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Optimization of Thermal Processes: Techniques and Applications in Engineering

This lecture series on "Optimization of Thermal Processes" covers essential concepts of optimization, focusing on engineering applications and methods. Key topics include constrained vs. unconstrained problems, linear vs. nonlinear challenges, and classical versus modern optimization techniques such as genetic algorithms and simulated annealing. The material is designed for students and professionals aiming to enhance their understanding of how optimization is applied in design and resource allocation, particularly in thermal machinery and related fields. Various engineering examples illustrate practical applications, ensuring a comprehensive grasp of the subject.

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Optimization of Thermal Processes: Techniques and Applications in Engineering

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  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

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