Large power transformers are regarded as crucial and expensive assets in power systems. Due to the competing global market, to make a good and competing power transformer design, a non-linear optimization problem should be solved in a very short time in the preliminary design stage. The paper shows and compares the performance of four different methods to solve this problem for three phase core type power transformers. The first algorithm is a novel meta-heuristic technique which combines the geometric programming with the method of branch and bound. Then this conventional multi design method is solved by a simple iterative technique and two novel evolutionary algorithms to enhance the convergence speed. One of these algorithms is the particle swarm optimization technique which is used by many other researchers and the grey wolf optimization algorithm which is a new method in this optimization sub-problem. An example design on an 80 MVA, three phase core type power transformer using these four methods is presented and its performances are analyzed. The results demonstrate that the grey wolf optimization is a good alternative for this optimization problem.