In this study, expected total cost, which is composed of structural cost and expected maintenance cost, is introduced as a reasonable utility function for the multi-objective optimization design problem such as maximum safety and minimum cost. The optimum design procedure is proposed for offshore platforms minimizing the expected total cost. The design variables are the geometrical dimensions of the structure while its configuration and the materials to be used are given. Partial failure due to formation of plastic hinges and/or fatigue cracks of the critical sections during design life is considered. The design is performed for the platforms subjected to wave loads. In addition, the effect of periodic inspection is investigated. The optimum design problem contains many parameters which are difficult to estimate exactly, and thus the optimum solution may not be absolute. However, the failure probability corresponding to the optimum solution is used as an index for specifying the allowable failure probability in probabilistic optimum design problems. Numerical examples for a jacket-type offshore platform are provided to illustrate the applicability of the proposed method.