Minimizing the power consumption of electronic systems is one of the most critical concerns in the design of integrated circuits for very large-scale integration (VLSI). Despite the reality that VLSI design is known for its compact size, low power, low price, excellent dependability, and high functionality, the design stage remains difficult to improve in terms of time and power. Several optimization algorithms have been designed to tackle the present issues in VLSI design. This study discusses a bi-objective optimization technique for circuit partitioning based on a genetic algorithm. The motivation for the proposed research is derived from the basic concept that, if some portions of a circuit's system are deactivated during the processor's idle time, the circuit's power consumption is automatically reduced. To reduce the overall system's power consumption, maximization of sleep time and minimization of net cuts are required. To achieve these, an effective fitness function has been constructed in such a way that the balance criteria are also maintained. The approach has been tested on a set of net lists from the ISPD'98 benchmark suite, each containing 10 to 30 nodes. The experimental results are compared with two existing methods that clearly indicate the acceptability of the suggested method. The suggested strategy achieves an average reduction of 24.69% and 31.46% for net cut, whereas average extensions of 15.20% and 12.31% are observed in sleep time when compared with two existing methods. The proposed method also achieves an average power efficiency of 14.98% and 12.09% with respect to these two state-of-the-art methods.