Difference between revisions of "BSc: Introduction to Optimization.F22"
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==== Section 1 ==== |
==== Section 1 ==== |
||
# A steel company must decide how to allocate next week’s time on a rolling mill, which is a machine that takes unfinished slabs of steel as input and can produce either of two semi-finished products: bands and coils. The mill’s two products come off the rolling line at different rates: |
# A steel company must decide how to allocate next week’s time on a rolling mill, which is a machine that takes unfinished slabs of steel as input and can produce either of two semi-finished products: bands and coils. The mill’s two products come off the rolling line at different rates: |
||
| − | :: Bands 200 tons/hr |
+ | ::: Bands 200 tons/hr |
| − | :: Coils 140 tons/hr. |
+ | ::: Coils 140 tons/hr. |
| − | : They also produce different profits: |
+ | :: They also produce different profits: |
| − | :: Bands $ 25/ton |
+ | ::: Bands $ 25/ton |
| − | :: Coils $ 30/ton. |
+ | ::: Coils $ 30/ton. |
| − | : Based on currently booked orders, the following upper bounds are placed on the amount of each product to produce: |
+ | :: Based on currently booked orders, the following upper bounds are placed on the amount of each product to produce: |
| − | :: Bands 6000 tons |
+ | ::: Bands 6000 tons |
| − | :: Coils 4000 tons. |
+ | ::: Coils 4000 tons. |
| − | : Given that there are 40 hours of production time available this week, the problem is to decide how many tons of bands and how many tons of coils should be produced to yield the greatest profit. Formulate this problem as a linear programming problem. Can you solve this problem by inspection? |
+ | :: Given that there are 40 hours of production time available this week, the problem is to decide how many tons of bands and how many tons of coils should be produced to yield the greatest profit. Formulate this problem as a linear programming problem. Can you solve this problem by inspection? |
==== Section 2 ==== |
==== Section 2 ==== |
||
Revision as of 12:45, 23 June 2022
Introduction to Optimization
- Course name: Introduction to Optimization
- Code discipline: CSE???
- Subject area: Data Science and Artificial Intelligence
Short Description
The course outlines the classification and mathematical foundations of optimization methods, and presents algorithms for solving linear and nonlinear optimization. The purpose of the course is to introduce students to methods of linear and convex optimization and their application in solving problems of linear, network, integer, and nonlinear optimization. Course starts with linear programming and moving on to more complex problems. primal and dual simplex methods, network flow algorithms, branch and bound, interior point methods, Newton and quasi-Newton methods, and heuristic methods. Current states, literature, techniques, theories, and methodologies are presented and discussed during the semester.
Prerequisites
Prerequisite subjects
- CSE201: Mathematical Analysis I
- CSE202: Analytical Geometry and Linear Algebra I
- CSE203: Mathematical Analysis II
- CSE204: Analytical Geometry and Linear Algebra II
Prerequisite topics
- Basic programming skills.
- OOP, and software design.
Course Topics
| Section | Topics within the section |
|---|---|
| Linear programming |
|
| Nonlinear programming |
|
| Extensions |
|
Intended Learning Outcomes (ILOs)
What is the main purpose of this course?
The main purpose of this course is to enable a student to go from an idea to implementation of different optimization algorithms to solve problems in different fields of studies like machine and deep learning, etc.
ILOs defined at three levels
We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
Level 1: What concepts should a student know/remember/explain?
By the end of the course, the students should be able to ...
- remember the different classifications and mathematical foundations of optimization methods
- remember basic properties of the corresponding mathematical objects
- remember the fundamental concepts, laws, and methods of linear and convex optimization
- distinguish between different types of optimization methods
Level 2: What basic practical skills should a student be able to perform?
By the end of the course, the students should be able to ...
- Funderstand the basic concepts of optimization problems
- evaluate the correctness of problem statements
- explain which algorithm is suitable for solving problems
- evaluate the correctness of results
Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
By the end of the course, the students should be able to ...
- understand the basic foundations behind optimization problems.
- classify optimization problems.
- choose a proper algorithm to solve optimization problems.
- validate algorithms that students choose to solve optimization problems.
Grading
Course grading range
| Grade | Range | Description of performance |
|---|---|---|
| A. Excellent | 90-100 | - |
| B. Good | 75-89 | - |
| C. Satisfactory | 60-74 | - |
| D. Fail | 0-59 | - |
Course activities and grading breakdown
| Activity Type | Percentage of the overall course grade |
|---|---|
| Midterm | 25 |
| 2 Intermediate tests | 30 (15 for each) |
| Final exam | 30 |
| Final presentation | 15 |
Recommendations for students on how to succeed in the course
- Participation is important. Attending lectures is the key to success in this course.
- Review lecture materials before classes to do well.
- Reading the recommended literature is optional, and will give you a deeper understanding of the material.
Resources, literature and reference materials
Open access resources
- Convex Optimization – Boyd and Vandenberghe. Cambridge University Press.
Closed access resources
- Engineering Optimization: Theory and Practice, by Singiresu S. Rao, John Wiley and Sons.
- Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997. ISBN: 9781886529199.
Software and tools used within the course
- MATLAB
- Python
- Excel
Activities and Teaching Methods
| Teaching Techniques | Section 1 | Section 2 | Section 3 |
|---|---|---|---|
| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 0 | 0 | 0 |
| Project-based learning (students work on a project) | 1 | 1 | 1 |
| Modular learning (facilitated self-study) | 0 | 0 | 0 |
| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1 |
| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0 |
| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0 |
| Inquiry-based learning | 0 | 0 | 0 |
| Just-in-time teaching | 0 | 0 | 0 |
| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0 |
| Studio-based learning | 0 | 0 | 0 |
| Universal design for learning | 0 | 0 | 0 |
| Task-based learning | 0 | 0 | 0 |
| Learning Activities | Section 1 | Section 2 | Section 3 |
|---|---|---|---|
| Lectures | 1 | 1 | 1 |
| Interactive Lectures | 1 | 1 | 1 |
| Lab exercises | 1 | 1 | 1 |
| Experiments | 0 | 0 | 0 |
| Modeling | 0 | 0 | 0 |
| Cases studies | 0 | 0 | 0 |
| Development of individual parts of software product code | 0 | 0 | 0 |
| Individual Projects | 1 | 1 | 1 |
| Group projects | 0 | 0 | 0 |
| Flipped classroom | 0 | 0 | 0 |
| Quizzes (written or computer based) | 0 | 0 | 0 |
| Peer Review | 0 | 0 | 0 |
| Discussions | 1 | 1 | 1 |
| Presentations by students | 1 | 1 | 1 |
| Written reports | 0 | 0 | 0 |
| Simulations and role-plays | 0 | 0 | 0 |
| Essays | 0 | 0 | 0 |
| Oral Reports | 0 | 0 | 0 |
Formative Assessment and Course Activities
Ongoing performance assessment
Section 1
- A steel company must decide how to allocate next week’s time on a rolling mill, which is a machine that takes unfinished slabs of steel as input and can produce either of two semi-finished products: bands and coils. The mill’s two products come off the rolling line at different rates:
- Bands 200 tons/hr
- Coils 140 tons/hr.
- They also produce different profits:
- Bands $ 25/ton
- Coils $ 30/ton.
- Based on currently booked orders, the following upper bounds are placed on the amount of each product to produce:
- Bands 6000 tons
- Coils 4000 tons.
- Given that there are 40 hours of production time available this week, the problem is to decide how many tons of bands and how many tons of coils should be produced to yield the greatest profit. Formulate this problem as a linear programming problem. Can you solve this problem by inspection?
Section 2
Section 3
Final assessment
Section 1
Section 2
Section 3
The retake exam
Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.