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<!DOCTYPE html>
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<i class="title"> Iago A. Carvalho </i> <br/>
<i class="subtitle"> Operations research and optimization </i>
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<h1>Research /</h1>
<p>Here are my main research topics</p>
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<h3>Brief summary</h3>
<p>
I have interest in <span class="violet"> operations research, optimization, evolutionary algorithms,</span> and <span class="violet">experiments planning</span>.
My main research topic consists in the development of <span class="violet"> mathematical models </span> and <span class="violet">algorithms </span> for mixed-integer linear optimization problems.
Such problems are solved by <span class="violet"> exact methods</span>, such as branch-and-bound based algorithms,
dynamic programming, cutting-plane methods, or other advanced decomposition methods. Besides, <span class="violet">heuristic algorithms</span>, such as local search-based techniques,
evolutionary algorithms and lagrangian heuristics, are also used to get good solutions for hard instances.
Such methods and algorithms are generally applied to solve a class of problems, or a specific problem of great practical relevance.
</p>
<p>
I also have interest in studying <span class="violet">evolutionary algorithms</span>, researching new operators for different problem's classes. Besides, another interesting research field is
to study the <span class="violet">population dynamics</span> of such algorithms, characterizing how individuals (solutions) interact with each other by means of the genetic operators.
</p>
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<h2> Research topics </h2>
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<div class="col-sm-9 wow fadeInUp">
<h3> Heuristics </h3>
<p>
Techniques designed for <span class="violet">quickly</span> obtaining a solution for a problem. Heuristis are used when exact methods are too slow, or for finding an <span class="violet">approximate solution</span> when classic methods fail to find any exact solution. This is achieved by trading optimality, completeness, accuracy, or precision for speed.
</p>
<p>
The objective of a heuristic is to produce a <span class="violet">solution</span> in a reasonable <span class="violet">time span</span> that is good enough for solving the problem at hand. This solution may not be the best of all the actual solutions to this problem, or it may simply <span class="violet">approximate</span> the exact <span class="violet">solution</span>. But it is still valuable because finding it does <span class="violet">not require</span> a prohibitively <span class="violet">long time</span>.
</p>
<p>
Heuristics may produce results by themselves, or they may be used in conjunction with other <span class="violet">optimization algorithms</span> to improve their efficiency (e.g., they may be used to generate <span class="violet">initial solutions/bounds</span> for exact algorithms). They also can be combined with each other, resulting in <span class="violet">hybrid heuristic methods</span>. Besides, it is also possible to develop <span class="violet">metaheuristics</span>, i.e. general heuristic methods that can be applied to a wide range of problems.
</p>
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<div class="col-sm-3 research-illustration wow fadeInDown">
<a class="view-work" alt="An antenna potography" href="assets/img/research/antenna.png">
<img class="research heuristic" src="assets/img/research/antenna.png" />
</a>
<p class="research heuristic">
<a href="https://ti.arc.nasa.gov/m/pub-archive/1244h/1244%20(Hornby).pdf" target="_blank">An antenna design developed by NASA with the aid of heuristics</a>.
</p>
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<h3> Mathematical programming </h3>
<p>
Consists in developing and solving <span class="violet">mathematical models</span>, particularly <span class="violet">optimization models</span>, to assist in decision making. These models consists in optimizing a <span class="violet">objective function</span> of many <span class="violet">variables</span>, often subject to a set of <span class="violet">constraints</span>. Mathematical programming is usually used to find the <span class="violet">optimal solution</span> of a given problem. However, mathematical models can also be used as <span class="violet">heuristic</span> algorithms.
</p>
<p>
Several branches of mathematical programming exists:
</p>
<p>
<ul>
<li> <span class="violet">Linear programming</span>: The objective function and the constraints are linear. </li>
<li> <span class="violet">Integer programming</span>: As in linear programming, both objective function and constraints are linear. However, the solution only accepts integer-valued variables. </li>
<li> <span class="violet">Quadratic programming</span>: The objective function is quadratic and convex, while the constraints are all linear and non-linear inequalities.</li>
<li> <span class="violet">Optimization under uncertainty</span>: The problem data is subject to uncertainty. This uncertainty can be represented as an interval of values (or a discrete set of values) in the case of robust optimization, or as a probability function, in the case of stochastic optimization. Also, the problem can vary over time, being a dynamic optimization problem.</li>
</ul>
</p>
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<a class="view-work" alt="A mathematical model for the Travelling Salesman Problem" href="assets/img/research/tsp.png">
<img class="research heuristic" src="assets/img/research/tsp.png" />
</a>
<p class="research heuristic">
<a href="https://link.springer.com/chapter/10.1007/3-540-36626-1_5" target="_blank">A mathematical model for the Traveling Salesman Problem</a>.
</p>
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<h3> Evolutionary algorithms </h3>
<p>
Metaheuristics that evolves a pool of solutions, called <span class="violet">population</span>. Each solution of this population is said to be an <span class="violet">individual</span>. Individuals are assigned with a <span class="violet">fitness value</span>, which represents the solution's quality. An Evolutinary Algorithm evolves it's population by means of <span class="violet">genetic operators</span>, such as reproduction, mutation, recombination, and selection. These operators are iteratively applied until a <span class="violet">stopping criterion</span> is met.
</p>
<p>
The key aspect when designing evolutionary algorithms is the balance between <span class="violet">exploration</span> and <span class="violet">intensification</span>. Exploration is used to <span class="violet">explore</span> the search space. In addition, it is also responsible to <span class="violet">escape</span> from <span class="violet">local optimas</span>. On the other hand, intensification is needed to <span class="violet">improve</span> promissing solutions' fitness, thus better aproximating the problem's solution.
</p>
<p>
Evolutionary algorithms often perform well <span class="violet">approximating solutions</span> to all types of <span class="violet">problems</span>. They find applications in telecommunications, engineering, economics, chemistry, among other areas, being an important computational intelligence technique.
</p>
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<div class="col-sm-3 wow fadeInDown">
<a class="view-work" alt="A mathematical model for the Travelling Salesman Problem" href="assets/img/research/ea.png">
<img class="research heuristic" src="assets/img/research/ea.png" />
</a>
<p class="research ea">
<a href="http://neo.lcc.uma.es/opticomm/introea.html" target="_blank"> A scheme of a simple evolutionary algorithm, representing three different genetic operators. </a>
</p>
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<h3> Computational intelligence </h3>
<p>
Computational intelligence is a set methodologies and approaches that addresses <span class="violet">complex</span> real-world <span class="violet">problems</span> to which mathematical or traditional modelling can be useless. Such problems might contain some <span class="violet">uncertainties</span> during the process, or the process might simply be <span class="violet">stochastic</span> in nature. Indeed, many <span class="violet">real-life</span> problems cannot be translated into binary language for computers to process it. Computational Intelligence therefore <span class="violet">provides solutions</span> for such <span class="violet">problems</span>.
</p>
<p>
Evolutionary algorithms, mathematical modelling, heuristics and metaheuristics, neural networks, and fuzzy logic are the <span class="violet">main approaches</span> employed in computational intelligence, among other <span class="violet">stochastic</span> methods.
</p>
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<a class="view-work" alt="Cloudtag of the most important Computational Intelligence topics" href="assets/img/research/intelligence.png">
<img class="research intelligence" src="assets/img/research/intelligence.png" />
</a>
<a href="https://en.wikipedia.org/wiki/Computational_intelligence" target="_blank">
<p>Cloudtag of the most important Computational Intelligence topics</p>
</a>
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<h3>A Scenario Based Heuristic for the Robust Shortest Path Tree Problem</h3>
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<h3>Solving a Multiobjective Caloric-Restricted Diet Problem using Differential Evolution</h3>
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<h3>A Scenario Based Heuristic for the Robust Shortest Path Tree Problem</h3>
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<h3>Solving a Multiobjective Caloric-Restricted Diet Problem using Differential Evolution</h3>
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<h3>A Scenario Based Heuristic for the Robust Shortest Path Tree Problem</h3>
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My name is <span class="violet">Iago Augusto Carvalho</span>. I obtained a <span class="violet"> Ph.D.
</span> degree in Computer Science from the <a href="http://www.dcc.ufmg.br/pos" target="_blank"> UFMG
Computer Science Department</a>. Currently, I am working as an Assistant Professor <a
href="https://www.bcc.unifal-mg.edu.br/" target="_blank"> Computer Science Department </a> from <a
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