This paper addresses a new method of generalized genarating sequences (GGS) in reliability-cost optimization problem. The GGS is an extension based on some modifications of the standard universal genarating function (UGF). This method is convenient for computerized calculation of enumeration combinatorial problems thst arise in discrete optimization problem as encountred in parallel-series power systems. This method will be convenient to the complex combinatorial optimization problem as described below in the context of optimal redundancy-investment allocation problems (PRIOP). The GGS is used in bi-objective optimization functions PRIOP.