The "volume-point" heat conduction model with triangular heat trees is considered in this paper. Several high conductivity channels are distributed in the heat generating body, and the size effects are present in these channels. The minimization of the entransy dissipation rate (EDR) is chosen as the optimization objective. The optimal constructs of the triangular heat trees at different scales are obtained by using the local optimization and global optimization constructal design methods, respectively. The results show that the optimal construct at micro and nanoscales is evidently different from that at convectional scale. The heat conduction performance of the triangular heat trees based on local optimization constructal design method can be further improved compared with that based on the global one. The optimal constructs of the triangular second order assembly (TSOA) with minimum EDR and minimum maximum temperature difference (MTD) are evidently different, and the same conclusion can be obtained for the comparison between the optimization objectives of EDR and entropy generation rate (EGR). (C) 2015 Elsevier Ltd. All rights reserved.