Search for the most reliable network of fixed connectivity using genetic algorithm

Reliability is one of the important measures of how well a system meets its design objective, and mathematically is the probability that a system will perform satisfactorily for a given period of time. When the system is described by a network of N components (nodes) and L connections (links), the reliability of the system becomes a network design problem that is an NP-hard combinatorial optimization problem. In this paper, genetic algorithm is applied to find the most reliable connected network with the same connectivity, (i.e. with given N and L). The accuracy and efficiency of genetic algorithm in the search of the most reliable network(s) of same connectivity is verified by exhaustive search. Our results not only demonstrate the efficiency of our algorithm for optimization problem for graphs, but also suggest that the most reliable network will have high symmetry.