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 an dupper 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 RPBILprocedure 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
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