A novel efficient hybrid method based on random sampling-high dimensional model representations (RS-HDMR) and genetic algorithm coupled with a local unconstrained multivariable minimization function is proposed in this study for optimization of FRP composite web core bridge deck panels. The optimization is performed for lightweight design of FRP composite bridge deck panels based on deflection limit, stresses, buckling and failure criteria and subsequently the representative design curves are developed considering normal as well as skew configurations of FRP bridge decks. Sensitivity analysis is also performed to study the effect of variation in geometry of the bridge deck to its deflection, stress and buckling behaviours. High level of computational efficiency can be achieved without compromising the accuracy of results for optimization of high dimensional systems following the proposed approach.