1. Optimization of thermal processes2007/2008 Optimization of thermal processes Maciej Marek Czestochowa University of Technology Institute of Thermal Machinery Lecture 1

2. Optimization of thermal processes2007/2008 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 processes2007/2008 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 of thermal processes2007/2008 What is optimization? Optimization is the process of finding the best result under given circumstances. Optimization techniqueObjective functionConstraints

5. Optimization of thermal processes2007/2008 Optimization problem Objective function (criterion or merit function) Constraints (restrictions) x Minimum ofMaximum of

6. Optimization of thermal processes2007/2008 Formal statement of an (constrained) optimization problem Find which minimizes subject to the constraints Design vector Inequality constraint Equality constraint Decision (design) variables

7. Optimization of thermal processes2007/2008 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 processes2007/2008 Classification of optimization problems based 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 processes2007/2008 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 Typical optimization procedure

10. Optimization of thermal processes2007/2008 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: III A45 B52 C38 ABC 10 12

11. Optimization of thermal processes2007/2008 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). Decision variables - number of units of product I - number of units of product II Design vectorObjective function

12. Optimization of thermal processes2007/2008 Example optimization problem Constraints

13. Optimization of thermal processes2007/2008 Thank you for your attention