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      Preface

      This book is about the use of metaheuristic algorithms on two different but closely related subjects, namely structural design and structural analysis. Indeed, these subjects are different, but every engineer knows that structural design involves structural analysis, most of the time applied many times in order to finish the design.

      Applications of metaheuristic algorithms on design problems began as early as the first appearance of these algorithms, in the second half of the 20th century. In these works, analysis of parts were being performed by using the well-known finite element method (FEM) or some other techniques. In the literature, we can find an important accumulation of such applications, predominantly in scientific media. Despite the abundance of these works, engineers are still far from using them extensively in practice. The studies are still at the academic level except for certain problems, like some structural parts or components and some simple trusses.

      The existence of FEM enabled engineers to easily and accurately analyze the behavior of common structures in a very large domain. But for some uncommon problems involving nonlinearities and discontinuities, the elegant FEM ceases to be sufficient and efficient. The use of energy principles combined with basic concepts of FEM – recently referred to as the Finite Element Method with Energy Minimization (FEMEM) – is shown to be able to solve these special problems with the help of metaheuristic algorithms. The studies in this field are also still at a primitive level, and far from being available in practice.

Thus, it can be said that applications of metaheuristic algorithms are not sufficiently developed for engineers, either in design or in analysis. But in both fields, the trend is for great advances to be made continuously, in every corner of the world, so that the subject is a highly dynamic one, and the goal to be attained is still way ahead.

      Writing a book on a subject that is ever advancing in many aspects is generally rather difficult to do. Such an undertaking requires a certain kind of encouragement; for this book, that encouragement was provided by Patrick Siarry from Paris-Est Créteil University, France. The authors also thank those at Wiley-ISTE who were very helpful during each step of the preparation of the book. Special thanks go to Emeritus Professor Fuat Erbatur from Middle East Technical University, Ankara, Turkey, for introducing these algorithms to the authors back in 2000.

      We hope that readers find this book to be a thorough evaluation of the state of the art for applications of metaheuristic algorithms in structural design and analysis.

      Yusuf Cengiz TOKLU

      Beykent University

      Istanbul, Turkey

      Gebrail BEKDAŞ

      Istanbul University-Cerrahpaşa

      Turkey

      Sinan Melih NIGDELI

      Istanbul University-Cerrahpaşa

      Turkey

      March 2021

      Introduction

      I.1. Generalities

      Everything in our universe is related to some kind of optimization, minimization in losses and expenditures and maximization in gains. This is true for everything, from a stone or flowing water looking for the minimum potential energy position to living organisms trying to find the best solution when they come across a problem. As we all know from the laws of life, evolution is always towards the best fit, the word “best” pointing again to an optimization process.

      In human life also, whether performed using their own intelligence or by artificial intelligence developed by them, optimization is everywhere: from engineering design to construction planning, from personal economics to world economics, from transportation to water supply, from space research to deep-sea analysis, from self-care activities to organization of hospitals, from art activities to educational systems.

      Optimization is sometimes influenced by limited financial, physical and timely resources, sometimes influenced by certain intangible motivations like aesthetics and desire, and, most of the time, by a multitude of reasons. In real life, optimization concerning one single objective is very rare compared to multi-objective optimization. While performing optimization, we are usually bound by certain restrictions which are the constraints of the problem: the number of machines to be used in a production process, the magnitude of gravitational force that a pilot can withstand, or the strength limit of a given material. Thus, a general optimization problem can be formulated as

      [I.1]

      [I.2]

      where F(x) is a set of functions to be minimized called objective functions, g(x) is a set of equality constraints, h(x) is a set of inequality constraints and x is the set of unknowns over which all functions and constraints are defined. Optimization here is shown as minimization without losing generality, since a maximization function can be turned

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