Given the reference (distortion-free) image, full-reference image quality assessment (FR-IQA) algorithms seek to assess the perceptual quality of the test image. Over the years, many effective, hand-crafted FR-IQA metrics have been proposed in the literature. In this work, we present a novel framework for FR-IQA that combines multiple metrics and tries to leverage the strength of each by formulating FR-IQA as an optimization problem. Following the idea of other fusion-based metrics, the perceptual quality of a test image is defined as the weighted product of several already existing, hand-crafted FR-IQA metrics. Unlike other methods, the weights are determined in an optimization-based framework and the objective function is defined to maximize the correlation and minimize the root mean square error between the predicted and ground-truth quality scores. The obtained metrics are evaluated on four popular benchmark IQA databases and compared to the state of the art. This comparison has revealed that the compiled fusion-based metrics are able to outperform other competing algorithms, including deep learning-based ones.