It is important to determine supporting locations for structural stability when a structure is loaded with non-uniform load or supporting locations as well as the number of the supporting structures are restricted by the problem of space. Moreover, the supporting location optimization of complex structure in real world is frequently faced with discontinuous design space. Therefore, the traditional optimization methods based on derivative are not suitable Whereas, Genetic Algorithm (CA) based on stochastic search technique is a very robust and general method. The KSTAR in-vessel control coil installed in vacuum vessel is loaded with non- uniform electro-magnetic load and supporting locations are restricted by the problem of space. This paper shows the supporting location optimization for structural stability of the in-vessel control coil. Optimization has been performed by means of a developed program. It consists of a Finite Element Analysis interfaced with a Genetic Algorithm. In addition, this paper presents an algorithm to find an optimum solution in discontinuous space using continuous design variables.