Penalty guided bees search for redundancy allocation problems with a mix of components in series-parallel systems

This paper uses a penalty guided strategy based on an artificial bee colony algorithm (PGBC) to solve the redundancy allocation problem (RAP) in reliability series–parallel systems. The penalty strategy was designed to eliminate the equalities in constraints and formulate new objective operators which guarantee feasibility within a reasonable execution time. The PGBC is used to deal with two kinds of RAPs with a mix of components. In the first example, the RAPs are designed to find the appropriate mix of components and redundancies within a system in order to either minimize the cost in the context of a minimum level of reliability, or maximize reliability subject to a maximum cost and weight. The second example involves RAPs of multi-state series–parallel reliability structures, wherein each subsystem can consist of a maximum of two types of redundant components. The objective is to minimize the total investment cost of system design while satisfying system reliability constraints and the consumer load demands. There are five multi-state system design problems which have been solved for illustration in this example. The experimental results show that the PGBC can significantly outperform other existing methods in the literature with less cost, higher reliability, and a significantly shorter computational time. & 2012 Elsevier Ltd. All rights reserved.