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Über dieses Buch

This book is about optimization techniques and is subdivided into two parts. In the first part a wide overview on optimization theory is presented. Optimization is presented as being composed of five topics, namely: design of experiment, response surface modeling, deterministic optimization, stochastic optimization, and robust engineering design. Each chapter, after presenting the main techniques for each part, draws application oriented conclusions including didactic examples. In the second part some applications are presented to guide the reader through the process of setting up a few optimization exercises, analyzing critically the choices which are made step by step, and showing how the different topics that constitute the optimization theory can be used jointly in an optimization process. The applications which are presented are mainly in the field of thermodynamics and fluid dynamics due to the author's background.



Chapter 1. Introduction

The concept of optimization is introduced and the different topics of the optimization theory that will be treated in the rest of the book are briefly described. The layout of the book is presented in the end of the chapter. The generic optimization process is presented as a five steps path involving design of experiments, response surface modelling, deterministic optimization, stochastic optimization, and robust design analysis. Even though, strictly speaking, only the third and the fourth steps are optimization algorithms, these are often insufficient due to the large complexity of real-life optimization problems such as those that may be found in industry. This is the reason why other aspects that may help in setting up a methodology for tackling complicated problems are introduced in steps one and two. Yet, this is not sufficient as optimization algorithms can find optimum solutions for the problem at hand, but they are not able to grant us these solutions are also reliable, or robust. The role of reliability is not to be underestimated, and this is what we try to address in the fifth step.

Marco Cavazzuti

Optimization theory

Chapter 2. Design of Experiments

Design of experiments is introduced and its development from its birth within the statistics environment to its role in optimization is briefly described. Several DOE techniques are presented from a theoretical point of view after having introduced the terminology which is used in this field. These goes from more classical methods such as factorials and central composites, to latin hypercubes and pseudo-random techniques, passing through economical models for large problems (e.g. Plackett-Burman), total quality control method as presented by Taguchi, and many others. In the conclusions the techniques are discussed in view of their suitability for different types of optimization problems.

Marco Cavazzuti

Chapter 3. Response Surface Modelling

Response surface modelling is introduced and its bond to design of experiments is discussed. Several RSM techniques are presented from a theoretical point of view throughout the chapter. Among the various techniques described the typical approximation by least squares method is found, as well as the different weighted-average interpolating methods such as Kriging, Gaussian processes, radial basis functions, neural networks. In the conclusions the aspects to be kept in mind when choosing the most suitable RSM are discussed. A few examples of DOE


RSM coupling are presented and discussed for a simple test case.

Marco Cavazzuti

Chapter 4. Deterministic Optimization

Among the possible classifications of the optimization algorithms we decided to divide them into two categories: deterministic and stochastic. By deterministic optimization all the algorithms that follow a rigorous mathematical approach are intended. Strictly speaking this refers to mathematical programming. After introducing the terminology used in this field, line-search and trust region strategies are described. The chapter is further subdivided into two major sections: unconstrained and constrained optimization. In the first several optimization methods are introduced such as simplex, Newton and quasi-Newton, conjugate directions, and Levenberg–Marquardt. In the latter, due to the complexity of the topic only a brief discussion on the main aspects and approaches found in constrained optimization algorithms is given. These are elimination methods, Lagrangian methods, active set methods, 0s methods. Sequential quadratic programming and mixed integer programming are also introduced. In the conclusions, the different algorithms are discussed in terms of their simplicity, reliability, and efficiency.

Marco Cavazzuti

Chapter 5. Stochastic Optimization

As opposed to deterministic optimization, by stochastic optimization we refer to those algorithms, often population-based, in which random elements are introduced at some point. This is a completely different approach to optimization, having different characteristics and also a different aims compared to the more classical methods discussed in the previous chapter. The concepts of multi-objective optimization and Pareto optimality are introduced in the beginning, and a comparison with the deterministic optimization algorithms is performed stressing out the pros and the cons of these different approaches to optimization. Several algorithms for stochastic optimization are presented such as particle swarm optimization, game theory optimization, evolutionary and genetic algorithms. Some guidelines on how to choose the most suitable stochastic optimization algorithm depending on the problem to be addressed are given in the end.

Marco Cavazzuti

Chapter 6. Robust Design Analysis

The idea behind robust design analysis is to test the robustness of an optimum solution found by means of the optimization algorithms previously discussed. By robustness we mean the ability of a given configuration not to lose its nominal performance characteristics when small changes are applied to it. These changes may stand, for instance, for an operating condition other than the design one in a machine, or for uncertainties in a mechanical component due to manufacturing tolerances or to its deterioration with use. The concept of RDA is introduced and two different general approaches are presented, namely: multi-objective robust design optimization, and reliability analysis. Specific reliability analysis algorithms are presented such as Monte Carlo, FORM, SORM, importance sampling. The differences between the two general approaches are stressed in the conclusions.

Marco Cavazzuti



Chapter 7. General Guidelines: How to Proceed in an Optimization Exercise

In this chapter a summary of the features of all the techniques discussed up to this point is given. The aim is to draw general guidelines on the choice of the most suitable techniques for a given optimization process. It is stressed out that an optimization process should not be a one-shot application of a certain algorithm. It must generally be composed of different steps, if not all, of the optimization theory used jointly. This is due to the fact that each topic in optimization theory has its own scope that should be exploited knowledgeably.

Marco Cavazzuti

Chapter 8. A Forced Convection Application: Surface Optimization for Enhanced Heat Transfer

In the last chapters of the book a few application examples of optimization algorithms are given in the light of the discussion made in the previous chapter. The examples proposed are dealing with thermodynamics and fluid-dynamics problems due to the author background. It must be reminded, however, that optimization is an inherently interdisciplinary and multidisciplinary topic and the discussion which is made in these chapters is still valid for any other kind of applications. In this chapter a forced convection optimization exercise is presented. The exercise is about heat exchangers surface optimization for enhanced heat transfer. After the problem is presented, the set-up of the optimization process is discussed and the choices made critically analysed from the methodology point of view. A five-steps approach to optimization involving a two-stages stochastic optimization, one deterministic optimization and two RDAs are presented. The analyses are carried out by means of computational fluid dynamics simulations and the results of the process are presented and discussed focusing on the optimization aspects.

Marco Cavazzuti

Chapter 9. A Natural Convection Application: Optimization of Rib Roughened Chimneys

In this chapter a natural convection optimization exercise is presented. The exercise is about heat and mass transfer enhancement in rib roughened chimneys. Following the same scheme of the previous chapter the problem is presented and the set-up of the optimization process discussed focusing on the methodology aspects. A rather large seven-steps approach to optimization is proposed mainly for educational purpose. The optimization process includes: two different full factorial DOEs, one sensitivity analysis on the main parameters characterizing the problem, two RSMs based on the DOE data (namely, Sobol and Gaussian processes), one stochastic optimization using multi-objective genetic algorithm, and one deterministic optimization by means of Nelder and Mead simplex method. The analyses are carried out by means of computational fluid dynamics simulations and the results of the process are presented and discussed from the optimization point of view.

Marco Cavazzuti

Chapter 10. An Analytical Application: Optimization of a Stirling Engine Based on the Schmidt Analysis and on the Adiabatic Analysis

Stirling engines are external combustion engines converting thermal energy into mechanical energy by alternately compressing and expanding a fixed quantity of air or other gas (called the working or operating fluid) at different temperatures. Stirling engines were invented by Robert and James Stirling in 1818. Despite their high efficiency and quiet operation they have not imposed themselves over the Diesel and Otto engines. In recent years interest in Stirling engines has grown, since they are good candidates to become the core component of micro Combined Heat and Power (CHP) units. In this chapter, we discuss an optimization experiment performed on Stirling engines. In particular, optimization algorithms are applied to the Schmidt and to the adiabatic analyses. These are two simple and rather idealized analytical models of the Stirling machine. Before discussing the optimization issue we briefly recall the basic elements of the Stirling cycle, and the Schmidt and the adiabatic analyses.

Marco Cavazzuti

Chapter 11. Conclusions

On the basis of what has been developed both in the theoretical and in the applicative parts of the book, this final chapter tries to draw some conclusions on the characteristics of all the techniques discussed. Thus, the different topics in optimization theory are recalled and their scope summarized. Some considerations on how to choose the proper optimization set-up depending on the type and the complexity of the optimization problem at hand are discussed. The leitmotiv of this chapter is the question posed at its beginning “what would be the best thing do to?” when tackling an optimization problem. Aware that there is no final and unique answer to this question, we believe that some theoretical knowledge in the field of optimization and some ideas on how it can be put into practice should form a good basis to start from when making your own decisions. That’s what the book intended to do and hopefully managed to. Now it’s time for the reader to move his steps forward and ideally broaden the second part of this book with his own applications!

Marco Cavazzuti


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