Particle Swarm Optimization for Two-Stage Fuzzy Generalized Assignment Problem

This paper constructs a new class of two-stage fuzzy generalized assignment problems, in which the resource amounts consumed are uncertain and assumed to be characterized by fuzzy variables with known possibility distributions. Motivated by the definitions of the positive part and negative part, we can transform the second-stage programming to its equivalent one. To calculate the expected value in the objective function, an approximation approach (AA) is employed to turn the fuzzy GAP model into an approximating one. Since the approximating GAP model is neither linear nor convex, traditional optimization methods cannot be used to solve it. To overcome this difficulty, we design a hybrid algorithm integrating the approximation approach and particle swarm optimization (PSO) to solve the approximating two-stage GAP model. Finally, one numerical example with six tasks and three agents is presented to illustrate the effectiveness of the designed hybrid algorithm.