Discrete variable topology optimization problems are usually solved by using solid isotropic material with penalization (SIMP), genetic algorithms (GA), or mixed-integer nonlinear optimization (MINLO). In this paper, we propose formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem. Unlike SIMP and GA methods, MISOCO efficiently finds the problem’s globally optimal solution. Furthermore, in contrast with existing MISOCO formulations of discrete ply-angle optimization problems, our reformulations allow the structure to change topology, consider the more realistic Tsai–Wu stress yield criteria constraint, and eliminate checkerboard patterns using simple linear constraints. We address two types of discrete ply-angle and thickness problems: a structural mass minimization problem and a compliance optimization problem where the objective is to maximize the structural stiffness. For each element, one first chooses if the element is present or not in the structure. One can then choose the element’s ply-angle and thickness from a finite set of possibilities for the former case. The discrete design space for ply-angle and thickness is a result of manufacturing limitations. To improve the problem’s MISOCO solution approach, we develop valid inequality constraints to tighten the continuous relaxation of the MISOCO reformulation. We compare the performance of various MISOCO solvers: Gurobi, CPLEX, and MOSEK to solve the MISOCO reformulation. We also use BARON to solve the original MINLO formulations of the problems. Our results show that solving the MISOCO problem’s formulation using MOSEK is the most efficient solution approach.

离散变量拓扑优化问题通常通过使用带有罚分的固体各向同性材料（SIMP），遗传算法（GA）或混合整数非线性优化（MINLO）来解决。在本文中，我们提出将离散的层角和厚度拓扑优化问题表述为混合整数二阶锥优化（MISOCO）问题。与SIMP和GA方法不同，MISOCO有效地找到了问题的全局最优解决方案。此外，与现有的MISOCO离散层板角度优化问题公式相反，我们的重新制定公式允许结构更改拓扑结构，考虑更实际的Tsai-Wu应力屈服准则约束，并使用简单的线性约束消除棋盘图案。我们处理两种类型的离散层角度和厚度问题：结构质量最小化问题和顺应性优化问题，其目的是使结构刚度最大化。对于每个元素，首先选择该元素在结构中是否存在。然后，可以从前一种情况的一组有限可能性中选择元素的帘布层角度和厚度。帘布层角度和厚度的离散设计空间是制造限制的结果。为了改善问题的MISOCO解决方案，我们开发了有效的不等式约束以加强MISOCO重新制定的持续放松。我们比较了各种MISOCO解算器（Gurobi，CPLEX和MOSEK）的性能，以解决MISOCO重新制定的问题。我们还使用BARON来解决原始MINLO公式的问题。