Floating, production, storage and offloading (FPSO) is a production facility that refines and saves the drilled crude oil from a drilling facility in the ocean. The flare system in the FPSO is a major part of the pressure relieving system for hydrocarbon processing plants. The flare system consists of a number of pipes and complicated connection systems. Decision of pipe support types is important since the load on the support and the stress in the pipe are influenced by the pipe support type. In this study, we optimally determined the pipe support types that minimized the support cost while satisfying the design constraints on maximum support load, maximum nozzle load and maximum pipe stress ratio. Performance indices included in the design constraints for a specified design were evaluated by pipe structural analysis using CAESAR II. Since pipe support types were all discrete design variables, an evolutionary algorithm (EA) was used as an optimizer. We successfully obtained the optimal solution that reduced the support cost by 27.2% compared to the initial support cost while all the design requirements were satisfied.