ID:
509005
Durata (ore):
56
CFU:
6
SSD:
RICERCA OPERATIVA
Anno:
2024
Dati Generali
Periodo di attività
Secondo Semestre (03/03/2025 - 13/06/2025)
Syllabus
Obiettivi Formativi
The course is a comprehensive introduction to the theory, models, and algorithms of mathematical optimization. The goals of this course are the following:
1. To present students with knowledge of the state-of-the-art of theory and practice of solving optimization problems.
2. To help each student develop his or her own intuition about modeling and solving large-scale real-world problems using optimization software.
1. To present students with knowledge of the state-of-the-art of theory and practice of solving optimization problems.
2. To help each student develop his or her own intuition about modeling and solving large-scale real-world problems using optimization software.
Prerequisiti
This course is an applied math course dedicated to math and engineering students. The students of this course should have followed and given the exams of the fundamental courses in programming (Programming 1 and Programming 2), Analysis, and Linear Algebra. All the content of these fundamental courses are a prerequisite for this course.
Metodi didattici
Lectures and Guided exercise sessions in Computer Labs.
For the lectures, the teacher will use personal slides available on KIRO, our Moodle.
For the lab session, all the material will be available on a GitHub web page.
The teacher will teaching principles of "active learning", encouraging as much as possible the active partecipation of the students during the lectures.
For the lectures, the teacher will use personal slides available on KIRO, our Moodle.
For the lab session, all the material will be available on a GitHub web page.
The teacher will teaching principles of "active learning", encouraging as much as possible the active partecipation of the students during the lectures.
Verifica Apprendimento
The course is organized in four parts. During each part, we will use as running examples, large-scale optimization problems currently solved in Computational Biology (e.g., Alignment of Genomic Sequencing, Metabolic Networks, Haplotype Analysis), Transportation Planning and Scheduling (Home Health Care Routing, Nurse Scheduling), and Machine Learning (e.g., Regression, Clustering, Optimal Classification Trees).
The final grade will have a maximum score of 30. The lab project will count for 75% of the final grade.
During the presentation the student should use a maximum number of 15 slides.
The final grade will have a maximum score of 30. The lab project will count for 75% of the final grade.
During the presentation the student should use a maximum number of 15 slides.
Testi
Book References (Selected Chapters):
• H.P. Williams. Model building in mathematical programming. John Wiley & Sons, 2013.
• D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization, Athena Scientific, 1997.
• Conforti, M., Cornuéjols, G., Zambelli, G., Conforti, M., Cornuéjols, G. and Zambelli, G., 2014. Integer programming models (pp. 45-84). Springer International Publishing.
• H.P. Williams. Model building in mathematical programming. John Wiley & Sons, 2013.
• D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization, Athena Scientific, 1997.
• Conforti, M., Cornuéjols, G., Zambelli, G., Conforti, M., Cornuéjols, G. and Zambelli, G., 2014. Integer programming models (pp. 45-84). Springer International Publishing.
Contenuti
Part I: Optimization Modeling
Optimization modeling is the skill of reducing a messy computational or engineering problem to a mathematical form that can be solved by using optimization software. By recognizing mathematical patterns in real-world problems, students will develop an intuition for which problems are solvable using optimization modeling techniques and gain the knowledge and skills to then solve them.
Part II: Network flows
Network flow problems form a subclass of linear programming problems with several applications. This part of the course will focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem.
Part III: Linear Optimization
The topics in linear optimization include: The Simplex Method, Duality Theory, Sensitivity Analysis, Interior-Point Methods, Implementation Issues.
Part IV: Integer Optimization
The topics in integer optimization include: Branch and Bound, Cutting Plane Algorithms, Strong Valid Inequalities, Lagrangian Duality, Column Generation Algorithms, Heuristic Algorithms.
Optimization modeling is the skill of reducing a messy computational or engineering problem to a mathematical form that can be solved by using optimization software. By recognizing mathematical patterns in real-world problems, students will develop an intuition for which problems are solvable using optimization modeling techniques and gain the knowledge and skills to then solve them.
Part II: Network flows
Network flow problems form a subclass of linear programming problems with several applications. This part of the course will focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem.
Part III: Linear Optimization
The topics in linear optimization include: The Simplex Method, Duality Theory, Sensitivity Analysis, Interior-Point Methods, Implementation Issues.
Part IV: Integer Optimization
The topics in integer optimization include: Branch and Bound, Cutting Plane Algorithms, Strong Valid Inequalities, Lagrangian Duality, Column Generation Algorithms, Heuristic Algorithms.
Lingua Insegnamento
INGLESE
Altre informazioni
During the course the students will have the opportunity to partecipate to modelling "challenges" (e.g., see the MOPTA optimization challenge on Green Hydrogen as a Supplemental Power Source, at https://coral.ise.lehigh.edu/~mopta/competition)
Corsi
Corsi
INGEGNERIA COMPUTAZIONALE E MODELLISTICA PER MATERIALI, STRUTTURE E TECNOLOGIE SOSTENIBILI
Laurea Magistrale
2 anni
No Results Found
Persone
Persone
No Results Found