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Fiber-reinforced polymer (FRP) composite sandwich panels with core of sinusoidal geometry have been recently used in highway bridge and aquaculture tank applications. The selection of geometric shape and size of sinusoidal cores to meet given design requirements is critical in efficient applications of sandwich structures, and their effective transverse shear stiffness properties are important material properties in analysis and design. Based on a combined homogenization and multi-objective optimization technique, the effective transverse shear stiffness properties of sinusoidal cores are studied and optimized. An analytical approach using two-scale homogenization technique is used to predict the effective transverse shear stiffness properties of thin-walled sinusoidal honeycomb cores. The optimization problem is then solved using a sequential quadratic programming algorithm. Two types of optimization problems are presented: the maximization of effective transverse shear stiffness of honeycomb core with a given composite solid volume fraction and the minimization of composite solid volume with prescribed effective transverse shear stiffness. The geometric effects and weighting factors on the optimal design of sinusoidal cores are discussed. An optimization procedure using a response surface method and finite element analysis is also conducted to verify the proposed approach. The present combined homogenization and multi-objective optimization approach can be used to obtain favorable material performance behaviors and meet desired design requirements for honeycomb core structures. [ABSTRACT FROM AUTHOR]