By the development of technology, clean, reliable, and continuous energy has increased its importance. Transformers, one of the indispensable parts of this, have a role in the production, transmission, distribution, and consumption of electrical energy. Dry type transformers are more widely applied for industrial application because of its properties such as safety, incombustible structure, and eco-friendly. However, these transformers have some drawbacks related to dimension and cost depending on it. Therefore, the researchers have begun to study for reduction of dimension. Thus, the manufacturers will be supplied lower material cost. The idea of using new optimization methods is emerged to minimize the dimension of dry type transformer design This article presents the Invasive Weed Optimization (IWO) and the Firefly Algorithm (FA) which are newly introduced in the literature applied first time in the industry. First of all, the mathematical model of the three-phase dry-type transformer is described in detail. Secondly, the transformer is re-designed with the FA and the IWO by adjusting the current density (s) and the iron section compatibility factor (C). In addition, these optimization methods are compared with the performance with Particle Swarm Optimization (PSO), one of the most preferred optimization methods in the literature, in detail. The main contribution of this article is to optimize the weight and its related to cost of dry type transformer A 100 kVA three-phase dry-type transformer is used. The obtained results showed that the optimization of the weight and cost of the transformer are efficient. This article aims at providing a broad perspective on the status of optimum design for transformer fo the researchers and the application engineers dealing with these issues.