sparse matrices

The cycle basis of a graph arises in a wide range of engineering problems and has a variety of applications. Minimal and optimal cycle bases reduce the time and memory required for most of such applications. One of the important applications of cycle basis in civil engineering is its use in the force method to frame analysis to generate sparse flexibility matrices, which is needed for optimal analysis. In this paper, the simulated annealing algorithm has been employed to form suboptimal cycle basis. The simulated annealing algorithm works by using local search generating neighbor solution, and also escapes local optima by accepting worse solutions. The results show that this algorithm can be used to generate suboptimal and subminimal cycle bases. Compared to the existing heuristic algorithms, it provides better results. One of the advantages of this algorithm is its simplicity and its ease for implementation.