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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/operations-research-algorithms
课程评论：没有评论
课程名称：运筹学（2）：优化算法 概述：运筹学（OR）是一门利用数学和工程方法研究商业管理、经济学、计算机科学、土木工程、电气工程等领域优化问题的学科。该系列课程共分为三个部分，主要关注确定性优化技术，这是运筹学领域的重要组成部分。作为系列课程的第二部分，我们研究了一些高效的算法，用于解决线性规划、整数规划和非线性规划问题。同时，我们还介绍了不同程序求解的基本计算机实现，并讨论了算法应用的示例。 课程大纲： 1. **课程概述** 描述：在第一讲中，我们简要介绍了课程内容，并快速回顾了一些线性代数的基础知识，包括高斯消元法、高斯-约旦消元法和线性无关的定义。 2. **单纯形法** 描述：在Dr. George Dantzig开发单纯形法之前，复杂的线性规划难以求解。本周，我们首先介绍线性规划的标准形式和基本解，继而专注于单纯形法，并学习其如何高效地求解线性规划。最后，我们讨论无界问题和不可行问题的一些特性，这有助于我们识别一个问题是否存在最优解。 3. **分支定界法** 描述：整数规划是线性规划的一种特殊情况，其中某些变量必须取整数值。本周，我们介绍线性松弛的概念以及用于解决整数规划的分支定界算法。 4. **梯度下降法与牛顿法** 描述：在过去的两周中，我们讨论了线性和整数规划的求解算法，而这一次我们将重点放在非线性规划上。本周，我们首先复习了一些必要的知识，如梯度和海森矩阵。接着，我们介绍梯度下降法和牛顿法来解决非线性规划，最后比较这两种方法。 5. **启发式算法的设计与评估** 描述：作为本课程的最后一课，我们介绍了一个关于NEC台湾的案例，该公司提供云计算、人工智能、物联网等IT和网络解决方案。由于维护所有服务中心的成本过高，他们计划重新安排中心位置并重新分配每个中心的员工数量。课程中包含了一个算法，以解决NEC台湾面临的设施选址问题。 6. **课程总结与未来学习方向** 描述：在最后一周，我们回顾了所学的主题，并给学生做总结。此外，我们还简要预览了高级课程，以提供未来学习的方向。
Name:Course Overview
Description:In the first lecture, we briefly introduce the course and give a quick review about some basic knowledge of linear algebra, including Gaussian elimination, Gauss-Jordan elimination, and definition of linear independence.
Name:The Simplex Method
Description:Complicated linear programs were difficult to solve until Dr. George Dantzig developed the simplex method. In this week, we first introduce the standard form and the basic solutions of a linear program. With the above ideas, we focus on the simplex method and study how it efficiently solves a linear program. Finally, we discuss some properties of unbounded and infeasible problems, which can help us identify whether a problem has optimal solution.
Name:The Branch-and-Bound Algorithm
Description:Integer programming is a special case of linear programming, with some of the variables must only take integer values. In this week, we introduce the concept of linear relaxation and the Branch-and-Bound algorithm for solving integer programs.
Name:Gradient Descent and Newton’s Method
Description:In the past two weeks, we discuss the algorithms of solving linear and integer programs, while now we focus on nonlinear programs. In this week, we first review some necessary knowledge such as gradients and Hessians. Second, we introduce gradient descent and Newton’s method to solve nonlinear programs. We also compare these two methods in the end of the lesson.
Name:Design and Evaluation of Heuristic Algorithms
Description:As the last lesson of this course, we introduce a case of NEC Taiwan, which provides IT and network solutions including cloud computing, AI, IoT etc. Since maintaining all its service hubs is too costly, they plan to rearrange the locations of the hubs and reallocate the number of employees in each hub. An algorithm is included to solve the facility location problem faced by NEC Taiwan.
Name:Course Summary and Future Learning Directions
Description:In the final week, we review the topics that we have learned and give students a summary. Besides, we briefly preview the advanced course to provide future direction of studying.
Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc. The series of courses consists of three parts, we focus on deterministic optimization techniques, which is a major part of the field of OR. As the second part of the series, we study some efficient algorithms for solving linear programs, integer programs, and nonlinear programs. We also introduce the basic computer implementation of solving different programs, integer programs, and nonlinear programs and thus an example of algorithm application will be discussed.
