Abstract
In this work, we propose the Dengue Prize-collecting Arc Routing Problem (Dengue-PARP), which is the problem of finding optimal routes for spraying vehicles as a control measure of the mosquito population growth. In Dengue-PARP, each arc of a street block has a prize value related to the number of dengue cases. The goal of the Dengue-PARP is to maximize the prize collected in order to create a route that covers a subset of blocks. This work formulated the Dengue-PARP as an Integer Programming (IP) model, subjected to computational experiments with a set of 39 real-world instances with confirmed notified cases. The methodology achieved optimal values for 31 instances, being all the 25 instances that contain up to 372 vertices, and 6 of the largest instances, containing up to 1212 vertices. The model also obtained feasible solutions for the 8 remaining instances.

Abstract
In this work, we propose and explore a new variant of the Multicast Routing Problem (MRP) called Maximum Service in Multicast Routing with Quality of Service constraints (MS-MRP-QoS) applied in the context of vehicular ad-hoc networks, for which data must be sent from a root node to a set of terminal nodes. The use of all nodes is not mandatory and each connection between the root and a terminal aims to satisfy the quality of service according to the limits established for each metric. The objective is to maximize the number of serviced terminals according to the network's quality of service metrics. We present an integer programming formulation and four Lagrangian relaxations, to obtain good primal and dual bounds. We also develop a local search applied during the resolution of the Lagrangian relaxations. These methodologies were subjected to computational experiments with a set of 40 instances generated with characteristics of vehicular ad-hoc networks. Statistical analyzes were performed to compare the performances among the methodologies, and the results highlight the effectiveness of the approaches, since the model achieved optimal values for 29 instances, while the Lagrangian relaxations obtained competitive bounds, especially for large instances.

Abstract
This work addresses the problem of Maximum Service in Multicast Routing with Quality of Service constraints (MS-MRP-QoS) applied in the context of vehicular ad-hoc networks, where a vehicle network is provided for which it is desired send data from a root node to a set of terminal nodes. The use of all nodes is not mandatory and each connection between the root node and a terminal must satisfy the quality of service according to the limits established for each metric. The objective is to maximize the number of terminals served according to the network's quality of service metrics. In this dissertation, formulations of mixed integer programming and four Lagrangian relaxations were developed, aiming to obtain good quality primal and dual limits. A set of heuristics methods has also been developed, among them a local search in arborescences, applied during the resolution of the Lagrangian relaxations, and three BRKGA meta-heuristics with variations in the decoding method, one of them incorporating information from the Lagrange multipliers. The proposed methodologies were subjected to computational experiments with a set of instances generated with characteristics of ad-hoc vehicular networks. Statistical analyzes were performed to compare the performances between the methodologies. The results highlight the effectiveness of the mixed integer formulation in obtain high quality primal and dual limits for all instances of the set. The integer formulation, Lagrangian relaxations and BRKGA obtained good quality solutions and statistically similar.

Abstract
The Max-Cut problem consists of partitioning a set of n nodes into two subsets so that the sum of the edges between the subsets is large as possible. This Course Completion Paper presents 4 new versions of heuristics algorithms, based on Genetic Algorithm and Simulated Annealing, which use a set of valid inequalities in their structure. To the best of our knowledge, we are the first to use valid inequalities in the construction of metaheuristics for the Max-Cut Problem. The results of the computational experiments show that the use of these inequalities causes the algorithms to obtain better results than the classical version, that is, without the inequalities and also, in some cases, competitive with the state of the art for Max Cut.

Abstract
In the Maximally Diverse Grouping Problem, are given as input data a set of n elements and a function that provides the diversity degree between pair of elements. The problem is NP-hard and it aims at partitioning the set of elements into smaller subsets, called groups, in such a way that the diversity between the elements belonging to each group is as large as possible. In this paper, we present an integer linear programming model for this problem. The results from computational experiments show that the proposed model performs better when compared with the quadratic one from the literature.

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