By applying the core concept to solve a binary integer program (BIP), certain variables of the BIP are fixed to their anticipated values in the optimal solution. In contrast, the remaining variables, called core variables, are used to construct and solve a core problem (CP) instead of the BIP. A new approach for identifying CP utilizing a local branching (LB) alike constraint is presented in this article. By including the LB-like constraint in the linear programming relaxation of the BIP, this method transfers batches of variables to the set of core variables by analyzing changes to their reduced costs. This approach is sensitive to problem hardness because more variables are moved to the core set for hard problems compared to easy ones. This novel core identification approach is embedded in a multi-stage framework to solve the multidemand, multidimensional knapsack problems (MDMKP), where at each stage, more variables are added to the previous stage CP. The default branch and bound of CPLEX20.10 is used to solve the first stage, and a tabu search algorithm is used to solve subsequent stages until all variables are added to CP in the last stage. The new framework has shown equivalent to superior results compared to the state-of-the-art algorithms in solving large MDMKP instances having 500 and 1,000 variables.

中文翻译：

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一种采用新颖的核心识别启发式算法求解大规模多需求多维背包问题实例的优化框架


通过应用核心概念来求解二进制整数规划 （BIP），BIP 的某些变量在最优解中被固定到它们的预期值。相比之下，其余变量（称为核心变量）用于构建和解决核心问题 （CP），而不是 BIP。本文提出了一种利用本地分支 （LB） 类似约束来识别 CP 的新方法。通过在 BIP 的线性规划松弛中包含类似 LB 的约束，该方法通过分析其缩减成本的变化，将变量批次转移到核心变量集。这种方法对问题难度很敏感，因为与简单的问题相比，更多的变量被移动到困难问题的核心集中。这种新颖的核心识别方法嵌入到多阶段框架中，以解决多需求、多维背包问题 （MDMKP），其中在每个阶段，都会在前一阶段 CP 中添加更多变量。CPLEX20.10 的默认分支和边界用于解决第一阶段，使用禁忌搜索算法解决后续阶段，直到在最后阶段将所有变量添加到 CP 中。与最先进的算法相比，新框架在求解具有 500 和 1,000 个变量的大型 MDMKP 实例时显示出等效的卓越结果。