Senior Design Spring 2012: Optimization for Engineering Design by Kalyanmoy Deb

Summary of Preface and Introduction

It is always hard for engineers and researchers to under the importance of the roles played by optimization in engineering design.
After the introduction of computer, optimization has become key in minimizing the cost of production and maximizing the efficiency of production.
Two distinct type of optimization algorithms:

Deterministic optimization algorithms - specific rules for moving from one solution to the next.
Stochastic in nature with probabilistic transition rules, these algorithms are new and popular due properties that the deterministic algorithm does not have.
Designer must know the differences between the two and be able to choose te one that is needed for the problem he/she is facing.

Formulation of the design problem in a mathematical format in an important part of the optimal design.
Four different design problems are introduced in chapter 1.
It is simpler to explain single variable design process first, which is then done in chapter 2.
Chapter 3 present a number of algorithms that are used for optimizing multivariable functions that have unconstrained function.
Chapter 4 discusses how to solved constrained optimization problems.
Chapter 5 deal with two geometric programming problems.
Chapter 6 discusses two nontraditional optimization algorithms and the issue f finding the global optimal solutions.
Algorithms in chapter 4 use linar programming methods.
Each algorithm is presented in a step by step format so that way it can easily understood and coded in a computer language.
Each chapter contains at least one working code, that can be implemented to become an optimization algorithm presented in the chapter.
The primary objective is to introduce different algorithms to students and design engineers, and provide them with a easy understanding using computer code which are easy to understand.

Introduction

Optimizing algorithms are becoming more popular day by day in the engineering design.

Aerospace engineers worry about the components added to the overall weight of the aircraft.
Mechanical engineers design their components to achieve their goals of maximizing the life of the components or lowering the manufacturing costs.
Chemical engineers are interested in achieving the max rate of production.
Production engineers are interested to make sure the idle time of a machine is minimal, so they create a schedule that is constantly using the machines to create a higher rate of production.
Civil engineers design buildings, damns, or other structures to achieve the goal of safety or minimal cost overall.
Electrical engineers design way of communicating to achieve minimum time of communication from one node to another.

The above tasks involves some type of minimization or maximization of an objective.
As a designer performs these tasks, he/she will learn by practice. However, some designer should know some aspects of the formulation procedure, which can then help them choose a proper optimization algorithm.
1.1 Optimal Problem Formulation

Using knowledge that we already know, a naive optimal design is achieved by comparing up to ten alternative design solutions.
Naive method is followed because of certain limitations, also some designers are unaware of the existing optimization algorithms.
Since optimization algorithms look at several different number of design solutions, it is often time consuming and hard to compute.
Variable vary from time to time, and each design has different number of parameters.
Purpose is to create a mathematical model of the optimal design problem.
Steps involved in an optimal design formulation process.

Formulation of problem begins with finding the underlying design variables.
One parameter may be important with respect to minimizing the overal cost of the design and insignificant when maximizing the life of the component.
First thumb rule is to choose as few design variables as you can.

Now find the constraints of the problem.
In many problems, the constraints are formulated to satisfy stress and deflection limitations.
An algorithm or a mechanism is necessary to calculate the constraint.
Two types of constraints:

"Inequality type states the the functional relationship among design variables are either greater than, smaller than, or equal to, a resource value" (Deb, 5).
Equality type are more difficult to handle and are then avoided whenever designers possibly can.

Most constraints are inequality type.
Some constraints may be greater-than-equal to type.
Second thumb rule is that the number of complex equality constraints should be low.

Find the objective function using the design variables and other problem parameters.
There are problems that do not have mathematical forms of their objectives.

The designer choose the most important objective as the objective function of the optimization problem.
The objective function is not required to be expressed in a mathematical form.

Duality principle helps be allowing the same algorithm to be used for either or min or max with additional minor changes.

Final task is to set the min and max bounds of each design variable.
Optimal solutions lies between the two bounds.
After the four tasks have been completed, the optimization problem ca be written mathematically into a special format: (NLP) non-linear programming

Senior Design Spring 2012