The optimal design problem of heat conduction is solved by combining the level set method and the bidirectional evolutionary optimization (BESO) method. It is well known that the level set method is not able to nucleate holes in the structure during the optimization. In order to address this issue, the material removal scheme of the BESO is combined in the level set based topology optimization. In other words, hole is nucleated by using the material removal scheme. The criterion for hole nucleation is explained, and the optimization procedure is described. The results of numerical examples prove that the proposed method is effective and efficient. (C) 2018 Elsevier Ltd. All rights reserved.