### Genetic Algorithm for Distance Balancing in Set Partitioning Problems

#### Abstract

In this study balancing is taken into consideration in formation of groups according to total travel distance as a set partitioning problem (SPP). Fitness functions that can test imbalance are proposed and mathematical models including these fitness functions are presented. In order to make balanced groupings, four different fitness functions are used. First model aims to minimize total travel distance. Other two models are used for balancing and the last one constitutes a precedent as a multi-objective decision making problem. Genetic Algorithms (GAs) which is a meta-heuristic technique is used for the solution of the proposed models. Data is taken from the study of Akyurt et al. [1] and is used for balanced groupings in Football Leagues. Different groups are formed according to these models; effects of the results are examined among themselves and compared with the current situation. Additionally, all results are displayed on the maps.

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