Top PDF Route Elimination Heuristic for Vehicle Routing Problem with Time Windows

Route Elimination Heuristic for Vehicle Routing Problem with Time Windows

Route Elimination Heuristic for Vehicle Routing Problem with Time Windows

As we know, the application of exact methods in the VRP problem solving is quite limited because of the combinatorial “explosion”. During the decades different successful metaheuristics have been developed, for instance Simulated Annealing, Evolutionary Algorithms, and Tabu Search (TS) etc. If we analyse the TS we must admit that despite its indisputable success it has problems in special cases when the route elimination goes together with considerable cost increment. Normally the object function of the TS is designed for finding cheaper solutions. Depending on the length of the tabu list the algorithm is able to reveal new regions. We can in the meantime change the object function and the length of the tabu-list but despite of these techniques it is difficult for the pure TS algorithm to get out from “deep valleys”, so the chance for eliminating a route is quite limited and the search is basically guided by the second priority objective. This topic is detailed in [2]. To leave such kind of deep valleys we have to find effective oscillation – sometimes it is called diversification – methods. In the route elimination respect – although it is the primary objective – the pure TS loses to other – lately developed – metaheuristics first of all hybrid metaheuristics [3]. The purpose of this part of the research and this article is to develop an effective route elimination phase.
Mostrar mais

13 Ler mais

Multiple Charging Station Location-Routing Problem with Time Window of Electric Vehicle

Multiple Charging Station Location-Routing Problem with Time Window of Electric Vehicle

Objective function (1) minimizes a mixed cost, where the first term denotes the construction cost of charging stations, the second term the cost of electricity recharged at depot and stations, and the third term the diver wage associated with working time. Constraints (2) guarantee that each customer is visited exactly once. Constraints (3) ensure that the number of incoming arcs is equal to that of outgoing arcs for each vertex, except for the instances of the depot. Constraints (4) and (5) ensure that all the employed vehicles start and end routes at the depot. Constraints (6) and (7) enforce the fulfillment of demands at customer nodes, and Constraints (8) restrict the initial cargo load level of a vehicle to its capacity. Constraints (9) link the battery levels of the vehicle at the vertices i and j of a traveled arc ( , ) i j . Both Constraints (6) and (9) adopt the idea from the big-M method. Constraints (10) and (11) ensure that each vehicle leaves the depot or a located station with a fully charged battery. Constraints (12) confine the type of infrastructure located at a candidate site to be one. Constraints (13) define the simplified relationship between charging time and charging amount at located charging stations. Constraints (14) prevent a vehicle from charging at a vertex from a customer set. Constraints (15) guarantee that each vehicle has sufficient power to reach a located station or depot. Constraints (16) and (17) establish the relation between arrival times at vertices i and j if the arc ( , ) i j is traveled. Constraints (17) particularly cover the condition, where the arc ( , ) i j starts with a charging station. Constraints (18) ensure that all customer vertices are visited within their time windows. Constraints (19) to (21) define the natural features of the variables.
Mostrar mais

12 Ler mais

Planning of vehicle routing with backup provisioning using wireless sensor technologies

Planning of vehicle routing with backup provisioning using wireless sensor technologies

Wireless sensors have been used for monitoring and tracking in several areas. With regard to their use in smart cities, these can be used to improve traffic control in large cities [13,14], collect information of passenger volume [15], provide optimal routes in real time [16], to reduce greenhouse gas (GHG) emissions [17], in rescue scenarios after a disaster [18] and even to aid the blind [19]. In [15], the system used for data gathering is discussed, but no further planning using such information is done. Our work on vehicle routing with backup provisioning goes further and uses the gathered data for vehicle route planning. The problem addressed in [16] is different from ours and can be considered more like a dynamic vehicle routing problem (DVRP), which has a wide range of real-world applications, as stated in [20]. In DVRP, real-time communication between vehicles and planners is required, and adjustments of the optimized routes can be performed during the execution process. This kind of problem, however, is not adequate when stops must be previously defined, which is the case that we are studying. The problem addressed in [17] falls into the category of green vehicle routing problems (GVRP), and the objective is to find routes while minimizing GHG emissions. In rescue scenarios, considered in [18], the demand-related information is quite limited in the initial rescue period and is intuitively unpredictable using historical data, and the emergency resources may be insufficient. The problems addressed in [17,18] are, therefore, different from the one considered in this article.
Mostrar mais

22 Ler mais

A multi-objective Pareto ant colony algorithm for the Multi-Depot Vehicle Routing problem with Backhauls

A multi-objective Pareto ant colony algorithm for the Multi-Depot Vehicle Routing problem with Backhauls

Surveys of existing methods for multi-objective problems were presented in Jozefowiez et al. (2008) and Zhou et al. (2011). In Jozefowiez et al. (2008), the authors examined multiobjective versions of several variants of the Vehicle Routing Problem (VRP) in terms of their objectives, their characteristics and the types of proposed algorithms to solve them. A survey of the state of the art of the multi-objective evolutionary algorithms was proposed by Zhou et al. (2011). This papers covers algorithms frameworks for multiobjective combinatorial problems during the last eight years. However, in the literature reviewed, there are few works considering the multi-objective version of the MDVRPB. Multiobjective metaheuristic approaches for combinatorial problems were presented in Doerner et al. (2004), Liu et al. (2006) and Lau et al. (2009). A multiobjective methodology by Pareto Ant Colony Optimization for solving a portfolio problem was introduced by Doerner et al. (2004). A multi-objective mixed zero-one integer-programming model for the vehicle routing problem with balanced workload and delivery time was introduced by Liu et al. (2006). In this work, a heuristic-based solution method was developed. A fuzzy multi-objective evolutionary algorithm for the problem of optimization of vehicle routing problems with multiple depots, multiple customers, and multiple products was proposed by Lau et al. (2009). In this work, two objectives were considered: minimization of the traveling distance and also the traveling time.
Mostrar mais

14 Ler mais

Assignment Problem and Vehicle Routing Problem for an Improvement of Cash Distribution

Assignment Problem and Vehicle Routing Problem for an Improvement of Cash Distribution

One of the most important extensions of the CVRP is the Vehicle Routing Problem with Time Window (VRPTW) which is each customer must be served within a specific time window. The objective is to minimize the vehicle fleet with the sum of travel time and waiting time needed to supply all customers in their required hour [10], [12]. A variety of exact algorithms and efficient heuristics have already been proposed for VRPTW by many researchers as shown in Table 1. In addition, Table 2 represents the various methods applying in exact algorithm, classical heuristic algorithms and metaheuristic algorithms for various type of VRP.
Mostrar mais

5 Ler mais

Ant Colony Optimization for Capacitated Vehicle Routing Problem

Ant Colony Optimization for Capacitated Vehicle Routing Problem

Abstract: Problem statement: The Capacitated Vehicle Routing Problem (CVRP) is a well-known combinatorial optimization problem which is concerned with the distribution of goods between the depot and customers. It is of economic importance to businesses as approximately 10-20% of the final cost of the goods is contributed by the transportation process. Approach: This problem was tackled using an Ant Colony Optimization (ACO) combined with heuristic approaches that act as the route improvement strategies. The proposed ACO utilized a pheromone evaporation procedure of standard ant algorithm in order to introduce an evaporation rate that depends on the solutions found by the artificial ants. Results: Computational experiments were conducted on benchmark data set and the results obtained from the proposed algorithms shown that the application of combination of two different heuristics in the ACO had the capability to improve the ants’ solutions better than ACO embedded with only one heuristic. Conclusion: ACO with swap and 3-opt heuristic has the capability to tackle the CVRP with satisfactory solution quality and run time. It is a viable alternative for solving the CVRP.
Mostrar mais

7 Ler mais

Algoritmos para o problema de roteamento de veículos capacitado com restrições de carregamento bidimensional

Algoritmos para o problema de roteamento de veículos capacitado com restrições de carregamento bidimensional

Além do CVRP, outras versões do VRP são muito estudadas. O Problema de Roteamento de Veículos com Janelas de Tempo (VRPTW, do inglês Vehicle Routing Problem with Time Windows) é uma extensão do CVRP onde cada cliente deve ter seu atendimento iniciado em uma janela de tempo e o veículo associado deve atendê-lo durante um tempo previamente estipulado. Por sua vez, o Problema de Roteamento de Veículos com Backhauls (VRPB, do inglês Vehicle Routing Problem with Backhauls) consiste em um CVRP onde o conjunto de clientes é particionado em dois subconjuntos: linehaul e backhaul. O primeiro subconjunto consiste nos clientes que necessitam de itens a serem entregues, enquanto o segundo representa os clientes que dispõem de itens a serem coletados. No VRPB, todos os clientes linehaul devem ser visitados antes dos clientes backhaul. Uma outra variação do VRP é o Problema de Roteamento de Veículos com Coleta e Entrega (VRPPD, do inglês Vehicle Routing Problem with Pick-ups and Deliveries), onde uma requisição de transporte é associada a dois clientes, de tal forma que a demanda é coletada em um deles e entregue no outro. Nesse problema, uma solução viável requer que a coleta de uma requisição seja feita antes de sua entrega, e que ambas operações ocorram na mesma rota. Informações sobre os trabalhos propostos e os detalhes do VRPTW, VRPB e VRPPD, podem ser encontrados em Alvarenga et al. [2007], Toth & Vigo [2001c] e Desaulniers et al. [2001], respectivamente.
Mostrar mais

134 Ler mais

Contributions to the single and multiple vehicle routing problems with deliveries and selective pickups

Contributions to the single and multiple vehicle routing problems with deliveries and selective pickups

Su¨ral and Bookbinder [30] are the first to directly address this problem. They present the problem using the notation α/β/γ, where α denotes the number of ve- hicles (1 for single and M for multiple), β the pickup service options (must or f ree if the pickup is respectively mandatory or optional) and γ the precedence order for visiting the customers (prec if all deliveries must precede the pickups, or any if they can be visited in any order). While the SVRPDSP is 1/free/any, according to this notation, the MVRPDSP can be described as M/free/any. They cited papers dealing with the 1/free/prec and 1/must/any problems, and claimed to be the first to address the 1/free/any. For the multiple vehicle versions, they list papers for the M/must/prec and M/free/prec, however no mention is made about the M/free/any, which is one of our objects of study. They propose a mixed integer linear programming formulation for the SVRPDSP along with some improvements on the constraints to strenghten the formulation, such as constraint disaggregation, coefficient improvement, cover and logi- cal inequalities, and lifted subtour elimination constraints. They modified 24 instances from the literature, with sizes of 10, 20 and 30 customers, to test their formulation. These instances were adapted for the SVRPDSP by setting some of the delivery de- mands as pickups in 3 different ways (20% of the customers reset as pickups, then 30% and 40%), generating a total of 72 instances, which were tested with some combina- tions of the formulation and the improvements resulting in about 75% of the instances optimally solved in a reasonable computational time for the best combination.
Mostrar mais

89 Ler mais

A multi agent based system to enable dynamic vehicle routing

A multi agent based system to enable dynamic vehicle routing

Abstract: The transport activities usually involves several actors and vehicles spread out on a network of streets. This complex system intricate the techniques to deal with dynamic events usually present in transport operations. In this context, as could be noted in the literature review, the use of multi-agent systems (MAS) seems suitable to support the autonomous decision-making. This work presents an agent based system to deal with a dynamic vehicle routing problem, more precisely, in a pick-up problem, where some tasks assigned to vehicles at the beginning of the operation could be transferred to others vehicles. The task transfer happens when the vehicle agents perceive that the cycle time can exceed the daily limit of working hours, and is done through a negotiation protocol called Vickrey. The proposed system allows a collaborative decision- making among the agents, which makes possible adjustments during the course of the planned route.
Mostrar mais

9 Ler mais

Vehicle routing and tour planning problem: a cement industry case study

Vehicle routing and tour planning problem: a cement industry case study

The cement industry is not an exception. Cement is the second most consumed substance in the world and with the great number of trucks arriving at cement facilities, every day, the supply chain management of this industry must encompass this management as well. With the lack of assistance and guidance clients have inside the cement facilities, both companies incur in additional costs and clients experience reduced levels of service quality. To overcome these issues, three algorithms were developed and implemented. Each algorithm has different specifications and different goals. However, all the developed algorithms improve the service quality, guiding the truck drivers – the clients – inside the plants and giving the routes in shorter periods of time. One algorithm guides the trucks through the minimum distance route and will serve as a comparison term for the other two. The other two algorithms, named equilibrium approaches, are the main contribution of this dissertation. These dynamic algorithms consider not only the traveled distance, but also the workload both in the servers and in the roads. The entrance management in the facilities is also a crucial aspect cement companies must be aware of. Several thought policies are presented and an algorithm for the entrance management is developed and implemented. With a simulation software, the developed algorithms were tested and simulated. The simulation results are reported and discussed.
Mostrar mais

141 Ler mais

A matheuristic for the consistent vehicle routing problem with service level agreements: a case study in the pharmaceutical distribution sector

A matheuristic for the consistent vehicle routing problem with service level agreements: a case study in the pharmaceutical distribution sector

The company currently defines its routes in a two step method. First, an instance with all the internal customers is created and is manually separated in geographical areas and in period of operation. The requests from the external customers, which are not period specific, are not considered during this phase because it is currently not possible to assign a route to each one of them on an operational level, even though they represent almost half of the total deliveries in one of the depots. Then, the nodes are used as input in a commercial route planner to define the robust routes for that period of operation. These routes are then used operationally until a new redefinition of the routes is performed, which does not have a defined frequency and is done very sporadically. All the customers that are not considered during the planning stage and, as such, do not have a specified route to be assigned to, are assigned daily on an operational level. A first rough assignment is made by having a manually created table that assigns every national postal code prefix to a route. However, some postal code prefixes correspond to a large area and some even have multiple routes going through them. In these cases, the drivers are given the task of reassigning some of the packages when they deem them to be in the wrong route. This procedure is time consuming and leads to mistakes and to deliveries that could be made in a better route. Moreover, the interchangeability of some deliveries, which may be delivered in any period of the day, is completely lost and every load is dispatched in the morning period unless it does not fit in the truck. This places a heavy burden on the morning routes, which often operate on tight schedules, and any delay in these early routes tends to spread to the remaining periods of the day as the drivers may be late for their next shift.
Mostrar mais

68 Ler mais

Contributions to the single and multiple vehicle routing problem with deliveries and selective pickup

Contributions to the single and multiple vehicle routing problem with deliveries and selective pickup

Su¨ral and Bookbinder [30] are the first to directly address this problem. They present the problem using the notation α/β/γ, where α denotes the number of ve- hicles (1 for single and M for multiple), β the pickup service options (must or f ree if the pickup is respectively mandatory or optional) and γ the precedence order for visiting the customers (prec if all deliveries must precede the pickups, or any if they can be visited in any order). While the SVRPDSP is 1/free/any, according to this notation, the MVRPDSP can be described as M/free/any. They cited papers dealing with the 1/free/prec and 1/must/any problems, and claimed to be the first to address the 1/free/any. For the multiple vehicle versions, they list papers for the M/must/prec and M/free/prec, however no mention is made about the M/free/any, which is one of our objects of study. They propose a mixed integer linear programming formulation for the SVRPDSP along with some improvements on the constraints to strenghten the formulation, such as constraint disaggregation, coefficient improvement, cover and logi- cal inequalities, and lifted subtour elimination constraints. They modified 24 instances from the literature, with sizes of 10, 20 and 30 customers, to test their formulation. These instances were adapted for the SVRPDSP by setting some of the delivery de- mands as pickups in 3 different ways (20% of the customers reset as pickups, then 30% and 40%), generating a total of 72 instances, which were tested with some combina- tions of the formulation and the improvements resulting in about 75% of the instances optimally solved in a reasonable computational time for the best combination.
Mostrar mais

87 Ler mais

Modelo matemático Two-echelon Capacitated Vehicle Routing Problem para a logística de distribuição de encomendas

Modelo matemático Two-echelon Capacitated Vehicle Routing Problem para a logística de distribuição de encomendas

Variações do 2E-CVRP também são encontradas na literatura. Crainic et al. (2009) apresentaram uma variação do 2E-CVRP, chamada de two-echelon, synchronized, scheduled, multi-depot, multiple-tour, heterogeneous vehi- cle routing problem with time windows (2SS-MDMT- VRPTW), ao tratar o gerenciamento da Logística Urbana. Esses autores desenvolveram um modelo e formulações ge- rais para a nova classe a partir de Programação Linear In- teira, mas não realizaram nenhum experimento computaci- onal para a mesma. Grangier et al. (2014) abordaram uma nova classe do 2E-CVRP, chamada two-echelon multiple- trip vehicle routing problem with sattelite synchronization (2E-MTVRP-SS) e utilizaram uma meta-heurística Adap- tive Large Neighborhood Search para resolução do pro- blema. Soysal et al. (2014) abordaram pela primeira vez a variação time-dependent em problemas 2E-CVRP, o Two- echelon Capacitated Vehicle Routing Problem with Time Dependent (2E-CVRPTD), assim como fatores que influen- ciam no consumo de combustível, como o tipo de veículo, a distância percorrida, a velocidade e a carga transportada pelo veículo. Esses autores desenvolveram um modelo ma- temético de PLIM baseada no modelo proposto por Jepsen et al. (2013) e testaram o modelo em um caso real, uma ca- deia de suprimentos localizada nos Países Baixos, com 1 depósito, 2 satélites e 16 clientes.
Mostrar mais

9 Ler mais

Multi-Objective Forest Vehicle Routing Using Savings-Insertion and Reactive Tabu with a Variable Threshold

Multi-Objective Forest Vehicle Routing Using Savings-Insertion and Reactive Tabu with a Variable Threshold

resolution method used was a bi-objective tabu search algorithm. The first objective is to minimize the total number of vehicles used, and the second, to minimize the total cost, which is the weighted sum of the total distance traveled and the corresponding total time. Ref. [13], based on the work of [12], established a multi-criteria optimization model of long-haul VRP and scheduling integrating working hours rules. The solution method used was a bi- objective tabu search algorithm determining a set of heuristic non-dominated solutions. The mechanism consists of a single thread in which the weights assigned to the two objectives, namely, operating costs and driver inconvenience, are dynamically modified, and in which dominated solutions are eliminated throughout the search. Ref. [14] proposed a multi-depot VRP with a simultaneous delivery and pick-up model. The resolution method used was the iterated local search embedded adaptive neighborhood selection approach. Ref. [15] tested local search move operators on the VRP with split deliveries and time windows. To that end, they used eight local search opera-tors, in combinations of up to three of them, paired with a max-min ant system. Ref. [16] developed a dynamic model for solving the mixed integer programming of forest plant location and design, as well as production levels and flows between origins and destinations. Ref. [17] proposed a multi-depot forest transportation model solving the tactical problem of the flow between origins and destinations without solving the operational problem of VRP. The solution method used was column generation. Ref. [6] proposed a model for forest transportation, solving the problem of flow between origins and destinations, and involving a sedimentation constraint
Mostrar mais

9 Ler mais

REPOSITORIO INSTITUCIONAL DA UFOP: A cooperative coevolutionary algorithm for the multi-depot vehicle routing problem.

REPOSITORIO INSTITUCIONAL DA UFOP: A cooperative coevolutionary algorithm for the multi-depot vehicle routing problem.

The Multi-Depot Vehicle Routing Problem (MDVRP) is an important variant of the classical Vehicle Routing Problem (VRP), where the customers can be served from a number of depots. This paper introduces a coop- erative coevolutionary algorithm to minimize the total route cost of the MDVRP. Coevolutionary algorithms are inspired by the simultaneous evolution process involving two or more species. In this approach, the prob- lem is decomposed into smaller subproblems and individuals from different populations are combined to create a complete solution to the original problem. This paper presents a problem decomposition approach for the MDVRP in which each subproblem becomes a single depot VRP and evolves independently in its do- main space. Customers are distributed among the depots based on their distance from the depots and their distance from their closest neighbor. A population is associated with each depot where the individuals rep- resent partial solutions to the problem, that is, sets of routes over customers assigned to the corresponding depot. The fitness of a partial solution depends on its ability to cooperate with partial solutions from other populations to form a complete solution to the MDVRP. As the problem is decomposed and each part evolves separately, this approach is strongly suitable to parallel environments. Therefore, a parallel evolution strategy environment with a variable length genotype coupled with local search operators is proposed. A large num- ber of experiments have been conducted to assess the performance of this approach. The results suggest that the proposed coevolutionary algorithm in a parallel environment is able to produce high-quality solutions to the MDVRP in low computational time.
Mostrar mais

14 Ler mais

A guide to vehicle routing heuristics

A guide to vehicle routing heuristics

Rochat and Taillard22 have developed an adaptive memory mechanism for the capacity and route duration constrained VRP and for the VRP with time windows, based on the earlier [r]

12 Ler mais

 Generalization of the MOACS algorithm for Many Objectives. An application to motorcycle distribution

Generalization of the MOACS algorithm for Many Objectives. An application to motorcycle distribution

The Mixed Fleet VRP (MFVRP), implies vehicles with different capabilities (or heterogeneous capabilities), with known fixed and variable costs related to each vehicle in a fleet that must serve a series of consumers with known demands. In [15], Golden, Assad, Levy and Gheysens describe a series of effective heuristic procedures for the problem of routing with a heterogeneous fleet, with the objective of determining the optimal truck fleet size and its capabilities, minimizing a cost function. The authors, Subramanian, Penna, Uchoa, and Ochi [16] studied the optimal composition of a fleet of vehicles through a hybrid algorithm, as well as determining the routes that would minimize travel expenses. Similarly, Salhi and Rand, in [17], and Taillard in [18], also attempt to find the ideal composition for a fleet of vehicles by solving the MFVRP. The authors of [19], Wassan and Osman, developed new Tabu Search (TS) variants in order to solve the heterogeneous fleet problem. At the same time, the article by Chen and Ching [20] suggests the alternative of employing an Ant Colony Optimization algorithm in order to solve the heterogeneous fleet routing problem, proving that ACO is a competitive algorithm for this VRP variant; another factor influencing its adoption for this work.
Mostrar mais

14 Ler mais

Scatter search para problemas de roteirização de veículos com frota heterogênea, janelas de tempo e entregas fracionadas.

Scatter search para problemas de roteirização de veículos com frota heterogênea, janelas de tempo e entregas fracionadas.

This work studies the implementation of heuristics and scatter search (SS) metaheuristic in a real heterogeneous fleet vehicle routing problem with time windows and split deliveries (HFVRPTWSD) in Brazil. In the vehicle routing problem with time windows and split deliveries (VRPSD) each client can be supplied by more than one vehicle. The problem is based in a single depot, the demand of each client can be greater than the vehicle’s capacity and beyond the time windows constraints, and there are also vehicle capacity and accessibility constraints (some customers cannot be served by some vehicles). The models were applied in one of the biggest retail market in Brazil that has 519 stores distributed in 12 Brazilian states. Results showed improvements over current solutions in a real case, reducing up to 8% the total cost of the operation.
Mostrar mais

15 Ler mais

A solution for a real-time stochastic capacitated vehicle routing problem with time windows

A solution for a real-time stochastic capacitated vehicle routing problem with time windows

Stage 3. Post optimization - The next stage is a cycle which is computed until all routes are closed by the ERP/administrator or all PFIH parameters are tested. The cycle starts by getting (and removing) the most promising solution from P F IHSet and setting an ejection rate value. A tabu list, T , is started which will contain all computed solutions before applying post-optimization, for each ejection rate. Then try at most M axT ries times to improve the solution by applying: (a) a 2-Opt operator (which iterates through all routes, one by one, and tries to rearrange the sequence by which the customers are visited in order to reduce the route distance, maintaining feasibility [CGF + 08]); (b) a cross route operator (similar to the One Point Crossover operator of the Genetic Algorithms [MaM13], receives two paths as input, and tries to find a point where the routes can be crossed, thus improving the total distance and without losing feasibility); and (c) a band ejection operator which is a generalization of the radial ejection [SSSWD00](selects a route and, based on the proximity and similarity of the nodes, for each customer located in the route ejects it and a certain number of geographical neighbors which are then reinserted in other routes, without violating the problem’s constraints). Please refer to [CSME15] for a more detailed explanation. The first two operators are capable of diminishing the total distance, i.e., doing route optimization. However, they are not capable of reducing the number of routes present in the original solution, which can be achieved using the third operator. The first two stages are quite fast. Therefore it is during the last stage that new orders arriving from the i3FR-Hub to the i3FR-Opt are treated. On other words, the i3FR-Opt/Server thread is responsible for the continuous communications with the i3FR- Hub, and whenever new orders arrive they are placed in shared memory. After each cycle the i3FR-Opt/Optimizer checks the shared memory for new orders that will be treated as ejected customers, i.e., it tries to insert them in the existing routes or creates a new route if that is not possible. As mentioned, during the process, improved solutions are sent from the i3FR-Opt to the i3FR-Hub which in turn resends them to the ERP/administrator.
Mostrar mais

10 Ler mais

A Clustering Approach for Vehicle Routing Problems with Hard Time Windows

A Clustering Approach for Vehicle Routing Problems with Hard Time Windows

The Vehicle Routing Problem (VRP) is a well known combinatorial optimization problem and many studies have been dedicated to it over the years since solving the VRP optimally or near-optimally for very large size problems has many practical applications (e.g. in various logistics systems). Vehicle Routing Problem with hard Time Windows (VRPTW) is probably the most studied variant of the VRP problem and the presence of time windows requires complex techniques to handle it. In fact, finding a feasible solution to the VRPTW when the number of vehicles is fixed is an NP-complete problem. However, VRPTW is well studied and many different approaches to solve it have been developed over the years.
Mostrar mais

70 Ler mais

Show all 10000 documents...