• Dizajn u mašinstvu, Semester 3, position 2
• Mašinstvo i informacione tehnologije, Semester 3, position 2

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.

After completing this course students are able to successfully apply the acquired theoretical and practical knowledge and are able to: •Identify relevant optimization variables, define the set of functional constraints and limitations for the corresponding optimization model of a given mechanical system. •Apply linear and non-linear numerical methods for solving the optimization problems and define the appropriate convergence criteria. •Develop and implement computer programs in software packages Python / MATLAB for solving the set of optimization tasks. •Analyze the results and check the validity of the proposed optimization models with respect to the change of input parameters. •Apply the stochastic - heuristic methods and develop hybridized heuristic methods to determine the global solution of the optimization problems of complex mechanical systems. •Develop new and apply existing numerical methods for solving complex optimization tasks, individually or as part of an appropriate team.

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. Constrained optimum design problems. Necessary conditions: equality constraints. Necessary conditions: inequality constraints - Karush-Kuhn-Tucker (KKT) conditions. Postoptimality analysis: physical meaning of Lagrange multipliers. Engineering design examples with MATLAB. 5. Linear Programming. Problem definition. Standard LP format. Graphical solution. Characteristics of the solution. Optimum solution for LP problems. 6. Numerical Solution - the Simplex Method. Basic Steps of the Simplex Method. Simplex Algorithm. Solution using MATLAB's optimization toolbox. 7. Nonlinear Programming. Problem formulation. Graphical solutions. Equality constrained problem. Inequality constrained optimization. Basic ideas and algorithms for step size determination. 8. Numerical methods - The One-dimensional Problem. Newton-Raphson method. Bisection method. Polynomial Approximation. Golden section method. Optimum design examples with MATLAB. 9. 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. 10. Numerical Methods for Constrained optimization Problem definition. Necessary conditions. Method of feasible directions.Gradient projection method. Exterior penalty function method. Optimum design examples with MATLAB.

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.

Total assigned hours: 75

New material: 30
Elaboration and examples (recapitulation): 0

Auditory exercises: 0
Laboratory exercises: 21
Calculation tasks: 0
Seminar paper: 7
Project: 2
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: 7
Review and grading of the project: 0
Test: 0
Test: 3
Final exam: 5

Activity during lectures: 5
Test/test: 35
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 30
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 35

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.