The main goal of this course for the student is to give the necessary knowledge of: • numerical analysis and optimization, • understanding general principles of design optimization • formulating the optimization problems and identify critical elements.

During this course, the student will carry out: • Overview of design optimization • Fundamentals of engineering optimization • Problem formulation • strategies for optimization

1.Introduction to Modeling and Optimum Design Process. Optimum design problem formulation. A general mathematical model for optimization. 2.Graphical Optimization.Identification of feasible region. Use of MATLAB for graphical optimization. 3. Unconstrained Optimum Design Problems. Optimality conditions for functions of several variables. 4.Engineering design examples with MATLAB. 5. Nonlinear Programming. Problem formulation. Equality constrained problem. Inequality constrained optimization. Basic ideas and algorithms for step size determination. 6. Numerical methods - The One-dimensional Problem. Optimum design examples with MATLAB. 7. Numerical Methods for Unconstrained Optimization. Numerical Methods - Nongradient methods. Powell's method. Numerical Methods-Gradient-Based Methods. Conjugate Gradient (Fletcher-Reeves) Method. Davidon-Fletcher- Powel (DFP) method. 8. Numerical Methods for Constrained optimization Problem definition. Necessary conditions. Method of feasible directions.Gradient projection method. Exterior penalty function method. 9. Introduction to the Formulation of the Multicriterion Optimization Problem. Decision variables. Constraints. Objective functions.Space of Decision Variables and Space of Objective Functions. Pareto Optimum. Min-Max optimum. 10. Decision Making Problem. Weighting Objectives Method. Goal Programming Method. Interactive Multicriterion optimization method. 11.Genetic Algorithm with MATLAB for optimum design examples.

Consists of the auditory and laboratory exercises. Projects are main component of this course.

Knowledge of linear algebra and numerical mathematics. Computer programming in MATLAB. Some knowledge of basic machine elements and mechanics.

Computer Usage: Students extensively use the computer and optimization toolbox using MATLAB program. Handout and books.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 15
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 0

Activity during lectures: 15
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 15
Project: 0
Final exam: 70
Requirement for taking the exam (required number of points): 30

Jasbir S. Arora " Introduction to Optimum Design", Elsevier Academic Press, 2017.; P. Venkataraman " Applied Optimization with Matlab Programming" John Wiley and sons, inc, 2009.; H. Eschenauer, J. Koski, A. Osyczka: "Multicriteria Design Optimization", Springer-Verlag, 1990.