In **the** **Single** **Vehicle** **Routing** **Problem** **with** **Deliveries** **and** **Selective** Pickups (SVR- PDSP) there are a set of customers **to** be served **and** a depot from where a **vehicle** departs **to** serve **the** customers. Each customer has a certain demand of goods either **to** be delivered or **to** be picked up, which generates a revenue if collected. It is possible for a customer **to** have both demands. In such case, if both are going **to** be served, they can be performed simultaneously or in two different visits, each completely fulfilling one of **the** demands. **The** **vehicle** that departs from **the** depot shall perform a route that visits a subset of customers performing **deliveries** **and** pickups, then return **to** **the** depot. All delivery demands must be fulfilled exactly once. **The** **pickup** demands, however, are not mandatory, therefore they are only performed if there is enough space in **the** **vehicle** **and** if they are profitable. Serving a **pickup** demand is profitable if **the** revenue generated by collecting it is greater than **the** additional **routing** cost. One can notice that some pickups might not be served at all **and** it is possible **to** argue that they would need **to** be performed at some point. **To** address this issue these **pickup** demands could either be delayed **to** be served in **the** following day, or a third party service can be used **to** collect these pickups, which could be a less costly option than forcing all pickups **to** be fulfilled or sending another **vehicle** only **to** perform a few pickups. **The** objective is **to** find a route that minimizes **the** total **routing** cost, which is **the** travel cost **to** visit **the** customers minus **the** revenue generated by **the** collected pickups. Fig- ure 1.1a shows a small example **with** 8 customers **and** a **vehicle** **with** capacity equals **to** 35. In **the** figure, d is **the** delivery demand of a customer, while p stands for **the** **pickup** demand **and** r is **the** revenue generated by performing **the** respective **pickup** demand of **the** customer. **The** transportation cost of **the** solution presented is equal **to** 5 + 4 + 4 + 1 + 10 + 8 + 5 + 4 = 41 **and** **the** total revenue generated by **the** three pickups collected is 5 + 20 + 8 = 33. Therefore **the** total cost of this solutions is 41 − 33 = 8. In

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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

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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.

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More recently, a variant of **the** classical VRP, called **the** open **vehicle** **routing** **problem** (OVRP), attracted **the** attention of practitioners **and** researchers. In this case, vehicles are not required **to** return **to** **the** depot after serving **the** last customer on a route [9]. This usually arises in real-world problems, like **the** planning of train services or bus routes (see [10]), or when industries do not own a **vehicle** fleet or their private fleet is inadequate **to** fully satisfy customer demand, **and** distribution services (or part of them) are either entrusted **to** external contractors or assigned **to** a hired **vehicle** fleet. In these cases, vehicles are not required **to** return **to** **the** central depot after their **deliveries** have been satisfied. **The** main difference between VRP **and** OVRP is that in VRP, **the** routes are Hamiltonian cycles, **and** in **the** OVRP, **the** routes are Hamiltonian paths originated at **the** depot **and** ending at one of **the** customers, so **the** shortest Hamiltonian path **problem** **with** a fixed source node has **to** be solved for each **vehicle** in **the** OVRP. **The** traveling salesperson **problem**, known **to** be NP-hard, consists of finding **the** Hamiltonian cycle **with** **the** lowest cost. This, together **with** **the** fact that **the** Hamiltonian cycle **problem** (HCP) is NP-hard **and** can be reduced **to** **the** Hamiltonian path **problem** (HPP) [11], allows us **to** conclude that **the** shortest HPP is NP-hard. Consequently, **the** OVRP is also an NP-hard **problem**, justifying **the** development of heuristics **and** meta-heuristics (see [12], where a new swarm intelligence approach is proposed). **The** **vehicle** **routing** **with** backup provisioning, under discussion here, can be seen as a variant of **the** OVRP applied **to** **the** transportation of persons, considering **multiple** depots **and** having **the** possibility of backup provision **to** certain critical stops. Therefore, **the** **vehicle** **routing** **with** backup provisioning is NP-hard.

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This research mainly focuses on a less studied VRP extension which is **the** conVRP. This optimization **problem** demands **the** definition of **vehicle** routes for several periods, maintaining a certain level of consistency on pre-selected metrics. For instance, when distribution companies make an agreement for **the** **deliveries** **to** be made always by same driver, they are adding consis- tency constraints in order **to** take into account customer satisfaction. Therefore, **the** objective is **to** achieve minimum cost **routing** plans satisfying **the** classical **routing** constraints as well as con- sistency requirements taking into account customer satisfaction. Generally, this type of customer- oriented **routing** considers two types of consistency for customer satisfaction: driver consistency, **and** time consistency (Kovacs et al., 2014a). Driver consistency is measured by **the** number of different drivers that visit a customer whereas time consistency is related **to** **the** maximum dif- ference between **the** earliest visit **and** **the** latest arrival at each customer. **The** conVRP arises in many industries where customer satisfaction is considered as a distinctive factor of competitive- ness. Particularly in industries transporting small packages, providing a standard service **with** a **single** driver **and** approximately at **the** same time of **the** day enables **the** customers **to** prepare them- selves for a delivery, strengthening supplier/customer relationships (Kovacs et al., 2014b). Since **the** conVRP considers several periods, it can be seen as a tactical extension of **the** classical VRP **with** customer-focused routes.

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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.

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A numerical **and** experimental study of **the** aerodynamics of a generic **pickup** was performed. Studied geometry was established on **the** dimensions of **the** most representative models of **the** light **pickup** fleet in Brazil. Baseline model is composed only by sharp edges **and** flat surfaces; a second version was prepared filleting those edges (rounded model). Numerical steady simulations (RANS) were performed on commercial software Star-CCM+ using **the** SST k-w turbulence model; tetraedrical meshes have an average of 8 million elements. All simulations were prepared on an i7 processor **with** 12 cores, 48 GB of RAM. For wind-tunnel testing, model was 3D printed in 1:10 scale. On experimental procedures, qualitative (wall tufts visualization) **and** quantitative (hot-wire anemometry velocity profiles) tests revealed main structures on wake **and** on **the** close wall.

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This work presented **the** **vehicle** **routing** optimization system developed **to** be integrated **with** an existing ERP. **The** optimization procedure takes into consideration **the** need for a near real-time **routing** solution under dynamic orders **and** interactions **with** **the** system administrator. In this sight, this work described **the** interactions **and** dependencies between **the** system’s four main components, namely: i3FR-Opt (where **the** computation of **the** routes is done), **the** i3FR-Hub (implementing a channel **to** all **the** communications inside **the** system **and** **to** **the** exterior), **the** i3FR-DB (provider of local storage **to** **the** information relevant **to** **the** optimization procedure), **and** i3FR-Maps (a cartography subsystem of **routing** informations). **With** this structure it is possible **to** deal **with** late orders **and** diﬀerent states for **the** routes, which allows **to** do a phased picking **and** loading of **the** vehicles. As mere examples, some results for **the** Algarve’s region were presented showing diﬀerent solution depending on **the** time windows restrictions.

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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]

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Furthermore, for attainment of improved solutions **to** **the** **problem**, we can use **the** route improvement strategies in **the** algorithms. One of these strategies involves **the** inclusion of a local exchange procedure **to** act as an improvement heuristic within **the** routes found by individual ants. One of **the** techniques used for this purpose is **the** common 2-opt heuristic where all possible pairwise exchanges of customer locations visited by individual **vehicle** are tested **to** see if an overall improvement in **the** objective function can be attained.

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Pheromone update: After all **the** artificial ants have improved **the** solutions through **the** heuristics, **the** pheromone trails will be updated. This is **the** main feature of an ACO algorithm which assists at improving future solutions since **the** updated pheromone trails would reflect **the** ants’ performance **and** **the** quality of their solutions found. In this context, there are two main phases of **the** pheromone update in an AS algorithm (Dorigo **and** Stutzle, 2004), which are **the** pheromone evaporation **and** **the** pheromone deposition. In **the** proposed ACO, modifications would be made **to** **the** usual pheromone evaporation whereas **the** pheromone deposition would be referred **to** Bullnheimer et al. (1999) which comprises of **the** elitist strategy **and** also **the** concept of ranking. **The** details of **the** pheromone update procedures implemented in **the** proposed ACO are described as follows:

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tasks in **the** sequence {15,16, … , 25} should be transferred **to** another **vehicle** agent. Then, **the** **vehicle** agent starts **to** examine which one of **the** 11 remaining tasks should be transferred. By examining task 16, it notes that there are prospective gains due **to** two types of reduction: (a) reduced mileage, **and** (b) reduced down time when visiting client 16, which should be transferred from **the** route of **the** regular **vehicle** agent. **The** gain is **the** difference between **the** cost generated by **the** remaining basic **routing** sequence, **and** **the** new **routing** that excludes **the** selected task. Therefore, by analyzing every **single** task on sequence {15,16, … , 25} **the** system will select **the** tasks **to** be transferred that will mostly reduce cost. **The** third form of selecting **the** task **to** be trans- ferred is an extension of **the** previous form. After some at- tempts **to** transfer a task from **the** **routing**, such as task 16, **the** VRP algorithm is once again applied **to** **the** other activ- ities, resetting **the** **routing** sequence but considering all **the** other remaining tasks except number 16. Finally, **the** task that most reduces mileage in **the** regular VRP sequence is chosen.

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geograficamente dispersas, encontrar o melhor conjunto de rotas para atender todos os. clientes[r]

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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.

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In this cast iron eutectic transformation takes place in **the** temperature of 7 C less, than in cast iron **with** 0,50% Cu, but it is still higher than in cast iron **with** chromium. Molybdenum pres- ence caused ledeburitic carbides forming (HKL thermal effect, Fig. 10 a). Copper increase caused small amount of martensite forming, but did not change significantly carbides amount. It is important, that ferrite amount is decreased **and** pearlite disap- peared in cast iron metal matrix microstructure.

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Remark 2 (About MIP Models **and** Complexity). Modeling VSR through a MIP (Mixed Integer Linear Program) is possible, but inefficient. **The** reason is that there is no a priori bound about **the** number of times a given station is going **to** be visited by a same carrier. As for complexity, in **the** case when K = 1 (α very large), v(x) values are equal **to** 1 or −1, CAP = 1 **and** δ = 0, our **problem** is equivalent **to** **the** Travelling Salesman **Problem** set on a bipartite graph (**the** excess stations on one side **and** **the** deficit ones on **the** other side), which is NP-Hard. Non Preemptive VSR also contains **the** Uncapacitated Swapping **Problem**, which is also NP-Hard (see [1]).

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In a cooperative coevolutionary algorithm, each population repre- sents a part of a complex decomposable **problem** (Engelbrecht, 2007). Accordingly, **the** true ﬁtness of an individual can only be obtained from its interaction **with** other individuals from **the** same or other populations. Each individual receives a reward or punishment, be- ing rewarded when it interacts well **with** **the** others while getting a punishment otherwise. A cooperative coevolutionary algorithm is considered in this work because **the** **problem** can be decomposed into smaller subproblems, each one evolving in parallel. Partial so- lutions for those subproblems cooperate **to** create a complete solu- tion for **the** MDVRP. In this situation, a competitive strategy would not be suitable because a complete solution is obtained from infor- mation gathered from all subproblems **and** there is no competition among these subproblems. Fig. 2 depicts a general cooperative coevo- lutionary algorithm **with** decomposition. A complex **problem** is ﬁrst decomposed into smaller subproblems. Each population is evolved on its subproblem **and**, after a number of generations, individuals from these populations are combined **to** create complete solutions **to** **the** original **problem**. Through this process, it is possible **to** compute **the** ﬁtness of these complete solutions. Some feedback information is then returned **to** each population, such as **the** best solution found so far, any required updates **to** **the** individuals in **the** population, etc.

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No processo de distribuição é necessário fazer a entrega de bens e serviços para clientes dispersos geograficamente, nesse processo encontra-se o **Vehicle** **Routing** **Problem** (VRP). O VRP, ou Problema de Roteirização de Veículos, é o nome de uma classe de problemas para definir a sequência de visita a clientes dispersos geograficamente com um conjunto finito de veículos a partir de um depósito comum. Para resolver este problema e analisar os resultados obtidos, foi desenvolvido um algoritmo utilizando a meta-heurística Variable Neighborhood Descent (VND), ou Descida em Vizinhança Variável, o qual foi aplicado em instâncias conhecidas na literatura e realizado um benchmarking com outros algoritmos. Esse problema aplica-se na prática em coleta de peças automobilísticas, coleta de lixo industrial, coleta de lixo residencial, limpeza de ruas, e entre outras situações. Os VRPs receberam muita atenção nos últimos anos devido a sua aplicabilidade e sua importância econômica na determinação de estratégias eficientes, com o objetivo de reduzir os custos operacionais. Os resultados obtidos com o algoritmo proposto foram próximos dos algoritmos estudados no benchmarking realizado. Contudo, superando alguns destes algoritmos em apenas uma das instâncias das oito instâncias utilizadas.

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