Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization

• We model the reliability redundancy allocation problem in an interval environment.
• We apply the particle swarm optimization directly on the interval values.
• A dominance relation for interval-valued multi-objective functions is defined.
• The crowding distance metric is extended to handle imprecise objective functions.

Most of the existing works addressing reliability redundancy allocation problems are based on the assumption of fixed reliabilities of components. In real-life situations, however, the reliabilities of individual components may be imprecise, most often given as intervals, under different operating or environmental conditions. This paper deals with reliability redundancy allocation problems modeled in an interval environment. An interval multi-objective optimization problem is formulated from the original crisp one, where system reliability and cost are simultaneously considered. To render the multi-objective particle swarm optimization (MOPSO) algorithm capable of dealing with interval multi-objective optimization problems, a dominance relation for interval-valued functions is defined with the help of our newly proposed order relations of interval-valued numbers. Then, the crowding distance is extended to the multi-objective interval-valued case. Finally, the effectiveness of the proposed approach has been demonstrated through two numerical examples and a case study of supervisory control and data acquisition (SCADA) system in water resource management.