-product inventory routing problem

We address a multi-product inventory routing problem and propose a two-phase Variable Neighborhood Search (VNS) metaheuristic to solve it. In the first phase, VNS is used to solve a capacitated vehicle routing problem at each period to find an initial solution without taking into account the inventory. In the second phase, we iteratively improve the initial solution while minimizing both the transportation and inventory costs. For this, we propose two different algorithms, a Variable Neighborhood Descent and a Variable Neighborhood Search. We present an heuristic and a Linear Programming formulation, which are applied after each local search move, to determine the amount of products to collect from each supplier at each period. During the exploration, we use priority rules for suppliers and vehicles, based on the current delivery schedule over the planning horizon. Computational results show the efficiency of the proposed two-phase approach.     

A variable neighborhood descent algorithm for a real waste collection problem with mobile depots

We consider a waste collection problem encountered in Due Carrare, a town located in Northern Italy. The original feature of the problem consists in the need for arranging appointments between vehicles along their routes so that small vehicles can dump their contents in the large ones and continue their work. This feature identifies the problem as a generalization of the well‐known Capacitated Arc Routing Problem (CARP). We propose a local search heuristic obtained from a variable neighborhood procedure suggested by Hertz and Mittaz (2001) for the CARP. In the Due Carrare instance, the proposed algorithm decreases the total route duration, apart from the required time for any feasible set of routes, of about 30% with respect to the routes so far adopted.     

A variable neighborhood search heuristic algorithm for the double vehicle routing problem with multiple stacks

This paper addresses the double vehicle routing problem with multiple stacks (DVRPMS) in which a fleet of vehicles must collect items in a pickup region and then travel to a delivery region where all items are delivered. The load compartment of all vehicles is divided into rows (horizontal stacks) of fixed profundity (horizontal heights), and on each row, the unloading process must respect the last‐in‐first‐out policy. The objective of the DVRPMS is to find optimal routes visiting all pickup and delivery points while ensuring the feasibility of the vehicle loading plans. We propose a new integer linear programming formulation, which was useful to find inconsistencies in the results of exact algorithms proposed in the literature, and a variable neighborhood search based algorithm that was able to find solutions with same or higher quality in shorter computational time for most instances when compared to the methods already present in the literature.     

A parallel hybrid metaheuristic for bicluster editing

The bicluster editing problem (BEP) consists of editing (adding or removing) the edges of a bipartite graph G in order to transform it into a vertex‐disjoint union of complete bipartite subgraphs, in such a way that the sum of the weights of the edited edges is minimum. In this paper, we propose five parallel strategies for the implementation of a hybrid metaheuristic for the BEP, consisting of a GRASP with VNS as local search. Computational experiments show near‐linear speedups on Linux cluster with 64 processors and better solutions than those of the sequential approach.     

A variable neighborhood search algorithm for the optimization of a dial-a-ride problem in a large city

On-demand transportation is becoming a new necessary service for modern (public and private) mobility and logistics providers. Large cities are demanding more and more share transportation services with flexible routes, resulting from user dynamic demands. In this study a new algorithm is proposed for solving the problem of computing the best routes that a public transportation company could offer to satisfy a number of customer requests. In this problem, known in the literature as the dial-a-ride problem, a number of passengers has to be transported between pickup and delivery locations trying to minimize the routing costs while respecting a set of pre-specified constraints (maximum pickup time, maximum ride duration and maximum load per vehicle). For optimizing this problem, a new variable neighborhood search has been developed and tested on a set of 24 different scenarios of a large-scale dial-a-ride problem in the city of San Francisco. The results have been compared against two state-of-the-art algorithms of the literature and validated by means of statistical procedures proving that the new algorithm has obtained the best overall results.