Approximation Algorithms for Combinatorial Optimization Problems

组合优化问题的近似算法

• 批准号: RGPIN-2020-06423
• 负责人: SolisOba, Roberto
• 金额: $ 1.75万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=741202
• 关键词: Approximation; Algorithms; Combinatorial; Optimization; Problems

Many optimization problems in manufacturing, transportation, communications, finances, and many other fields require solutions that optimize the use of available resources. An important class of these problems are combinatorial optimization problems. Many of these problems are too complex to solve without the use of computers and, hence, efficient computer algorithms for solving them are needed. However, there is strong theoretical evidence suggesting that even modern fast computers are not powerful enough to efficiently solve many of these optimization problems; these problems get the technical name of NP-hard. Despite the seeming impossibility for solving NP-hard problems efficiently (or,technically, in polynomial time), we still need to deal with them since they arise in industrial and commercial applications. One important tool for dealing with these problems is approximation algorithms; these are efficient algorithms that yield solutions whose values are within some factor c from the optimum. Knowing how close to optimal are the solutions produced by approximation algorithms helps us determine how well we can solve complex problems of practical relevance. This research focuses on the design of approximation algorithms for three kinds of problems: network, scheduling and packing problems. Networks are one of the most fundamental modelling tools in optimization and scheduling and packing problems are of great importance in domains requiring the effective management of limited resources. Goals: 1. To design efficient approximation algorithms that exploit the special structure of restricted instances of scheduling, packing, and network optimization problems that arise in practical applications. The inherent nature of practical applications many times restricts the set of inputs that my appear in instances of optimization problems arising from them. I plan to work on exploiting the structure of these restricted instances to discover good design techniques for them. 2. To formulate new techniques for the design of approximation algorithms for scheduling, packing, and network problems that yield approximation algorithms with practical running times. I will work on extending and combining existing design techniques for approximation algorithms so they are applicable to a larger set of problems. 3. To study the trade-off between the quality of solutions produced by approximation algorithms and their running times. In practical applications it is necessary to limit the amount of time that an algorithm can run. I plan to work on understanding what is the best solution that one can hope to obtain for a particular problem within a given amount of time. I expect my research to lead to approximation algorithms that are better suited than existing ones for practical applications of network, scheduling and packing problems, both with respect to approximation ratio and running time. This research is of theoretical and practical importance.

制造，运输，通信，财务和许多其他领域的许多优化问题都需要优化可用资源使用的解决方案。这些问题的重要类别是组合优化问题。这些问题中的许多问题太复杂了，无法在不使用计算机的情况下解决，因此需要有效的计算机算法来解决它们。但是，有强有力的理论证据表明，即使是现代快速计算机也不足以有效地解决许多此类优化问题。这些问题获得了NP-HARD的技术名称。尽管似乎不可能有效地解决NP硬性问题（或从技术上讲，在多项式时期），但由于它们在工业和商业应用中出现，因此我们仍然需要处理它们。解决这些问题的一种重要工具是近似算法。这些是有效的算法，它们的值从最佳限制中产生了一个在某个因素C之内的解决方案。知道通过近似算法产生的解决方案有多接近最佳，这有助于我们确定如何解决实际相关性的复杂问题。这项研究重点是针对三种问题的近似算法的设计：网络，调度和包装问题。网络是优化，调度和包装问题最基本的建模工具之一，在需要有效管理有限资源的域中非常重要。目标：1。设计有效的近似算法，以利用在实际应用中出现的调度，包装和网络优化问题的限制实例的特殊结构。实际应用的固有本质限制了我在其优化问题实例中出现的一组投入。我计划利用这些限制实例的结构，为它们发现良好的设计技术。 2。制定新技术，用于设计用于调度，包装和网络问题的近似算法，以产生具有实际运行时间的近似算法。我将致力于扩展和组合现有的设计技术以近似算法，以便它们适用于更大的问题。 3。研究近似算法产生的解决方案质量与其运行时间之间的权衡。在实际应用中，有必要限制算法可以运行的时间。我计划在特定时间内了解什么是最佳解决方案。 我希望我的研究会导致近似算法，这些算法比现有的算法更适合于网络，调度和包装问题的实际应用，无论是在近似比和运行时间方面。这项研究具有理论和实用性。