where x is a vector of design varia

where x is a vector of design variables sized n  1, n is the number of design variables, f is an objective function,and L and U are lower and upper limits of x respectively.RPBIL search is based on the concept that a real population (a set of design solutions)on each generation is generated from a current probability matrix [6,7].This implies that a population in the RPBIL
procedure is represented by the so-called probability matrix rather than carrying a matrix containing numerous design vectors throughout the search process.Let a probability matrix have size n  nI where nI is apredefined number of matrix columns.The parameter nI determines the number of subintervals of the bound constraints of the problem. For simplicity,
consider a2- dimensional box - constrained problem