Sensor nodes in a wireless sensor Network are assigned for different operational modes to perfume application-specific objectives. The decision to assign operational modes to nodes is a challenging problem in the presence of multiple criteria including energy-efficient, maintaining network connectivity, and fulfilling application goals. Several metaheuristic methods are introduced in the literature to address this NP-hard problem, however, these methods require further improvements in execution-time and finding the optimum solution. In this research, we propose an improved version of a metaheuristic method called Quadri-valent Quantum Inspired Gravitational Search Algorithm (QQIGSA) to solve Quadri-valent problems by applying a Not Q-Gate and paralleling QQIGSA method on the graphics processing unit. The proposed method employs a heterogeneous platform and justifies its parameters. The experimental results show that the performance enhancement from 1.8 to 2.25 compared to the previous parallel implementations. Moreover, we achieve the speedup of 8 by using the proposed heterogeneous paralleling technique.