发表机构
University of Central Florida（中佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对大规模固定费用网络流问题，提出基于迭代重加权最小二乘的连续优化算法，结合支持级搜索，在410个实例上平均差距1.316%，胜或平率90%，有效生成高质量可行解。
AI 中文摘要
固定费用网络流问题（FCNFP）将连续流量分配与离散弧激活决策相结合，使其成为各种网络设计和资源分配问题中典型但计算上具有挑战性的模型。精确的混合整数线性规划公式能够忠实地捕捉固定费用结构，但在大型网络上往往难以求解。我们提出了一种基于迭代重加权最小二乘（IRLS）框架的可扩展连续优化算法，用于大规模单商品FCNFP。该方法用光滑的非凸Lasry-Lions代理替代不连续的固定费用和线性弧成本目标，并求解一系列加权二次流子问题。每个子问题通过热启动的对偶半光滑牛顿方法求解，其牛顿系统具有加权图拉普拉斯结构，从而能够利用现代拉普拉斯求解器。为了进一步改进具有挑战性的底层组合问题的弧支持，我们还开发了一种算法变体，该变体结合了目标驱动的扰动重启和锚定并集受限搜索，共同利用IRLS和互补FCNFP启发式发现的支撑。在410个基准、合成和大规模实例上的计算实验表明，我们的方法在评估的可扩展FCNFP算法中获得了最佳目标质量，与时间限制的MILP参考相比平均差距为1.316%，在非MILP方法中胜或平率为90.0%。结果表明，将光滑连续优化与支持级搜索相结合是产生大规模FCNFP高质量可行解的有效策略。
英文摘要
The fixed-charge network flow problem (FCNFP) couples continuous flow allocation with discrete arc-activation decisions, making it a canonical but computationally challenging model for a variety of network design and resource allocation problems. Exact mixed-integer linear programming formulations capture the fixed-charge structure faithfully, but often become difficult to solve on large networks. We propose a scalable continuous-optimization algorithm for large-scale single-commodity FCNFP based on an iteratively reweighted least-squares (IRLS) framework. The method replaces the discontinuous fixed-charge and linear arc cost objective with a smooth nonconvex Lasry--Lions surrogate and solves a sequence of weighted quadratic flow subproblems. Each subproblem is solved by a warm-started dual semismooth Newton method whose Newton systems have weighted graph-Laplacian structure, enabling the use of modern Laplacian solvers. To further improve the discovered arc supports of the challenging underlying combinatorial problem, we also develop an algorithmic variant that incorporates objective-driven perturbation restarts and an anchor-union restricted search that jointly leverages supports discovered by IRLS and by complementary FCNFP heuristics. Computational experiments on 410 benchmark, synthetic, and large-scale instances show that our method obtains the best objective quality among the evaluated scalable FCNFP algorithms, with a mean gap of $1.316\%$ to a time-limited MILP reference and a win-or-tie rate of $90.0\%$ among the non-MILP methods. The results indicate that combining smooth continuous optimization with support-level search is an effective strategy for producing high-quality feasible solutions to large-scale FCNFP.
Comments20 pages
