Optimization of thermal processes 2007/2008

1. Optimization of thermal processes 2007/2008 Optimization of thermal processes Lecture 1 Maciej Marek Czestochowa University of Technology Institute of Thermal Machinery

2. Optimization of thermal processes 2007/2008 Main topics • Introduction • Fundamental concepts in optimization • Engineering applications of optimization • Types of optimization problems • Constrained, unconstrained • Linear, nonlinear • Static, dynamic • Classical optimization techniques • Analytical, numerical • Direct, indirect • Linear programming • Overview of some modern techniques • Genetic algorithms, simulated annealing, neural networks • Examples of engineering applications EXAM

3. Optimization of thermal processes 2007/2008 Literature • S. Rao "Engineering optimization, theory and practice„ • R. Klajny "Optymalizacja procesów cieplnych„ • P. Gill, W. Murray, M. Wright "Practical optimization„ • M. Bhatti "Practical optimization methods„ • S. Sieniutycz "Optymalizacja w inżynierii procesowej„ • S. Sieniutycz, Z. Szwast "Przykłady i zadania z optymalizacji procesowej„ • M. Sysło, N. Deo, J. Kowalik "Algorytmy optymalizacji dyskretnej„ • E. Majza "Przykłady zastosowań badań operacyjnych w energetyce cieplnej"

4. Optimization technique Objective function Constraints Optimization of thermal processes 2007/2008 What is optimization? Optimization is • the process of finding • the best result • under given circumstances.

5. Minimum of Maximum of Optimization of thermal processes 2007/2008 Optimization problem • Objective function(criterion or merit function) • Constraints (restrictions) x

6. Decision (design) variables Design vector Optimization of thermal processes 2007/2008 Formal statement of an (constrained) optimization problem • Find which minimizes • subject to the constraints Inequality constraint Equality constraint

7. Optimization of thermal processes 2007/2008 Engineering applications of optimization(mathematical programming) • Design of aircraft • Objective: minimum weight • Constraints: capacity, strength, cost • Design of pumps, turbines, heat transfer equipment • Objective: maximum efficiency • Constraints: weight, cost, noise level, impact on the enviroment etc. • Allocation of resources or services among several activities to maximize the benefit • Analysis of statistical data (approximation) • Optimal scheduling • Other examples?

8. Optimization of thermal processes 2007/2008 Classification of optimization problemsbased on • Nature of the decision variables • Static, dynamic • Nature of the equations (and inequalities) involved • Linear, quadratic, nonlinear • Number of objective functions • Single-, multiobjective problem • Overall objective function • Permissible values of the design variables • Integer programming

9. Optimization of thermal processes 2007/2008 Typical optimization procedure • Define objective function • Define decision variables and estimate their impact on the result • Find the design constraints and express them in the form of equalities and inequalities • Decide which technique of optimization is best for the problem • Use the chosen method and find the result • Analyse the result

10. Optimization of thermal processes 2007/2008 Example optimization problem Suppose that two products (denoted as I and II respectively) can be manufactured at the factory with the use of three ingredients: A, B and C. The amount of the ingredients required for one unit of each of the products is as follows: The total avalaible amount of the ingredients is:

11. Decision variables - number of units of product I - number of units of product II Design vector Objective function Optimization of thermal processes 2007/2008 Example optimization problem The profit for product I is 5 zl per unit, for product II – 3 zl per unit. Find the optimum structure of production (maximize the profit).

12. Optimization of thermal processes 2007/2008 Example optimization problem Constraints

13. Optimization of thermal processes 2007/2008 Thank you for your attention