A Genetic Algorithm with Semi-Greedy Heuristic Construction Phase for Multiple Fuzzy k-cardinality Assignment Problem with HOWA Approach

Abstract

The assignment problem is one of the well-known combinatorial optimization problems. It consistsof nding a maximum or a minimum weight matching in a weighted bigraph. k-cardinality assignment problem is a special case of the assignment problem with side constraints. The scope of this study is to be able to suggest kind of group assignment problem with side constraint. The aim of the study is to create groups of workers in order to minimize the cost of the assignment.In that problem, costs of workers are stated as fuzzy numbers. Also; with this model, evaluation criteria for every group could be di erent from each other. We make that happen by employing HOWA (Heavy Ordered Weighted Averaging) aggregation operator. Using of HOWA in the objective function of the model transforms the model into a fuzzy non-linear programming model. We implement our model to "gap12" data from OR-Library. We solve this model employing both Genetic Algorithm in which is constructing the initial population by a semi-greedy heuristic, along with Parametric Programming. We also develop a user friendly interface that reports ndings of the model to us.