基于半定规划的ε-约束方法求解双目标单行设施布局问题
An semidefinite programming-based $\varepsilon$-constraint method for the bi-objective single-row facility layout problem
AI总结：
针对双目标单行设施布局问题，提出基于半定规划的ε-约束方法，利用分支定界过程增强求解效率，并引入非二进制分支和节点重用等改进。
摘要：
在这项工作中，我们引入了著名的单行设施布局问题（SRFLP）的多目标版本。在SRFLP中，一组一维设施应沿一条直线放置，以最小化每对设施中心间距离的加权和。在我们的多目标扩展中，存在多个这样的加权和目标，我们在帕累托最优概念下考虑它们。我们开发了一种基于ε-约束方法的求解算法来解决双目标SRFLP。许多关于ε-约束方法的现有工作将整数线性规划（ILP）求解器作为黑盒使用，以解决该方法各个迭代中的问题。与此相反，我们使用基于半定规划（SDP）的自有分支定界过程，因为已知SDP松弛比ILP的线性规划松弛更有效地求解SRFLP。这使我们能够为我们的ε-约束方法提出若干增强过程，例如非二进制分支和重用分支定界树内的节点，这些在使用黑盒求解器时通常是不可能的。我们通过计算研究展示了我们的求解方法及其增强的有效性。
英文摘要：
In this work, we introduce a multi-objective version of the well-known single-row facility layout problem (SRFLP). In the SRFLP, a set of one-dimensional facilities should be placed along a single line such that the weighted sum of the center-to-center distances of each pair of facilities is minimized. In our multi-objective extension, there are multiple such weighted-sum objectives which we consider under the concept of Pareto optimality. We develop a solution algorithm based on the $\varepsilon$-constraint method to solve the bi-objective SRFLP. Many existing works on the $\varepsilon$-constraint method use integer linear programming (ILP) solvers in a black-box fashion for solving the problems at the individual iterations of the method. In contrast to that, we use our own branch-and-bound procedure based on semidefinite programming (SDP), as SDP relaxations are known to be more effective for solving the SRFLP than linear programming relaxations of ILPs. This allows us to propose several enhancements procedures for our $\varepsilon$-constraint approach, such as non-binary branching and reusing of nodes within the branch-and-bound trees, which are usually not possible when using black-box solvers. We present a computational study to demonstrate the effectiveness of our solution approach and its enhancements.
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