Problems in structural optimization typically involve decisions modeled as binary variables that lead to difficult combinatorial optimization problems. The literature presents different techniques to relax the binary variables in order to avoid the high computational costs required by the solution of combinatorial problems. This note develops a novel relaxation strategy to map a problem with binary variables into an equivalent problem with continuous variables. A set of theoretical results prove the equivalence of the proposed approach and the original binary optimization problem. The strategy is applied to the unassigned distance geometry problem, relying on the design of a new formulation for the problem. Computational studies illustrate the benefits of the proposed relaxation.

结构优化中的问题通常涉及将决策建模为二进制变量，从而导致困难的组合优化问题。文献提出了放松二进制变量的不同技术，以避免解决组合问题所需的高计算成本。本说明开发了一种新颖的松弛策略，可以将具有二进制变量的问题映射为具有连续变量的等效问题。一组理论结果证明了该方法与原始二元优化问题的等效性。将该策略应用于未分配的距离几何问题，这取决于该问题的新公式的设计。计算研究表明了所提议的放松的好处。