O'Reilly logo

An Introduction to Optimization, 4th Edition by Stanislaw H. Zak, Edwin K. P. Chong

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

CHAPTER 24

MULTIOBJECTIVE OPTIMIZATION

24.1 Introduction

When an optimization problem involves only one objective function, it is a single-objective optimization. Most engineering problems require the designer to optimize a number of conflicting objectives. The objectives are in conflict with each other if an improvement in one objective leads to deterioration in another. Multiobjective problems in which there is competition between objectives may have no single, unique optimal solution. Multiobjective optimization problems are also referred to as multicriteria or vector optimization problems. We can formulate a multiobjective optimization problem as follows: Find a decision variable that satisfies the given constraints and optimizes a vector function whose components are objective functions. Formally, the multiobjective optimization problem is stated as follows:

equation

where f : n and Ω ⊂ n. For example, the constraint set Ω can have the form

where

In general, we may have three different ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required