Solving fuzzy multiple objective generalized assignment problems directly via bees algorithm and fuzzy ranking

In this paper, a direct solution approach for solving fuzzy multiple objective generalized assignment problems is proposed. In the problem, the coefficients and right hand side values of the constraints and the objective function coefficients are defined as fuzzy numbers. The addressed problem also has a multiple objective structure where the goals are determined so as to minimize the total cost and the imbalance between the workload of the agents. The direct solution approach utilizes the fuzzy ranking methods to rank the objective function values and to determine the feasibility of the constraints within a metaheuristic search algorithm, known as bees algorithm. Different fuzzy ranking methods, namely signed distance, integral value and area based approach are used in bees algorithm. For the computational study, the effects of these fuzzy ranking methods on the quality of the solutions are also analyzed.