Full-reference image quality measures are a fundamental tool to approximate the human visual system in various applications for digital data management: from retrieval to compression to detection of unauthorized uses. Inspired by both the effectiveness and the simplicity of hand-crafted Structural Similarity Index Measure (SSIM), in this work, we present a framework for the formulation of SSIM-like image quality measures through genetic programming. We explore different terminal sets, defined from the building blocks of structural similarity at different levels of abstraction, and we propose a two-stage genetic optimization that exploits hoist mutation to constrain the complexity of the solutions. Our optimized measures are selected through a cross-dataset validation procedure, which results in superior performance against different versions of structural similarity, measured as correlation with human mean opinion scores. We also demonstrate how, by tuning on specific datasets, it is possible to obtain solutions that are competitive with (or even outperform) more complex image quality measures.