线性参数优化问题的精确与近似算法综述
A Survey of Exact and Approximation Algorithms for Linear-Parametric Optimization Problems
AI总结：
本综述系统梳理了线性参数优化问题的精确与近似算法，涵盖通用策略及特定问题（如最短路径、流、生成树、背包、匹配）的专门方法，并总结了1963至2024年间128篇文献的成果。
摘要：
线性参数优化将多个目标通过线性组合（以参数为系数）合并为单一目标，与优化领域的其他分支有着众多联系，并具有广泛的应用领域。本综述全面概述了精确和近似求解线性参数优化问题的结构结果和算法策略。从多目标优化等相关领域迁移概念可提供进一步的相关结果。本综述由两部分组成：首先，我们列出以通用方式工作且不依赖特定问题结构的策略；其次，我们考察经过充分研究的参数优化问题，并涵盖这些问题的重要理论结果和专门算法方法。这些问题包括最短路径问题、最小费用流和最大流问题、生成树问题、背包问题以及匹配问题的参数变体。总体而言，我们涵盖了1963年至2024年间发表的128篇出版物（并参考了33篇补充文献）的结果。
英文摘要：
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application areas. In this survey, we provide a comprehensive overview of structural results and algorithmic strategies for solving linear-parametric optimization problems exactly and approximately. Transferring concepts from related areas such as multi-objective optimization provides further relevant results. The survey consists of two parts: First, we list strategies that work in a general fashion and do not rely on specific problem structures. Second, we look at well-studied parametric optimization problems and cover both important theoretical results and specialized algorithmic approaches for these problems. Among these problems are parametric variants of shortest path problems, minimum cost flow and maximum flow problems, spanning tree problems, the knapsack problem, and matching problems. Overall, we cover the results from 128 publications (and refer to 33 supplemental works) published between 1963 and 2024.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
