Duration
30h Th, 12h Pr, 18h Proj.
Number of credits
Lecturer
Substitute(s)
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The primary objective of the course is to present a systematic and critical overview of the various numerical methods available to solve engineering optimization problems.
A second important goal is to familiarize participants with the introduction of optimization concepts into the engineering design process wich can be for instance encoutered in aerospace, in mechanical or electrical engineering. The basic concepts are illustrated throughout the course by solving simple optimization problems. In addition, several examples of application to real-life design problems are offered to demonstrate the high level of efficiency attained in modern numerical optimization methods. Although most examples are taken in the field of structural optimization, using finite element modeling and analysis, the same principles and methods can be easily applied to other design problems arising in various engineering disciplines such as structural engineering, electromagnetics systems or multidisciplinary optimization.
Content
Part I (P. Tossings) Introduction to numercial methods to solve optimization problems
- Fundamentals of Mathematical Programming (including KKT conditions)
- Unconstrained Optimization: Gradient Methods (including conjugate directions)
- Line Search Techniques
- Unconstrained Optimization: Newton, Newton-like and Quasi-Newton Methods
- Quasi-Unconstrained Optimization
- Linearly Constrained Optimization: Projected Gradient Method
- General Constrained Optimization: Dual Methods
- General Constrained Optimization: Transformation Methods (including SLP and SQP)
Part II Application to structural and multidisciplinary optimization
- Fundamental Concepts in Structural and Multidisciplinary Optimization
- Finite Element and Optimization
- Optimality Criteria (OC)
- Sensitivity Analysis for Finite Element Model
- Structural approximations
- Solving efficiently CONLIN and MMA using dual solvers
- Introduction to shape optimization
- Introduction to topology optimization
Learning outcomes of the learning unit
At the end of the course the participants will be familiar with the fundamental optimization concepts applied to automatic design process.
They will be able:
- to understand the principles of algorithms and optimization methods,
- to develop solution schemes to simple engineering optimization problems related to design or parameter identification (including the development of computer programs written in MATLAB or PYTHON language),
- to choose efficient formulations and optimization algorithms to solve their own problems using commercial tools,
- to get started with using an industrial optimization software tool (NX-TOPOL).
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.3, III.4, IV.1, IV.3, V.1, V.3, VI.1, VI.2, VII.2, VII.4 of the MSc in aerospace engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.3, III.4, IV.1, IV.3, V.1, V.3, VI.1, VI.2, VII.2, VII.4 of the MSc in electromechanical engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.3, III.4, IV.1, IV.3, V.1, V.3, VI.1, VI.2, VII.2, VII.4 of the MSc in mechanical engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.2, III.3, III.3, III.4, IV.1, V.1, V.3, VI.1, VI.2, VII.2, VII.4 of the MSc in engineering physics.
Prerequisite knowledge and skills
- Mathematical analysis of real functions
- Matrix algebra
- Matlab or Python programming (basic level)
- Finite Element Method
- Mechanical Vibrations: eigenfrequencies, eigenmodes, mechanical systems with N-degrees of freedom
Planned learning activities and teaching methods
- In person lectures
- Supervised computer work sessions (made in groups of 2 persons - to be defined for the beginning of the practical sessions)
- Exercises sessions
- For students who have no sufficient skills in MATLAB programming or in Finite Element Method, it is strongly recommended to attend preparation courses or to read recommended self learning material.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
Attending 60% of supervised computer work sessions is mandatory to access the exam (presence is notified by signing the attendance list).
Course materials and recommended or required readings
Copy of slides available on line on the platform eCampus.
All the class notes are in English
Reference books (recommended complementary lectures)
- Christensen P. and Klarbring A. An introduction to Structural Optimization. Springer 2010.
- Programmation mathématique: théorie et algorithmes (Tome 1). M. Minoux. Dunod, Paris, 1983.
- Foundations of Structural Optimization: A Unified Approach. A.J. Morris. John Wiley & Sons Ltd, 1982
- Haftka, R.T. and Gürdal, Z., Elements of Structural Optimization, 3rd edition, Springer, 1992
- J. Nocedal and S. Wright. Numerical Optimization. Springer 2006
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Written work / report
Continuous assessment
Further information:
- There is a theory written exam in the January session. Its weight is 60% of the final mark (half for each part of the course).
- The computer works are evaluated on the basis of reports (presented on slides or in full text, depending on the part of the course). Only one report is required for each group. The first one has to be submitted for October, 25, and the second one for December, 20 (11:59 PM). The regular implication into the sessions is also taken into account. The computer works weight 40% of the final mark.
- Participation to at least 60% of the practical sessions is mandatory to present the exam.
- The evaluation of the computer works can not be modified for the September session.
Work placement(s)
Organisational remarks and main changes to the course
The lectures are given on Tuessday afternoon (01:45-05:45 during full semester (September 17 - December 17).
Courses include both lectures and supervised computer work participation.
A Question & Answer session is organized in December.
The exam is scheduled during the January session.
Contacts
Michael BRUYNEEL
- Email: Michael.Bruyneel@uliege.be
Patricia TOSSINGS
- Mathématiques Générales
- Institut de Mathématique B37 0/57
- Tél: 04 366 9373
- Email. Patricia.Tossings@ULiege.be
Association of one or more MOOCs
There is no MOOC associated with this course.