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An inverse optimization algorithm based on Quantum-Behaved Particle Swarm Optimization (QPSO) is examined and applied to estimate the unknown transient heat flux applied to certain boundaries in transient heat conduction problems. Results demonstrate the accuracy, stability and validity of the QPSO method in inverse estimation of the heat flux without prior knowledge of the functional form of the unknown quantities. This paper also addresses the high computational costs of QPSO and proposes a hybrid method to reduce the computational costs by combining the advantages of a gradient method and a stochastic method. Finally comparison of the proposed hybrid method and Conjugate Gradient Method (CGM) is also included.