离散优化建模基础篇 Basic Modeling for Discrete Optimization

The Chinese University of Hong Kong via Coursera

Go to Course: https://www.coursera.org/learn/lisan-youhua-jianmo-jichupian

Introduction

### Course Review: Basic Modeling for Discrete Optimization on Coursera #### Overview In today’s data-driven world, optimization problems are fundamental in various decision-making processes across industries. The course **"Basic Modeling for Discrete Optimization"** (离散优化建模基础篇) on Coursera offers an in-depth perspective on how to tackle these challenges effectively. Whether you're interested in scheduling wedding seating arrangements or optimizing flight and crew member schedules, this course covers it all. The course content reveals how optimization techniques can lead to dramatically improved decision-making outcomes, enhancing profitability for businesses and improving everyday task efficiency from routing packages to school scheduling and energy distribution. Despite the ubiquitous nature of these problems, the complexity often requires advanced understanding—something this course promises to deliver. #### What You Can Expect This course is meticulously designed for anyone curious about the applications of optimization problems. It introduces learners to a novel method of approaching these challenges through the use of advanced modeling languages. The primary tool in focus is **MiniZinc**, a high-level modeling language tailored for discrete optimization. The structured curriculum equips students with both theoretical knowledge and practical skills essential for modeling various types of optimization problems. #### Syllabus Breakdown **1. Introduction to MiniZinc:** The first unit introduces MiniZinc, focusing on its syntax and capabilities. Students will learn to create basic MiniZinc models and understand existing simple models. This foundational knowledge is crucial as it sets the stage for more complex modeling tasks. **2. Set Modeling:** This unit dives into set selection problems. Students explore various methods for representing set variables, emphasizing the importance of effective decision-making and valid model decisions. The learning outcomes focus on constructing a MiniZinc model for set selection and choosing the right representation method. **3. Function Modeling:** Here, learners address pure assignment and partition problems, both framed as function modeling tasks. Application areas include duty scheduling and constraint clustering. Students will master techniques like common sub-expression elimination and the utility of global constraints, equipping them to create basic duty models. **4. Multiple Modeling:** In the final unit, the course emphasizes viewing discrete optimization problems from different angles, leading to diverse model construction. This multidisciplinary approach allows students to create models using various decision variables and ascertain the most suitable perspective for a given problem. #### Why You Should Enroll The **Basic Modeling for Discrete Optimization** course is perfect for anyone looking to deepen their understanding of optimization techniques and develop practical skills in modeling. It balances a solid academic foundation with real-world applications, making it a valuable resource whether you’re a student, industry professional, or simply someone interested in operations research. The course not only empowers you to solve seemingly complex problems with ease, thanks to its structured approach and focus on MiniZinc. Furthermore, with the backdrop of real-world applications—from logistics to production scheduling—moving through the lessons grants insights that are both academically enriching and practically applicable. #### Final Recommendation If you are eager to enhance your problem-solving capabilities and gain proficiency in optimization modeling, **"Basic Modeling for Discrete Optimization"** on Coursera is highly recommended. With engaging content, practical applications, and expert-led instructions, this course promises an intensive yet approachable way to master the fundamental concepts of discrete optimization. Don't miss out on this opportunity to revolutionize your understanding and approach to optimization—enroll today!

Syllabus

MiniZinc介绍

在第一单元中，你将学习到MiniZinc的基础知识。它是一门用于离散优化问题的高级建模语言。通过结合简洁的MiniZinc语言和业界开源项目强大的求解技术，你将学会如何轻松地解决一些应用问题，比如背包问题，涂色问题，生产规划和覆面算问题。这个模块的学习目标是： (1) 建立一个基本的MiniZinc模型。 (2)理解一个由他人创建的简单MiniZinc模型。

集合建模

在这个单元中，你将学到如何对集合选择问题进行建模。特别是你将学习到如何利用不同的方法来表示没有势约束的，固定势的，或有界势的集合变量。在建模时，你还需要确保所有的模型决策都是有效的决策，而每一个有效的决策刚好对应一个模型决策。这个模块的学习目标是：(1) 建立一个MiniZinc模型来选择一个集合 。 (2)选择一种最适合的表示方式来表示集合。

函数建模

在这个单元中，你将学习到如何对纯分配问题和划分问题建模，而实际上它们都是函数建模问题。这些问题可以应用到值勤安排或者约束聚类问题中。而在建模技术上，你将看到共同子表达式消除和中间变量的威力，还会初次接触到全局势约束。另外，MiniZinc还提供了约束来去除值对称。这个模块的学习目标是：(1) 创建MiniZinc模型来决定一个函数 。 (2)分析问题来洞察问题中是否含有赋值的子结构 。 (3)创建基本的值班模型。 (4)发现问题是否需要划分一个集合 。

多重建模

在最后一个单元中，你将会看到离散优化问题可以如何通过不同的视角来切入，和如何从不同的视角来建立完全不同的模型。每一个视角都有优劣，而实际上不同的视角的模型可以结合起来互补。 这个模块的学习目标是：(1) 创建可以用两种不同视角的决策变量的MiniZinc模型。 (2)决定使用哪一种视角（或者组合视角）的决策变量对某一类问题更适合。