A new development of continuous/relaxed topology optimization method of binary structures (continuous/relaxed TOBS) with integer linear programming

Abstract

This study presents a new topology optimization framework, termed continuous/relaxed topology optimization of binary structures (CTOBS), which enables a gradual and controlled transition to binary design variables. From the perspective of topology optimization, it remains challenging to achieve binary structural layouts without intermediate design variables, especially under highly nonlinear objective functions or multiphysics constraints. The conventional density-based methods, such as solid isotropic material with penalization (SIMP), often result in intermediate densities that are hard to fabricate, while binary approaches like topology optimization of binary structures (TOBS) suffer from poor convergence due to abrupt variable transitions. The present CTOBS method introduces a continuation scheme in which design variables initially span multiple discrete levels and are gradually refined to binary values. Integer linear programming (ILP) is adopted over a relaxed discrete space, enhancing convergence and robustness, especially in nonlinear and multiphysics problems. To investigate the effect of CTOBS, several numerical examples are considered. The results show that the present CTOBS effectively eliminates gray elements and offers stable and manufacturable designs. This approach broadens the applicability of topology optimization in complex engineering domains.