A Genetic Algorithm for K-node Set Reliability Optimization with Capacity Constraint of a Distributed System

In the reliability analysis of a distributed system (DS), k-node set reliability is defined as the probabilities that all the nodes in K are connected, where K denotes a subset of a set of processing elements. A k-node set reliability computation can be very difficult to perform with exponential in many cases. A k-node set reliability optimization with a capacity constraint problem is to select a k-node set of nodes in a distributed system such that the k-node set reliability is maximal and possesses sufficient node capacity. It is evident that this is an NP-hard problem. Relative investigation, namely exact method, has examined k-node set reliability optimization with capacity constraint. Although the exact method can obtain an optimal solution, it cannot reduce the computational time. Occasionally, an efficiency algorithm with an exact or nearly exact solution is attractive. Thus, in this paper, we present a method based on a genetic algorithm used to evolve the best k-node sets. Because the final number of best k-node sets is only one, less time is needed to compute the reliability of the k-node set. The exact solution can be obtained in most cases using the proposed method. When it fails to give an exact solution, the deviation from the exact solution is very small. In addition, the proposed algorithm is compared with the exact method for various DS topologies. The results demonstrate that the proposed algorithm is more efficient in execution time. In summary, the proposed algorithm can efficiently obtain the maximal or near maximal k-node set reliability with a capacity constraint.