Raw polarimetric images are captured by a focal plane polarimeter which is covered by a micro-polarizer array (MPA). The design of the MPA plays a crucial role in polarimetric imaging. MPAs are predominantly designed according to expert engineering experience and rules of thumb. Typically, only one optimization criterion, maximizing bandwidth, is used to design the MPA. To select a design, an exhaustive search is usually performed on a very limited set of available polarizing patterns, which must be constrained in order to make the search tractable. In contrast, this paper proposes a fully automated and optimal MPA design method (AO-MPA) which generates significantly improved MPAs. Instead of the single criterion of bandwidth, we propose six design principles, and show how they can be utilized to mutually optimize the MPA design by formulating a tri-objective optimization problem with multiple constraints. A much larger set of possible MPA patterns is rapidly and automatically searched by applying advanced multi-objective optimization techniques. We have tested AO-MPA using two groups of experiments, in which AO-MPA is compared against several other leading MPA design methods, and the patterns generated by AO-MPA are compared against state-of-the-art patterns from the literature. The results, obtained using a public benchmark dataset, show that the AO-MPA method is very computationally efficient, and can find all optimal MPA patterns for all array sizes. Moreover, for each size, AO-MPA obtains all optimal layouts simultaneously. AO-MPA generates designs which require fewer polarization orientations, while also yielding better performance in estimating intensity measurements, Stokes vector and the degree of linear polarization. This results in MPAs which are easier to manufacture while also being more robust to noise.