formation of sparse null bases for optimal force method analysis using charged system search algorithm

in this paper, an algorithm is presented for the formation of optimal null basis vectors corresponding to sparse flexibility matrices. for controlling the independence of the vectors, a generator is selected in each corresponding self-equilibrating systems, and the sequence of generators is modeled as decision variables. since the equilibrium conditions and uniqueness of generators consists a underdetermined linear system, a linear mixed integer programming model is presented for finding sparse solution. in charged system search algorithm, the movement of charged particles is tracked in a continuous domain, therefore it is modified for using in a discrete binary space, and also a new operator called probability of mutation is defined in this paper. the numerical examples shows that the proposed method enables to find suboptimal solution, while using short computational time and resulting good accuracy.