The optimization approach based on the biological evolution principle is used to construct the heat transport paths for volume-to-point problem. The transport paths are constructed by inserting high conductivity materials in the heat conduction domain where uniform or nonuniform heat sources exist. In the bionic optimization process, the optimal constructs of the high conductivity material are obtained by numerically simulating the evolution and degeneration process according to the uniformity principle of the temperature gradient. Finally, preserving the features of the optimal constructs, the constructs are regularized for the convenience of engineering manufacture. The results show that the construct obtained by bionic optimization is approximate to that obtained by the tree-network constructal theory when the heat conduction is enhanced for the domain with a uniform heat source and high conductivity ratio of the inserting material to the substrate, the high conductivity materials are mainly concentrated on the heat outlet for the case with a uniform heat source and low thermal conductivity ratio, and for the case with nonuniform heat sources, the high conductivity material is concentrated in the heat source regions and construacts several highly effective heat transport paths to connect the regions to the outlet.