A fuzzy lifetime-based particle swarm optimisation with varying swarm size to solve a production inventory model

Abstract

Here, a modified particle swarm optimisation (MPSO) algorithm with varying swarm size for constrained optimisation problem is proposed. In this MPSO, a life time is assigned to each particle at the time of generation depending on its fitness. After completion of a generation, if no movement is made by the particle, its age is increased by unity. When age of a particle exceeds the lifetime, it is discarded from the swarm. Diversity in the swarm is maintained using information entropy theory. A fuzzy possibility/necessity-based fitness evolution is proposed to deal with fuzzy optimisation problems using this MPSO. Efficiency of the algorithm is tested against a list of crisp valued standard benchmark nonlinear test functions. This algorithm is used to solve a production inventory model with fuzzy costs, where lifetime of the product is random in nature. At the beginning of planning horizon price discount is offered to the customers for few cycles to boost the demand. Demand also depends on stock and selling price. The model is illustrated with numerical examples and some sensitivity analyses have been made.