Issues in selecting a representative set for multi-objective integer programs

Özarık, Sami Serkan
Multi-objective Integer Programs (MOIPs) have many areas of application in real life since it allows the decision makers to consider conflicting objectives simultaneously. However, the optimal solution is not unique for MOIPs and the number of nondominated points of multi-objective integer programs increases exponentially with the problem size. Therefore, finding all nondominated points is computationally hard and not practical for the decision maker. Instead of generating all nondominated points, it is reasonable to generate a set of points that represents the nondominated set with a desired quality level. In this thesis, we develop algorithms to generate representative sets for different MOIPs using a new quality measure that considers the distribution of points over the nondominated set. We first introduce a density measure and analyze typical distributions of nondominated points for different MOIPs. We then develop an approach that approximates the nondominated set, categorizes the approximate nondominated set into regions based on their estimated densities and generate distribution-based representative sets. 


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Citation Formats
S. S. Özarık, “Issues in selecting a representative set for multi-objective integer programs,” M.S. - Master of Science, Middle East Technical University, 2017.