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The study and resolution of combinatorial optimization problems with one or more objectives constitute an important field of work within Operations Research and Computer Science. In this context, Transportation and Logistics problems stand out, where the aim is to determine optimal solutions considering one or more criteria. For these and other problems of a similar nature, a significant number of authors have dedicated considerable effort, resulting in relevant contributions published in books and high-impact journals. The strategic planning process in public transportation is usually divided into three steps: network design, route planning, and route scheduling. Efficient network optimization tools are necessary at all these steps due to the enormous scale of these problems in general. This project will analyze the theoretical foundations, present the lines of research developed in the existing literature on the subject, study the algorithms already proposed, construct new procedures, and conduct a comparative study that highlights the advantages and disadvantages of the different models. In some existing models for transportation problems, the resulting model consists of variations of the multiple flow problem in a network. Generally, the exact solution of these problems combines classical mathematical programming tools that do not typically exploit the underlying network model. However, from a computational standpoint, it is preferable to design ad hoc algorithms that are more efficient than those currently available. To this end, we will consider mathematical models for which we will develop intelligent enumeration schemes that will allow us to solve these problems exactly, even when the problem dimensions are large. The proposed enumeration tools are based on the efficient algorithms developed by our research group for enumerating solutions to classical combinatorial optimization problems. These tools enable the solution of transportation problems, since these are classical combinatorial optimization problems with additional constraints. The proposed methodology will also allow us to initiate a line of research that we call evolutionary algorithms with genealogy and hard extinction mechanisms. This line of research arises from the consideration of the tools to be developed in this project and will be applied to problems in the fields of transportation and planning. Part of this new line will be the doctoral thesis of a doctoral student supervised by the principal investigator of this project.
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One of the research fields in Operations Research and in Computer Science with a great importance is the study of Combinatorial Optimization problems with one objective or several objectives and the development of approaches to solve them. In this framework, it is possible to emphasize several problems as Transport and Logistics wherein it is required to find optimal solutions considering one or several criteria. An important number of authors have dedicated a noteworthy effort for these problems and other problems with similar nature. Their work has yielded in relevant contributions published in scientific books and journals with a great impact. Part of our work is dedicated to studying these problems. The strategic planning process in public transport is usually divided into three steps: network design, planning and programming lines. In all these steps are necessary efficient tools from network optimization, because of the huge data in these problems. In this project, we will analyze the theoretical, we will describe the lines developed in the literature on the subject. Furthermore, we will study the existing algorithms and propose new procedures. Then, we will compare the performance of these methods in order to show the advantages and disadvantages of the different models. In some existing transportation problems, the corresponding models are variations of the multy-commodity flow problem. In general, the exact resolution of these problems combines classical mathematical programming tools that do not usually exploit the underlying network model of the problem. However, from a computational point of view, it is preferable to design ""ad hoc"" algorithms that be more efficient than the existing ones. For this, we will consider the mathematical models that allow developing smart enumerative schemes to solve these problems in an exact way, even when the dimensions of the problem are large. The proposed enumerative tools are based on efficient algorithms developed by our research group for the enumeration of solutions of classical Combinatorial Optimization problems. These tools enable troubleshooting of Transportation, since these are classic combinatorial optimization problems with additional constraints. In addition, the proposed methodology will allow starting a new investigation line denominated as Evolutive algorithms with genealogy and hard extinction mechanisms. This new line emanates from the consideration of the approaches studied in this project and the results in this new line will be applied to combinatorial optimization problems with a single objective and with various objectives and additionally, to some problems that lies in the scope of the transport and logistics problems. This new line will be the doctoral thesis of one investigator under the supervision of the main investigator of this project.
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