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# Multiobjective Optimization

Pareto sets via genetic or pattern search algorithms, with or without constraints

When you have several objective functions that you want to optimize simultaneously, these solvers find the optimal tradeoffs between the competing objective functions.

## Functions

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 `gamultiobj` Find Pareto front of multiple fitness functions using genetic algorithm `paretosearch` Find points in Pareto set
 `optimoptions` Create optimization options `resetoptions` Reset options

## Topics

### Create Pareto Front

Pareto Front for Two Objectives

Shows an example of how to create a Pareto front and visualize it.

Design Optimization of a Welded Beam

Shows tradeoffs between cost and strength of a welded beam.

Compare paretosearch and gamultiobj

Solve the same problem using `paretosearch` and `gamultiobj` to see the characteristics of each solver.

Performing a Multiobjective Optimization Using the Genetic Algorithm

Solve a simple multiobjective problem using plot functions and vectorization.

Multiobjective Genetic Algorithm Options

Shows the effects of some options on the `gamultiobj` solution process.

Plot 3-D Pareto Front

Plot a Pareto set in three dimensions.

### Multiobjective Background

What Is Multiobjective Optimization?

Describes Pareto-optimal sets.

gamultiobj Algorithm

How the `gamultiobj` algorithm works.

paretosearch Algorithm

Describes the `paretosearch` algorithm.

gamultiobj Options and Syntax: Differences from ga

Describes differences between the options for `ga` and `gamultiobj`.

Genetic Algorithm Options

Describes the options for the genetic algorithm.

Pattern Search Options

Describes the options for pattern search.

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