The complex function optimization problems, which have properties like multimodality, high dimensionality, non-differentiability, non-linear parameter interactions, are challenging and hard to solve. A number of meta-heuristic algorithms are proposed to find near optimal solution to these complex problems. However, most of them suffer from poor exploration and get caught in local optima. In order to overcome this problem, we present an enhanced Quantum behaved Particle Swarm Optimization (e-QPSO) algorithm, which improves the exploration and the exploitation properties of the original QPSO for function optimization. We introduce the adaptive balance among the personal best and the global best positions using the parameter alpha and achieve the balance between the diversification and the intensification using the parameter gamma. Further, we re-initialize a percentage of the worst performing population to help escape the particle from the local optima. These three modifications in the e-QPSO play crucial role to enhance the performance of the original QPSO algorithm. The e-QPSO is validated on 59 well-known challenging benchmark problems including 5 engineering problems. The results of e-QPSO outperform those of existing twelve QPSO variants, two adaptive variants of PSO, as well as nine well-known evolutionary algorithms. Statistical tests also demonstrate the statistically significant performance of the e-QPSO compared to the other meta-heuristic methods.