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Additive manufacturing (AM) has an affinity with topology optimization to think of various designs with complex structures. Hence, this paper aims to optimize the design of a lattice-structured heat sink, which can be manufactured by AM. The design objectives are to maximize the thermal performance of convective heat transfer in natural convection simulated by computational fluid dynamics (CFD) and to minimize the material cost required for AM process at the same time. The lattice structure is represented as a node/edge system via graph theory with a moderate number of design variables. Bayesian optimization, which employs the non-dominated sorting genetic algorithm II and the Kriging surrogate model, is conducted to search for better designs with the minimum CFD cost. The present topology optimization successfully finds better lattice-structured heat sink designs than a reference fin-structured design regarding thermal performance and material cost. Also, several optimized lattice-structured designs outperform reference pin-fin-structured designs regarding thermal performance though the pin-fin structure is still advantageous for a material cost-oriented design. This paper also discusses the flow mechanism observed in the heat sink to explain how the optimized heat sink structure satisfies the competing design objectives simultaneously. [ABSTRACT FROM AUTHOR]