Extended guided tabu search and a new packing algorithm for the two-dimensional loading vehicle routing problem

In this paper, we develop an extended guided tabu search (EGTS) and a new heuristic packing algorithm for the two-dimensional loading vehicle routing problem (2L-CVRP). The 2L-CVRP is a combination of two well-known NP-hard problems, the capacitated vehicle routing problem, and the two-dimensional bin packing problem. It is very difficult to get a good performance solution in practice for these problems. We propose a meta-heuristic methodology EGTS which incorporates theories of tabu search and extended guided local search (EGLS). It has been proved that tabu search is a very good approach for the CVRP, and the guiding mechanism of the EGLS can help tabu search to escape effectively from local optimum. Furthermore, we have modified a collection of packing heuristics by adding a new packing heuristic to solve the loading constraints in 2L-CVRP, in order to improve the cost function significantly. The effectiveness of the proposed algorithm is tested, and proven by extensive computational experiments on benchmark instances.     

A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP

The Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) addresses practical constraints frequently encountered in the freight transportation industry. In this problem, the task is to serve all customers using a homogeneous fleet of vehicles at minimum traveling cost. The constraints imposed by the three-dimensional shape of the goods, the unloading order, item fragility, and the stability of the loading plan of each vehicle are explicitly considered. We improved two well-known packing heuristics, namely the Deepest-Bottom-Left-Fill heuristic and the Maximum Touching Area heuristic, for the three-dimensional loading sub-problem and provided efficient implementations. Based on these two new heuristics, an effective tabu search algorithm is given to address the overall problem. Computational experiments on publicly available test instances show our new approach outperforms the current best algorithms for 20 out of 27 instances. Our approach is also superior to the existing algorithm on benchmark data for the closely related problem variant M3L-CVRP (which uses a slightly different unloading order constraint compared to 3L-CVRP).     

A GRASP×ELS for the vehicle routing problem with basic three-dimensional loading constraints

This paper addresses an extension of the capacitated vehicle routing problem where the client demand consists of three-dimensional weighted items (3L-CVRP). The objective is to design a set of trips for a homogeneous fleet of vehicles based at a depot node which minimizes the total transportation cost. Items in each vehicle trip must satisfy the three-dimensional orthogonal packing constraints. This problem is strongly connected to real-life transportation systems where the packing of items to be delivered by each vehicle can have a significant impact on the routes. We propose a new way to solve the packing sub-problem. It consists of a two-step procedure in which the z-constraints are first relaxed to get a (x,y) positioning of the items. Then, a compatible z-coordinate is computed to get a packing solution. Items can be rotated but additional constraints such as item fragility, support and LIFO are not considered. This method is included in a GRASP×ELS hybrid algorithm dedicated to the computation of VRP routes. The route optimization alternates between two search spaces: the space of VRP routes and the space of giant trips. The projection from one to the other is done by dedicated procedures (namely the Split and the concatenation algorithms). Moreover, a Local Search is defined on each search space. Furthermore, hash tables are used to store the result of the packing checks and thus save a substantial amount of CPU time. The effectiveness of our approach is illustrated by computational experiments on 3L-CVRP instances from the literature. A new set of realistic instances based on the 96 French districts are also proposed. They range from 19 nodes for the small instances to 255 nodes for the large instances and they can be stated as realistic since they are based on true travel distances in kilometers between French cities. The impact of the hash tables is illustrated as well.     

An effective tabu search approach with improved loading algorithms for the 3L-CVRP

In this paper, we consider the Three-Dimensional Loading Capacitated Vehicle Routing Problem(3L-CVRP) which combines the routing of a fleet of vehicles and the loading of three-dimensional shaped goods into the vehicles while minimizing the total travel distance incurred. Apparently, 3L-CVRP is a combination of capacitated vehicle routing and three-dimensional bin packing problem and thus of high complexity. Different from most of previous works, we propose an innovative approach, called improved least waste heuristic for solving the loading subproblem, which is iteratively invoked by a simple tabu search algorithm for the routing. The good performance in terms of the solution quality and computational efficiency of our approach is shown through the numerical experiments on the benchmark instances from literature.     

Local search techniques for a routing-packing problem

We propose a complex real-world problem in logistics that integrates routing and packing aspects. It can be seen as an extension of the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) introduced by Gendreau, Iori, Laporte, and Martello (2006). The 3L-CVRP consists in finding a set of routes that satisfies the demand of all customers, minimizes the total routing cost, and guarantees a packing of items that is feasible according to loading constraints. Our problem formulation includes additional constraints in relation to the stability of the cargo, to the fragility of items, and to the loading and unloading policy. In addition, it considers the possibility of split deliveries, so that each customer can be visited more than once. We propose a local search approach that considers the overall problem in a single stage. It is based on a composite strategy that interleaves simulated annealing with large-neighborhood search. We test our solver on 13 real-world instances provided by our industrial partner, which are very diverse in size and features. In addition, we compare our solver on benchmarks from the literature of the 3L-CVRP showing that our solver performs well compared to other approaches proposed in the literature.     

Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts

This paper deals with the two-dimensional bin packing problem with conflicts (BPC-2D). Given a finite set of rectangular items, an unlimited number of rectangular bins and a conflict graph, the goal is to find a conflict-free packing of the items minimizing the number of bins used. In this paper, we propose a new framework based on a tree-decomposition for solving this problem. It proceeds by decomposing a BPC-2D instance into subproblems to be solved independently. Applying this decomposition method is not straightforward, since merging partial solutions is hard. Several heuristic strategies are proposed to make an effective use of the decomposition. Computational experiments show the practical effectiveness of our approach.     

A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints

The capacitated vehicle routing problem with three-dimensional loading constraints combines capacitated vehicle routing and three-dimensional loading with additional packing constraints concerning, for example, unloading operations. An efficient hybrid algorithm including a tabu search algorithm for routing and a tree search algorithm for loading is introduced. Computational results are presented for all publicly available test instances. Most of the best solutions previously reported in literature have been improved while the computational effort is drastically reduced compared to other methods.     

Multi-start iterated local search for the periodic vehicle routing problem with time windows and time spread constraints on services

In the field of high-value shipment transportation, companies are faced to the malevolence problem. The risk of ambush increases with the predictability of vehicle routes. This paper addresses a very hard periodic vehicle routing problem with time windows, submitted by a software company specialized in transportation problems with security constraints. The hours of visits to each customer over the planning horizon must be spread in the customer's time window. As the aim is to solve real instances, the running time must be reasonable. A mixed integer linear model and a multi-start iterated local search are proposed. Results are reported on instances derived from classical benchmarks for the vehicle routing problem with time windows, and on two practical instances. Experiments are also conducted on a particular case with a single period, the vehicle routing problem with soft time windows: the new metaheuristic competes with two published algorithms and improves six 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.     

面向纸板三维装箱问题的剩余空间最优算法

针对瓦楞纸板在装箱过程中遇到的多种实际约束,提出一种基于剩余空间最优和多种实际约束的快速求解算法.该算法先根据纸板的先进后出和组合装载约束,确定纸板的装箱序列,接着将三维装箱问题转换成带高度约束的二维装箱问题,再基于剩余空间最优策略,选择空间的分割方式和纸板的放置方式,并对剩下的空间进行合并和重新分割,从而求解得到纸板...     

A GRASP × ELS approach for the job-shop with a web service paradigm packaging

The Job-Shop Scheduling Problem (JSSP) is well known for its complexity as an NP-hard disjunctive scheduling problem. The problem addressed in this paper is JSSPs with an objective of minimizing makespan while satisfying a number of hard constraints. An efficient GRASP × ELS approach is introduced for solving this problem. The efficiency is evaluated using the widely known 40 Laurence’s instances which encompass medium and large scale instances. The computational results prove that the proposed method competes with the best published methods in both quality of results and computational time. Recently, Web services have generated great interest in researchers. Such application architecture is based on the client–server model using existing Internet protocols and open standards. It provides new approaches to optimization methods. The proposed GRASP × ELS is packaged into a Web Service (WS), i.e., it offers for the research community an open access to our optimization approach. Moreover, the proposed web service can be even included in research future works with a very small programming effort.To favor utilization of the web service and to prove the facility in which the service could be used, we provide an example in Java proving that it is possible to obtain in less than 10 min a client application using the different methods exposed by this web service. Such usage extends to classical library inclusion in program with the difference that a method is called in the client side and represents an execution on the server.The Web Service paradigm is a new approach in spreading algorithms and therefore this paper stands at the crossroads of optimization research community and the web service community expectations. The GRASP × ELS provided in the web service, is a state of the art method which competes with previously published ones and which has the advantage of being available for free, in any languages, everywhere contributing in spreading operational research contribution.     

Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings

Much excitement has been generated by the success of stochastic local search procedures at finding solutions to large, very hard satisfiability problems. Many of the problems on which these procedures have been effective are non-Boolean in that they are most naturally formulated in terms of variables with domain sizes greater than two. Approaches to solving non-Boolean satisfiability problems fall into two categories. In the direct approach, the problem is tackled by an algorithm for non-Boolean problems. In the transformation approach, the non-Boolean problem is reformulated as an equivalent Boolean problem and then a Boolean solver is used. This paper compares four methods for solving non-Boolean problems: one direct and three transformational. The comparison first examines the search spaces confronted by the four methods, and then tests their ability to solve random formulas, the round-robin sports scheduling problem, and the quasigroup completion problem. The experiments show that the relative performance of the methods depends on the domain size of the problem and that the direct method scales better as domain size increases. Along the route to performing these comparisons we make three other contributions. First, we generalize Walksat, a highly successful stochastic local search procedure for Boolean satisfiability problems, to work on problems with domains of any finite size. Second, we introduce a new method for transforming non-Boolean problems to Boolean problems and improve on an existing transformation. Third, we identify sufficient conditions for omitting at-least-one and at-most-one clauses from a transformed formula. Fourth, for use in our experiments we propose a model for generating random formulas that vary in domain size but are similar in other respects.     

Active-guided evolution strategies for large-scale capacitated vehicle routing problems

We present an adaptation of the active-guided evolution strategies metaheuristic for the capacitated vehicle routing problem. The capacitated vehicle routing problem is a classical problem in operations research in which a set of minimum total cost routes must be determined for a fleet of identical capacitated vehicles in order to service a number of demand or supply points. The applied metaheuristic combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. The computational experiments were carried out on a set of 76 benchmark problems. The results demonstrate that the suggested method is highly competitive, providing the best-known solutions to 70 test instances.     

Heuristics for the multi-item capacitated lot-sizing problem with lost sales

This paper deals with the multi-item capacitated lot-sizing problem with setup times and lost sales. Because of lost sales, demands can be partially or totally lost. To find a good lower bound, we use a Lagrangian relaxation of the capacity constraints, when single-item uncapacitated lot-sizing problems with lost sales have to be solved. Each subproblem is solved using an adaptation of the O(T²)$O(T^2)$ dynamic programming algorithm of Aksen et al. [5]. To find feasible solutions, we propose a non-myopic heuristic based on a probing strategy and a refining procedure. We also propose a metaheuristic based on the adaptive large neighborhood search principle to improve solutions. Some computational experiments showing the effectiveness and limitation of each approach are presented.     

Mission design for a group of autonomous guided vehicles

In this paper, a generic approach for the integration of vehicle routing and scheduling and motion planning for a group of autonomous guided vehicles (AGVs) is proposed. The AGVs are requested to serve all the work stations in a two-dimensional environment while taking into account kinematics constraints and the environment’s geometry during their motion. The problem objective is the simultaneous determination of time-optimum and collision-free paths for all AGVs. The proposed method is investigated and discussed through a number of simulated experiments using a variety of environments and different initial conditions.     

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.     

A biased‐randomized algorithm for the two‐dimensional vehicle routing problem with and without item rotations

This paper proposes an efficient algorithm, with a reduced number of parameters, for solving the two‐dimensional loading‐capacitated vehicle routing problem (2L‐CVRP). This problem combines two of the most important issues in logistics, that is, vehicle routing and packing problems. Our approach contemplates unrestricted loading including the possibility of applying 90° rotations to each rectangular‐shaped item while loading it into the vehicle, which is a realistic assumption seldom considered in the existing literature. The algorithm uses a multistart approach that is designed to avoid local minima and also to make the algorithm an easily parallelizable one. At each restart, a biased randomization of a savings‐based routing algorithm is combined with an enhanced version of a classical packing heuristic to produce feasible good solutions for the 2L‐CVRP. The proposed algorithm has been compared with the classical benchmarks for two different 2L‐CVRP variants, that is, with and without item rotations. Experimental results show that our approach outperforms several best‐known solutions from previous work, both in terms of quality and the computational time needed to obtain them.     

CSNEO:协同服务器与网络能耗优化的VM映射算法

已有针对虚拟机映射问题的研究,主要以提高服务器资源及能耗效率为目标.综合考虑虚拟机映射过程中对服务器及网络设备能耗的影响,在对物理服务器、虚拟机资源及状态,虚拟机映射、网络通信矩阵等概念定义的基础上,对协同能耗优化及网络优化的虚拟机映射问题进行了建模.将问题抽象为多资源约束下的装箱问题与二次分配QAP问题,并设计了基于蚁群算法ACO与局部搜索算法2-exchange结合的虚拟机映射算法CSNEO来进行问题的求解.通过与MDBP-ACO、vector-VM等四种算法的对比实验结果表明:CSNEO算法一方面在满足多维资源约束的前提下,实现了更高的虚拟机映射效率;另一方面,相比只考虑网络优化的虚拟机放置算法,CSNEO在实现网络优化的同时具有更好的能耗效率.     

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem with flexible fleet size (GVRP‐flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.     

A simheuristic approach for the two-dimensional vehicle routing problem with stochastic travel times

The two-dimensional vehicle routing problem (2L-VRP) is a realistic extension of the classical vehicle routing problem in which customers’ demands are composed by sets of non-stackable items. Examples can be found in real-life applications such as the transportation of furniture or industrial machinery. Often, it is necessary to consider stochastic travel times due to traffic conditions or customers availability. However, there is a lack of works discussing stochastic versions of the 2L-VRP. This paper offers a model of the 2L-VRP with stochastic travel times that also includes penalty costs generated by overtime. To solve this stochastic and non-smooth version of the 2L-VRP, a hybrid simheuristic algorithm is proposed. Our approach combines Monte Carlo simulation, an iterated local search framework, and biased-randomised routing and packing heuristics. Our algorithm is tested on an extensive benchmark, which extends the deterministic one for the 2L-VRP with unrestricted and non-oriented loading.