Solving equilibrium standby redundancy optimization problem by hybrid PSO algorithm

Redundancy allocation is a direct way of enhancing the series-parallel system lifetime and reliability. Since it is difficult to obtain the exact probability distributions about the lifetimes of components, fuzzy random variables are used to characterize them. Under the given system weights and cost constraints, we maximize the equilibrium optimistic system lifetime of redundant elements. This paper proposes an equilibrium optimization model for the standby redundancy system. Since the exact analytical expressions of the equilibrium optimistic system lifetimes are unavailable in general case, the proposed model cannot be analytically solved. Under mild assumptions, the new equilibrium model can be divided into its equivalent stochastic programming subproblems. Moreover, a new approximation method is proposed to solve the general equilibrium model. For the equivalent stochastic programming subproblems, sample average approximation (SAA) is adapted to gain their SAA problems. A hybrid particle swarm optimization algorithm with local search is designed to solve the SAA problems. Several numerical experiments are conducted to investigate the effectiveness of proposed model and designed solution method. The comparative studies indicate the randomness, and fuzziness cannot be ignored in the equilibrium standby redundancy optimization problem.