Minimum Violations Ranking Using Evolutionary Optimization and Binary Integer Linear Program Approaches
Pedings, Kathyrn E.
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Ranking items is very natural to our society. We rank the top 100 movies of the century, book lists, and of course, we always care about whether or not our sports team is in the number one position. The field of ranking is one of great interest to many both in and out of the field of mathematics. There is often a structure to data that mathematicians can exploit to obtain a ranking. This thesis presents two new ways to rank sets of objects. This work mainly focuses on ranking sports teams, but each of these methods can be applied to many other types of data. The first method uses evolutionary optimization, a method that follows Darwinian ideas of mating, mutating, fitness, and survival of the fittest in a mathematical setting to determine which ranking is best. The second method is a binary integer linear program that works with the same theory as the evolutionary optimization algorithm, but guarantees optimal results. This thesis will explain, in detail, these two algorithms with examples of their applications in the field of ranking sports teams.