This paper introduces combined deep drawing and electromagnetic sharp edge forming to improve the formability of advanced high strength steels. It includes a feasibility study of combined deep drawing and electromagnetic sharp edge forming of DP980 steel sheet with a thickness of 1.2 mm. A feasible approach of the combined forming process is investigated with numerical analysis which consists of pre-forming and electromagnetic sharp edge forming using the pre-formed sheet. Pre-forming analyses are conducted to check the formability of the material by utilizing a fracture forming limit diagram developed. Then electromagnetic forming is applied to the pre-formed workpiece to obtain a sharp edge that fails to form at the conventional pre-forming. In electromagnetic sharp edge forming, process parameters related to the forming force are optimized so that the desired shape is formed as close as possible. The optimization of the forming force is carried out satisfying the objective function and constraint functions established to minimize the deviation of a deformed shape from the desired shape without exceeding the forming limits. In order to induce the optimized forming force, the electromagnetic tool coil is designed with topology optimization. A new electromagnetic topology optimization formulation is developed for the design of an efficient tool coil. Numerical results and conclusions demonstrate the applicability of this combined forming process. (C) 2017 Elsevier B.V. All rights reserved.