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Discrete Optimization · LearnSpace
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Discrete Optimization

Курс от Georgia Institute of Technology
Средний≈ 65.2 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Tired of solving Sudokus by hand? This class teaches you how to solve complex search problems with discrete optimization concepts and algorithms, including constraint programming, local search, and mixed-integer programming. Optimization technology is ubiquitous in our society. It schedules planes and their crews, coordinates the production of steel, and organizes the transportation of iron ore from the mines to the ports. Optimization clears the day-ahead and real-time markets to deliver electricity to millions of people. It organizes kidney exchanges and cancer treatments and helps scientists understand the fundamental fabric of life, control complex chemical reactions, and design drugs that may benefit billions of individuals. This class is an introduction to discrete optimization and exposes students to some of the most fundamental concepts and algorithms in the field. It covers constraint programming, local search, and mixed-integer programming from their foundations to their applications for complex practical problems in areas such as scheduling, vehicle routing, supply-chain optimization, and resource allocation.

Навыки, которые вы освоите

Model OptimizationMathematical ModelingAlgorithmsComputational LogicCombinatoricsApplied MathematicsLinear AlgebraTheoretical Computer ScienceOperations ResearchComputational Thinking

Программа курса

8 модулей · 63 учебных материалов

01Welcome7 материалов

Welcome and Motivation

Course PromoВидеоCourse Motivation - Indiana Jones, challenges, applicationsВидеоStart of Course SurveyЧтение

Preliminaries

Course Introduction - philosophy, design, grading rubricВидео

Учитесь у экспертов

Professor Pascal Van Hentenryck

A. Russell Chandler III Chair and Professor

Dr. Carleton Coffrin

Staff Scientist

Discrete Optimization
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Обучение на Coursera

≈ 65.2 ч

8 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Course SyllabusЧтение

Assignment

Assignments Introduction & Any IntegerВидеоAny IntegerПрограммирование
02Knapsack10 материалов

The Knapsack Problem

Knapsack 1 - intuitionВидеоKnapsack 2 - greedy algorithmsВидеоKnapsack 3 - modelingВидеоKnapsack 4 - dynamic programmingВидеоKnapsack 5 - relaxation, branch and boundВидеоKnapsack 6 - search strategies, depth first, best first, least discrepancyВидео

Assignment

Assignments Getting StartedВидеоKnapsack & External SolverВидеоKnapsackПрограммирование

Next Steps

Exploring the Material - open course design, optimization landscape, picking your adventureВидео
03Constraint Programming16 материалов

Constraint Programming

CP 1 - intuition, computational paradigm, map coloring, n-queensВидеоCP 2 - propagation, arithmetic constraints, send+more=moneyВидеоCP 3 - reification, element constraint, magic series, stable marriageВидеоCP 4 - global constraint intuition, table constraint, sudokuВидеоCP 5 - symmetry breaking, BIBD, scene allocationВидеоCP 6 - redundant constraints, magic series, market splitВидеоCP 7 - car sequencing, dual modelingВидеоCP 8 - global constraints in detail, knapsack, alldifferentВидеоCP 9 - search, first-fail, euler knight, ESDDВидеоCP 10 - value/variable labeling, domain splitting, symmetry breaking in searchВидео

Assignment

Graph ColoringВидеоGraph ColoringПрограммирование

Optimization Tools (optional)

Optimization ToolsВидеоOptimization ToolsЧтение

Open Source Assignment (optional)

Set CoverВидеоSet CoverПрограммирование
04Local Search11 материалов

Local Search

LS 1 - intuition, n-queensВидеоLS 2 - swap neighborhood, car sequencing, magic squareВидеоLS 3 - optimization, warehouse location, traveling salesman, 2-opt, k-optВидеоLS 4 - optimality vs feasibility, graph coloringВидеоLS 5 - complex neighborhoods, sports schedulingВидеоLS 6 - escaping local minima, connectivityВидеоLS 7 - formalization, heuristics, meta-heuristics introductionВидеоLS 8 - iterated location search, metropolis heuristic, simulated annealing, tabu search intuitionВидеоLS 9 - tabu search formalized, aspiration, car sequencing, n-queensВидео

Assignment

Traveling SalesmanВидеоTraveling SalesmanПрограммирование
05Linear Programming6 материалов

Linear Programming

LP 1 - intuition, convexity, geometric viewВидеоLP 2 - algebraic view, naive algorithmВидеоLP 3 - the simplex algorithmВидеоLP 4 - matrix notation, the tableauВидеоLP 5 - duality derivationВидеоLP 6 - duality interpretation and usesВидео
06Mixed Integer Programming7 материалов

Mixed Integer Programming

MIP 1 - intuition, relaxation, branch and bound, knapsack, warehouse locationВидеоMIP 2 - modeling, big-M, warehouse location, graph coloringВидеоMIP 3 - cutting planes, Gomory cutsВидеоMIP 4 - convex hull, polyhedral cuts, warehouse location, node packing, graph coloringВидеоMIP 5 - cover cuts, branch and cut, seven bridges, traveling salesmanВидео

Assignment

Facility LocationВидеоFacility LocationПрограммирование
07Advanced Topics: Part I3 материалов

Scheduling

Scheduling - jobshop, disjunctive global constraintВидео

Assignment

Vehicle RoutingВидеоVehicle RoutingПрограммирование
08Advanced Topics: Part II3 материалов

Decomposition Techniques

Large Neighborhood Search - asymmetric TSP with time windowsВидеоColumn Generation - branch and price, cutting stockВидеоEnd of course surveyЧтение