An interval particle swarm optimization method for interval nonlinear uncertain optimization problems

For nonlinear optimization problems involving interval variables or parameters, the interval possibility degree or interval order relation is conventionally adopted to convert them into a deterministic corresponding counterpart and then can be solved with linear programing approaches, through which computational resources and costs have been preserved to a certain extent. However, some information and computational accuracy will be discounted during the model transformation. In this paper, an interval optimization algorithm based on particle swarm optimization is proposed aiming to cut down the loss of useful information by means of straight optimization instead of model deterministic converting so as to enhance calculation accuracy with few growths of computing expenses. The proposed method firstly employs an interval satisfaction value to cope with the constraints. Consequently, the particle swarm optimization method is used to seek the optimum solution sets without the model deterministic converting. And a criterion based on the satisfaction value model of interval possibility degree plays the role in individual selecting out of the above solution sets. Finally, the effectiveness of the proposed method is verified by investigating four examples.