Optical data communication based on the orbital angular momentum (OAM) of light is a recently proposed method to enhance the transmission capacity of optical fibers. This requires a new type of optical fiber, the main part of the optical communication system, to be designed. Typically, these fibers have a ring-shaped refractive index profile. We aim to find an optimized cross section refractive index profile for an OAM fiber in which the number of supported OAM modes (channels), mode purity, and the effective refractive index separation of OAM modes to other fibers modes are maximized. However, the complexity of the relationship between structural parameters and optical transmission properties of these fibers has resulted in the lack of a comprehensive analytical method to design them. In this paper, we investigate the process of designing OAM fibers and propose a framework to design such fibers by using artificial intelligence optimizers. It is worth mentioning here that this problem is intrinsically a multiobjective optimization problem, and the actual solution for such problems is not unique and leads to a set of optimum solutions. Therefore, at the end of the optimization process, a wide range of optimal designs will be obtained in which a trade-off is established in each of the solutions. We solve this problem with the multiobjective gray wolf optimizer (GWO) and compare the results with that of the single-objective GWO. The framework can easily find many optimal designs that support more than 20 OAM modes. The obtained results show that the proposed method is comprehensive and can optimize the structure of any OAM fibers. No human involvement, simplicity, and being straightforward are the main advantages of the proposed framework.