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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 into a minimization function by just a simple multiplication with -1. The same is true between “smaller than” and “greater than” conditions.

There have been very elegant techniques using classical tools of mathematics for solving this optimization problem, in cases where functions in F(x) are well defined and differentiable. Unfortunately, all of these methods are valid only in their range of applicability, as in linear programming, nonlinear programming, integer programming, gradient methods, etc. (Nocedal and Wright 2006; Fletcher 2013). In real life, most of the objective functions are such that they cannot be written down as a mathematical function, let alone a differentiable one. On the other hand, the unknowns may be any type of quantity, floating or integer numbers, names, directional expressions, the order of some activities, etc. Therefore, we can surely conclude that mathematical optimization methods cannot handle these problems, which form the great majority of problems encountered in real life.

Metaheuristic methods, fortunately, are capable of handling all of these problems. Properly designed, they can help in making decisions on the best topology of a structural element, an economic activity with maximum income, the best hourly schedule in a school, the best route to follow between two points, etc. The term “metaheuristic” was first coined for the tabu search method, viewing it as “a metaheuristic superimposed on another heuristic” (Glover 1986). Humans started to use these techniques consciously in the 20th century, although nature was probably using them from the very beginning. For instance, evolutionary theory shows that living organisms of today started from single-celled beings, following the optimization rule of best fit, under an unimaginable number and variety of constraints. A genetic algorithm, a popular metaheuristic algorithm, is just an imitation of this process. Currently, there are hundreds of metaheuristic algorithms, as well as hybrid ones, that are applied to a wide variety of optimization problems in science, engineering, economics, arts, etc.

Metaheuristic algorithms are also considered to be one of the most useful tools of artificial intelligence, taking into account that self-learning and rule-of-thumb decisions are their two basic properties.

This book is intended to give a review of metaheuristic algorithms and their applications in a very specific field: structural design and analysis. It is to be noted that this is the first book to deal with the application of metaheuristic algorithms to structural analysis.

I.2. Structure of the book

This book is organized in the following manner.

Chapter 1 gives a short history of structural analysis and design, from the times when these activities were performed using intuition and experience, without making any calculations, to times when tools used in artificial intelligence became frequent applications. This chapter emphasizes that the finite element method (FEM) plays a special role, whilst also noting that every step in this long voyage had a certain importance.

Chapter 2 gives an overview of metaheuristic algorithms (MAs). These algorithms started to be consciously used in the second half of the 20th century, enabling optimization problems to be solved that were untouchable before that time. In the beginning, there were only a handful of MAs, now the number certainly runs into the hundreds. In this chapter, some general properties of all of these algorithms are discussed, and about ten are investigated in detail.

Metaheuristic algorithms are successfully applied to structural problems. A general overview of these applications is given in Chapter 3, with emphasis on various aspects of the aims of optimization, i.e. the objectives. Examples are given in terms of weight, cost, effectiveness optimization, minimization of CO₂ emissions and dealing with limitations of stresses, deformations, stability, fatigue and national and international specifications.

The following four chapters are dedicated to design optimization. Generalities about applications of metaheuristic algorithms on structural design are discussed in Chapter 4. Chapter 5 deals with trusses and truss-like structures, Chapter 6 focuses on optimization of structural elements, and optimization of structural control members is the subject of Chapter 7. In all three of these chapters, after providing basic information about the subject, relevant numerical examples are given. Thus, in this part, the reader can find solutions for the optimization of an I-beam, a tubular column, a cantilever beam, trusses with elements – in which the number changes between 5 and 200 – reinforced concrete members, frames, walls and tuned mass dampers.

As stated in Chapter 3, optimization procedures can be useful not only in structural design but also in structural analysis. This subject is addressed in Chapter 8. The idea of these applications is the direct use of the minimum potential energy principle of mechanics in determining the equilibrium position of a structure. It is explained in the chapter that a method, named Total Potential Optimization using Metaheuristic Algorithms (TPO/MAs), was launched for this purpose, which can also be looked upon as Finite Element Method with Energy Minimization (FEMEM). In the chapter, the fundamentals of the method are given, together with applications on trusses, truss-like structures and plates.

Applications of metaheuristic algorithms on the design and analysis of structures are a relatively new subject with advances made every year and in every corner of the globe. In the concluding chapter, future expectations on this subject are discussed. It is stated that the tools used nowadays are basic tools of Artificial Intelligence (AI) and that with the amalgamation of design and analysis – along with other aspects of construction like management, planning, financing, controlling and site work – a huge problem lies ahead, requiring much more elaborate tools in order to be solved. When one considers that these operations will not only be carried out in familiar environments, but also perhaps in remote areas with harsh conditions, the difficulty of the task awaiting humanity can somehow be envisaged.