Soft Computing Techniques for Engineering Optimization

Kaushik Kumar, Supriyo Roy, J. Paulo Davim

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9780429620744
• Topic: Mathematics
• Subtopic: Arithmetic
• Index: Mathematics

This book covers the issues related to optimization of engineering and management problems using soft computing techniques with an industrial outlook. It covers a broad area related to real life complex decision making problems using a heuristics approach. It also explores a wide perspective and future directions in industrial engineering research on a global platform/scenario. The book highlights the concept of optimization, presents various soft computing techniques, offers sample problems, and discusses related software programs complete with illustrations.

Features

• Explains the concept of optimization and relevance to soft computing techniques towards optimal solution in engineering and management
• Presents various soft computing techniques
• Offers problems and their optimization using various soft computing techniques
• Discusses related software programs, with illustrations
• Provides a step-by-step tutorial on how to handle relevant software for obtaining the optimal solution to various engineering problems

Section I

Introduction to Soft Computing Techniques

1

Introduction to Optimization and Relevance of Soft Computing towards Optimal Solution

1.1 Optimization

Optimization is a systematic procedure of ‘making anything better’. It is fundamentally a ‘procedure of changing inputs’ to accomplish ‘either the least or the most extreme yield’ for any recognized issue. The idea of optimization is fundamentally what we do in our day-to-day lives: a want to improve the situation or be best in some fields. In engineering, the basic concepts of optimization may be defined as follows: any process or methodology towards any design, system or even decision that may be fully/partially perfect, functional or effective as possible; specifically, in line of mathematical modelling or procedures involved in it.

In any implicational field, we wish to deliver the most ideal outcome with accessible assets. In a profoundly focused business world, it is not any more adequate to outline a framework whose execution of required errand is simply tasteful. The basic idea is to configure the best framework in a best optimal manner. Accordingly, by ‘designing’ new items in fields such as aviation, car, electrical, biomedical and horticultural, we endeavour to utilize design tools that give wanted outcomes in a convenient and prudent way.

Related to the field of engineering applications, optimization is considered as an extremely broad robotized design procedure. Using this strategy, it is critical to recognize analysis and design the same. Analysis is a procedure for deciding the response of determined framework to a certain mix of information parameters. Design, on the other hand, implies a procedure for characterizing any framework.

We move on to the world of modelling in its most basic terms. Optimization is a choice discipline of mathematical modelling that generally concerns to find the extreme (maxima and minima) of numbers, functions or systems. Great ancient philosophers and mathematicians created its foundations by defining the choice of optimum (as an extreme, maximum or minimum) over several fundamental domains such as numbers, geometrical shapes, optics, physics and astronomy.

In a research view of observation, optimization is defined by different researchers in different ways at different times. A conventional view of optimization may be presented as follows:

Individuals’ want for flawlessness discovers articulation in principle of Optimization. It examines how to depict and accomplish what is Best, once one knows how to quantify and change what is great or terrible… hypothesis of Optimization incorporates quantitative investigation of optima and methods for discovering them.

In nature, the method of optimization moves from the concept of ‘free of constraints’ (unconstrained) to ‘constraints’ (constrained) one. If the design of any system is at a stage where no constraints are active, then the process of determining search direction and travel distance for minimizing the objective function that involves an unconstrained minimization algorithm. Of course, in such a case, one has to constantly watch for constraint violations during the move towards design space. All unconstrained optimization methods are of ‘iterative nature’, which begin from an ‘initial trial solution’ and moves to an optimum point in a sequential process. All these methods require an initial point X₁ to start and differ from one another: only methods generating point X_i+1 (from X_i) and testing point X_i+1 for optimality. Any constrained optimization problem can be cast as an unconstrained minimization problem even if constraints are active.

1.2 Single-Objective Mathematical Programming

The Problem of Optimization (either maximizing or minimizing) of an algebraic or transcendental function of one or more variables subject to some specific constraints is called mathematical programming problem or constraint optimization problem or precisely a single-objective mathematical programming problem (SOMPP), which may be stated mathematically as follows:

Determine the values of variable x=(x1,x2,…,xn) that optimize function (called objective function or criterion function)

Optimizef(x)(1.1)

Subject to constraints:

gi(x)≤0∀i=1,2,…,mhj(x)=0∀j=1,2,…,lx≥0(1.2)

where f(x),g1(x),…,gm(x),h1(x),…,hl(x) are functions designated on an n-dimensional set and x is defined as a vector of n components x1,x2,…,xn. For both, objective function and constraints are linear, and SOMPP evolves into single-objective linear programming problem (SOLPP).

In illustrating SOLPP, let us consider a minimization problem. This implies no loss of generality since, if the objective is to maximize F(x), this can be converted to an equivalent minimization problem by taking f(x)=−F(x) Similarly, gi(x)≥0 type constraints can be easily converted into Gi(x)≤0 type (Gi(x)=−gi(x)).

An ideal SOLPP is therefore represented as follows:

Minimizeg0(x)(1.3)

Subject to constraints:

gk(x)≤ai;∀k=1,2,…,mhj(x)=bj;∀j=1,2,…,lxi≥0;∀i=1,2,…,n(1.4)

where x=(x1,x2,…,xn)T is a vector of decision variables.

Any vector x fulfilling every constraint of equation (1.4) is said to be a feasible solution to the problem. Accumulation of ev...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Authors
• Section I Introduction to Soft Computing Techniques
• Section II Various Case Studies Comprising Industrial Problems and Their Optimal Solutions Using Different Techniques
• Section III Hands-On Training on Various Software Dedicated for the Usage of Techniques
• References
• Index