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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The underdevelopment of Brazilian rural families is largely explained by their historical process of formation and by their poor access to a functional education and transportation systems. In the last decade, the federal government has been encouraging the nucleation of rural schools to offer better structured schools to the rural students. Multi-grade rural schools, often located closer to the rural families but with students of different grades being taught by the same teacher at the same class, are being shutdown and transfered to bigger, better installed facilities located near to the counties’ downtown area. The success of such endeavor relies on offering a transportation system for the rural students. Hence the Brazilian federal government has been making a great effort to support local administrators to provide better transport to rural students. One of such efforts gave rise to a central decision support system which solves the mixed load capacitated rural school bus **routing** **problem** with **heterogeneous** **fleet**. The mixed load feature allows students from different schools to ride the same bus during at the same time. This is an important but neglected **problem** in **vehicle** **routing** literature. In this thesis, four based meta-heuristic algorithms are devised and embedded into the support system. The computation performance of the proposed algorithms was assessed on solving four different datasets, including a real case from Brazil. The proposed methods were also compared with one known method from the literature. The attained cost savings and reduction of the number of buses required to serve the rural students showed the suitability of the mixed load approach over the single load one for the Brazilian rural context. Furthermore four based meta-heuristic based multi-objective algorithms to solve the multi-objective capacitated mixed load rural bus **routing** **problem** with **heterogeneous** **fleet** were also devised. The three involved objectives were the **routing** costs, the average weighted riding distances and the routes balance. The proposed multi-objective methods were compared with one from literature adapted for the **problem** and evaluated by assessing the metrics of cardinality, coverage and hyper-volume, followed by a statistical analyses. The work also introduces a new approach to help decision makers to selected a suitable solution from a Pareto set. All of the four devised multi-objective heuristics outperformed the literature procedure.

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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.

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We consider in this chapter the capacitated **vehicle** **routing** **problem** (CVRP), in which a fixed **fleet** of delivery vehicles of the same capacity must service known customer demands for a single commodity from a common de- pot at minimum transit costs. The CVRP has been studied in a large number of separate works in the literature, but (to our knowledge) no work addresses all the available benchmarks together, since it means solving 160 different instances. We use such a large set of instances to test the behavior of our algorithm in many different scenarios in order to give a deep analysis of it and a general view of this **problem** not biased by any ad hoc selection of indi- vidual instances. The included instances are characterized by many different features: instances from real world, theoretically motivated ones, clustered, non-clustered, with homogeneous or **heterogeneous** demands on customers, with the existence of drop times or not, etc.

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Na primeira, supõe-se que o número de veículos de cada tipo é ilimitado e o objetivo é encontrar o conjunto ótimo de veículos. Esse problema é chamado de FSMVRP, que é usualmente adotado para decisões táticas onde a frota ainda não está paga e a seleção do número de veículos tem que ser realizada. No segundo tipo, há uma frota fixa de veículos, o que significa que a frota e o número de veículos de cada tipo é fixo. Esse problema é chamado de **Heterogeneous** Fixed **Fleet** **Vehicle** **Routing** **Problem** (HFFVRP), ou Problema de Roteirização de Veículos com Frota Heterogênea Fixa, que é usualmente aplicada em decisões operacionais, onde é necessário computar viagens e atribuir veículos para elas. O FSMVRP pode ser considerado como um HFFVRP particular, onde o número de veículos de cada tipo é igual ao número de clientes (MIRHASSANI; SAADATI, 2014, tradução nossa).

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The MDVRPB can be defined as the following graph theory **problem**. Let � = (�, �) be a complete undirected graph, where � = {1. . . . . �} is the set of vertices, and � is the set of edges. The set � is partitioned into two subsets: the set of customers � = {1. . . . . �} and the set of potential depots � = {1. . . . . �}. Additionally, the set � is divided into a subset of Linehaul nodes (Linehaul customers - �), and the Backhaul nodes (Backhaul customers – �). Therefore, � = � ∪ �. The Linehaul customers ask for delivering products while Backhaul customers require the collection of products. Each customer has a nonnegative amount � � ( � ∈ �) of product to be delivered (� ∈ �) or to be picked up (� ∈ �). Each depot has a fictitious demand. i.e. � � = 0, with � ∈ �. A set of � identical vehicles with a given capacity � � is initially placed at each depot. It must be clarified that all vehicles are not necessarily used. For each

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The annual costs of each tractor were estimated based on the power and the age of the good, being directly proportional to these two variables. In other words, if three machines with the same age are compared, there is a clear advantage of tractor A (the defender of **problem** 1) over the other two, considering its lower operating cost, lower acquisition cost, and, consequently, lower depreciation values and a decrease of market price. Evidence can be clearly verified in the simulation results. In these tests, the tractor in use should be kept until the end when the tractor A is the defender (**problem** 1); however, when being the challenger (problems 2 and 3), the tractor in use should be exchanged at the earliest opportunity.

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The results show that our coevolutionary algorithm produces competitive solutions when compared with the best known so- lutions, even improving some of them. Besides, it is faster than HGSDAC+, which is the best method reported in the literature. The beneﬁt of our approach comes from its ability to decompose complex problems into simpler subproblems and evolve solutions to the subproblems in parallel. The decomposition approach also makes the method more scalable. In large MDVRP instances, it is unlikely that customers close to a depot will be allocated to a distant depot. Therefore, the coevolutionary algorithm incorporates important characteristics of a **problem** instance and allows a reduc- tion of the search space. Moreover, the evolutionary engine leads to simpler representations and genetic operators. Finally, the coevolu- tionary algorithm proposed in this work would greatly beneﬁt from cloud computing architectures, cluster computing and GPU program- ming.

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Three types of dynamic events can be highlighted: 1) the first are related to the business itself and are handled by decision makers personally because they require human in- tervention in order to adjust the planning process (e.g. new pick-up requests, activity priority changes , etc.); 2) random operational events that occur in the process and can be rep- resented by probability distributions (e.g. such as machine breakdown, **vehicle** breakdown, etc.); and 3) other stochas- tic situations which could be identified after some observa- tions are made (like traffic jams, weather conditions, etc.). The second and third types of event do not require human intervention, and can be represented by probability distribu- tions and identified by sensors. In this work, we made a pro- posal where vehicles could deal with traffic jams (an event of the third type).

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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.

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Constructive solutions will lead to connection of navigation systems and **fleet** management systems in order to provide information by one board device to manager and person who manages a **vehicle** base.The near future will bring effects directed to integration of Digital Tachograph Systems (DTS), Global Navigation Satellite Systems (GNSS) and also new technologies of data transferring (GPRS, UMTS). Integrated systems will improve many factors having important effect on improving safety and effectiveness of road transport.

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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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A fim de considerar o engarrafamento no planeja- mento da distribuição física, dentre os diversos conceitos de roteamento de veículos já estudados, o que mais se adere a esta realidade é o Time Dependent **Vehicle** **Routing** **Problem** (TDVRP). No TDVRP tem-se uma frota de veículos com capacidade limitada que deve coletar ou entregar cargas a clientes a partir de um depósito central. Os clientes devem ser designados aos veículos que realizam rotas, de forma que o tempo total gasto seja minimizado. O tempo de via- gem entre dois clientes ou entre um cliente e o depósito de- pende de suas distâncias e também do momento do dia que o transporte é feito; por exemplo, nos horários de pico o tempo para deslocamento é maior devido ao congestiona- mento. As janelas de tempo para servir os clientes, ou seja, o período que os clientes podem ser atendidos, devem ser consideradas assim como a máxima duração permitida para cada rota (horário de trabalho do motorista) (Malandraki e Daskin, 1992). O TDVRP é, então, uma extensão do Pro- blema de Roteamento de Veículos (VRP) que pode levar em

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49 envolving large scale accidents with cruise ships in order to assess the efficacy of the SAR system response. This study would consider different resources availability and location and would provide a sensitivity analysis regarding the efficacy of the response when more resources are available or are at different locations. The results from such study would provide rational arguments to sustain strategical alternatives regarding the acquisition of new SAR resources. The main idea with such study is to identify the capability gaps, as to resources availability, in the SAR system if a MRO would be required. In this sense, the MMRO **problem** can be understood as a special case of a Disaster Operations Management (DOM) **problem**. Altay and Green [146] review the literature on disaster operations management and group the activities of disaster operations management into four phases: mitigation, preparedness, response, and recovery. Caunhye et al. [147] categorize disaster operations between predisaster operations (short-notice evacuation, stock prepositioning, facility location for shelters, stores, and medical centers) and postdisaster activities (relief distribution, casualty transportation). In a more recent paper, Balcik [148] defines the Selective Assessment **Routing** **Problem** (SARP) which is formulated as a variant of the team orienteering **problem** (TOP) with a coverage objective. The purpose is to quickly evaluate the impact of a disaster on community groups within an affected region for estimating the need regarding humanitarian help. Sites may carry multiple characteristics (i.e., coastal and high impact) and the coverage objective is related with the number of “critical characteristics” observed by the teams. This assessment is made by selecting a number of sites in an affected region that must be visited by teams. A 3-index integer linear formulation is proposed for selecting the sites and **routing** the available teams. The structure of the SARP has similarities with the GVRP since the set of nodes carrying a particular critical characteristic can be considered as a cluster. In the SARP more than one node in each cluster can be visited in order to achieve the desired coveraged.

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following closely Archetti et al. [2015], four different problems can be identified, each one with a different solution. Figure 2.1 illustrates all the variants of the **problem**. The blue square shape represents the depot, which is the beginning and the end of routes, the circles represent the customers and the arrows the routes. In Figure 2.1a a separate **routing** **problem** is shown. In this case, a specific set of vehicles is dedicated to each commodity and any commodity is delivered to any customer with a single visit. A customer will receive as many visits as the number of commodities requested. This is the case of the classical **Vehicle** **Routing** **Problem**. In Figure 2.1b the mixed **routing** **problem** is displayed. In this case, any **vehicle** can deliver any set of commodities. All requests, regardless of consisting in one or more commodities, will be carried out in one visit so no customer can be visited more than once. This is the case of a single classical VRP. In Figure 2.1c, the split delivery mixed **routing** is illustrated. Any **vehicle** can deliver any set of commodities and both split deliveries and commodities are allowed. A customer may be visited several times if beneficial, even if only one commodity is requested. Finally, Figure 2.1d exhibits the split commodities mixed **routing** **problem**. It considers the **problem** where vehicles are flexible and can deliver any set of commodities. Multiple visits of a customer are allowed whenever the customer requests multiple commodities. When a commodity is delivered to a customer, the entire amount requested by the customer is delivered. If customers are visited more than once, the different vehicles will carry different commodities. This latter case is the one closest to our **problem**. However, for our **fleet** composition, two types of vehicles, SCV and MCV, are taken into account.

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To the best of our knowledge, the ﬁrst paper in the literature that involves an unlimited ﬂeet with ﬁxed costs was proposed by Golden, Assad, Levy, and Gheysens (1984). This **problem** is also referred as the **Fleet** Size and Mix VRP. The authors designed two heuristic methods to solve the **problem**: one based on best insertion and the other based on the classical Clarke and Wright Savings ( CWS ) heuristic (Clarke & Wright, 1964). The latter outperformed the former. They also de- veloped a mathematical formulation for the variant with dependent costs, and obtained the ﬁrst lower bounds for the VRP with unlimited ﬁxed ﬂeet. More studies on HVRPs with unlimited ﬂeet came there- after. Gendreau, Laporte, Musaraganyi, and Taillard (1999) included investment costs in the medium term and short-term operating costs that ﬂuctuated according to the speciﬁc customers attended per day. The authors suggested an algorithm based on Tabu Search ( TS ) with a tour construction phase and an improvement phase that consid- ered variable costs. They, however, assumed Euclidean problems only, where nodes were located in the same plane. Choi and Tcha (2007) obtained lower bounds for all variants of the unlimited ﬂeet prob- lem using a column generation approach based on the set covering **problem**. Baldacci and Mingozzi (2009) proposed a variant based on

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First question (Q1) aims to understand if any material collected in one ecoponto occupies less than the double or more than half the space inside the **vehicle** of other material collected simultaneously (criterion 1). Since this question evaluates demand (which is variable and only predictable based on historical data), it was established that if one collection point does not comply with the parameter established for criterion 1 (answer “No”), then it is automatically not eligible to be visited by a multi-compartment **vehicle**. If, however, it complies (answer “Yes”), then at least two capacity installed criteria – questions 2 (Q2), 3 (Q3) and 4 (Q4) – have to be fulfilled (meaning that the answer to at least two of these questions have to be “Yes”). These four questions combined intent to evaluate every ecoponto, by the listed order, resulting in a final decision for each one – question 5 (Q5): “Is the ecoponto (in analysis) eligible to be visited by a multi-compartment **vehicle**?”.

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The **vehicle** **routing** **problem** with backhauls and soft time windows contains two disjoint sets of customers: those that receive goods from the depot, who are called linehauls, and those that send goods to the depot, named backhauls. To each customer is associated an interval of time (time window), during which each one should be served. If a time window can be violated it is called soft, but this violation implies an additional cost. In this paper, only the upper limit of the interval can be exceeded. For solving this **problem** we created deterministic iterated local search algorithm, which was tested using a large set of benchmark problems taken from the literature. These computational tests have proven that this algorithm competes with best known algorithms in terms of the quality of the solutions andcomputing time. So far as we know, there is no published paper for this **problem** dealing with soft time windows, and, therefore, this comparison is only with the algorithms that do not allow time windows violation.

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. They did not address the VRP, and ignored the time windows constraint for customers. The resolution method used was the ant colony algorithm. Ref. [18] established a bi-level model using a genetic algorithm to solve the problems of locating and sizing mills and of transporting forest products. In their model, individual members of the initial population are found by solving the lo-cation and size of plants, at which point the VRP is solved for each individual. The authors do not integrate the time windows constraint for customers. Ref. [19] proposed a multi-depot forest transportation model. The resolution method they used involved the generation of transport nodes by solving the linear programming **problem** of flow distribution and **routing** of these nodes using a tabu search. Ref. [20] developed two linear programming models of planning for collaborative forest transportation for eight companies in the south of Sweden. The first model was based on the direct flow between supply and demand points, while the second one included backhauling. According to the authors, in the

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personalized services while ensuring a fair degree of privacy / non-intrusiveness. The goal of pervasive computing is to create ambient- intelligence, reliable connectivity, and secure and ubiquitous services in order to adapt to the associated context and activity. To make this envision a reality, various interconnected sensor networks have to be set up to collect context information, providing context-aware pervasive computing with adaptive capacity to dynamically changing environment. Wireless sensor networks (WSN) can help people to be aware of a lot of particular and reliable information anytime anywhere by monitoring, sensing, collecting and processing the information of various environments and scattered objects [24]. The flexibility, fault tolerance, high sensing, self- organization, fidelity, low-cost and rapid deployment characteristics of sensor networks are ideal to many new and exciting application areas such as military, environment monitoring, intelligent control, traffic management, medical treatment, manufacture industry, antiterrorism and so on [18,23]. Therefore, recent years have witnessed the rapid development of WSNs. In this paper, we address the issue of cross-layer networking for the pervasive networks , where the physical and MAC layer knowledge of the wireless medium is shared with network layer, in order to provide efficient **routing** scheme to prolong the network life time.

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