The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately leads to reduced overall solution times. In addition, we develop a simple heuristic method for obtaining good-quality CKP solutions that can be used to provide a warm start to the solver. Computational tests demonstrate the effectiveness of both our variable reordering strategy and heuristic method.

0-1立方背包问题（CKP）是经典0-1二次背包问题的推广，是一个极具挑战性的NP-hard组合优化问题。CKP 的一种有效的精确求解策略是将非线性问题重新表述为等价的线性形式，然后可以使用标准的混合整数规划求解器来求解。我们考虑了一种经典的线性化方法，并提出了一种最新技术的变体，用于对应用于 CKP 的 0-1 三次程序进行线性化。使用变量重新排序策略，我们展示了如何提高我们提出的重新制定的线性规划松弛的强度，这最终导致减少整体求解时间。此外，我们开发了一种简单的启发式方法来获得高质量的 CKP 解决方案，该解决方案可用于为求解器提供热启动。计算测试证明了我们的变量重新排序策略和启发式方法的有效性。