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Multi-Objective Genetic Algorithm (MOGA)

Multi-Objective Genetic Algorithm (MOGA)

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Multi-Objective Genetic Algorithm (MOGA)

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Multi-Objective Genetic Algorithm (MOGA) is an extension of Genetic Algorithm that solves multi-objective optimization (MOO) problems. In MOO problems, there is more than one objective function to be minimized or maximized and as such the goal is not to find an optimum but to find the Pareto front instead. Pareto front is a collection of non-dominated designs. Non-dominated designs are better than other designs because at least one of the objective functions are considered.

 

Usability Characteristics

In MOO methods, the challenge is to find a homege MOGA that uses a crowding distance evaluation to help create a good distribution of the points on the Pareto front.
MOGA terminates if one of the conditions below are met:
-The convergence criteria is satisfied. This occurs when the minimum number of allowable iterations (MINDES) are run, feasible designs are found (GMAX), and the non-dominated designs did not change in the last iteration.
-The maximum number of allowable iterations (MAXDES) is reached.
-An analysis fails and the “Terminate Optimization” option is the default (IGFAIL).

 

The flowchart below illustrates the different phases of the MOGA process.

MOGA_flowchart

 

Settings

In the Specifications step, you can change the settings of MOGA from the following tabs:

hmtoggle_arrow1Settings

In the Settings tab, you can access the settings listed below. Please note that for most applications the default settings work optimally, and you may only need to change the Maximum Iterations and On Failed Analysis.

Setting

Default

Range

Description

Maximum Iterations

(MAXDES)

50

> 0

Maximum number of iterations allowed.

Minimum Iterations

(MINDES)

25

> 0,

<= MAXDES

MOGA process at least MINDES iteration steps.

This can be used to prevent premature convergence.

To let MOGA perform determined number of iteration steps, you can set MINDES to be equal to MAXDES.

MOGA will be terminated if it has iterated the minimum iteration steps and feasible designs are found and the non-dominated designs did not change in the last iteration.

Population size

(GAPOPS)

0

Integer > 1

If GAPOPS is 0, then population size is calculated according to the following function, where bign is the number of input variables.

moga1

If GAPOPS is greater than 0, then population size uses the user defined value.

If the allowable computational effort is limited, please set your own value.  In general, it is better to allow MOGA process at least 25 iteration steps.

Constraint violation tol.

GMAX)

1.0

> 0.0

Global maximum allowable percentage constraint violation.  Constraints must not be violated by more than this value in the converged design.

On failed analysis

(IGFAIL)

0

0 or 1

0

MOGA terminates with an error message when an analysis run fails (default).

1

MOGA ignores the failed analysis run.

 

hmtoggle_arrow1More

In the More tab, you can access the setting listed below. Please note that for most applications, the default settings work optimally.

Setting

Default

Range

Description

ND Points

(MAXNDP)

500

>0

The maximum number of non-dominated points which will be shown in the result file.  If MAXNDP is less than the population size, then it will be reset to the number of population size.

Crowding Distance

(CRODIS)

0

0, 1, 2

Determines in which space the crowding distance is evaluated.  Default value is 0 which means the crowding distance is evaluated in design space.  1 means the crowding distance is evaluated in solution space.  2 means the crowding distance is evaluated in both of the two spaces.

The crowding distance evaluation strategy allows users to get solutions more uniformly distributed in the selected space.

Discrete states

(GADISC)

1024

Integer > 1

Number of discrete values uniformly covering the range of continuous variables including upper and lower bound.  Recommendation: select as a power of 2, e.g. 64 = 2^6, 1024 =2^10, etc.

A larger value allows for higher solution precision, but more computational effort is needed to find the optima.

Mutation rate

(GAMUTR)

0.01

0.0 – 1.0

Mutation rate (probability).

Larger value introduces more random effect.  As a result, GA can explore more globally.  But the convergence could be slower.

Recommended range: 0.001 - 0.05.

Elite population %

(GAELIT)

10

1.0 – 50.0

Percentage of population that belongs to elite.

The one with high fitness value is directly passed to the next generation.  This is a very important strategy in GA to ensure the quality of solutions be non-decreasing.  A larger value means that more individuals will be directly passed to the next generation.  So a new gene has less of a chance to be introduced.  The convergence speed could be increased.  The drawback is that, too large a value could cause premature convergence.

Recommended range: 1.0 – 20.0.

Random Seed

(GAREPT)

0

Integer

0 to 10000

Controlling repeatability of runs depending on the way the sequence of random numbers is generated.

0

Random (non-repeatable).

> 0

Triggers a new sequence of pseudo-random numbers, repeatable if the same number is specified.

Number of contenders

(GATOUR)

2

Integer

2 to 5

Number of contenders in a tournament selection.

With a larger value, individuals with a lower fitness value have less of a chance of being selected.  Thus, the good individuals have more chance to produce offspring.  The bad effect is that diversity of the population is reduced.  MOGA could converge prematurely.

Penalty power

(GAPPOW)

1

> 0.0,

< 10.0

Penalty power in the formulation of the fitness function as exterior penalty function.

Recommended range: 1.0 – 2.0.

Penalty multiplier

(GAPMUL)

2.0

> 0.0

Initial penalty multiplier in the formulation of the fitness function as exterior penalty function.  Penalty multiplier will be increased gradually with iterating steps going on.

In general, a larger value allows the solution to become feasible with less iteration steps; but too large value could result in a worse solution.

Recommended range: 1.0 – 5.0.

Distribution Index

(GAINDX)

5

Integer

1 to 100

Distribution index used by real coded MOGA.

This parameter is to control offspring individuals to be close to or far away from the parent individuals.  Increasing the value will result in offspring individuals being closer to the parents.

Recommended range: 3 – 10.

Type

(GATYPE)

0

0 or 1

0  Real coded MOGA is used.

1  Binary coded MOGA is used.

In general, real coded MOGA performs better than binary coded MOGA.  For discrete optimization problem, binary coded MOGA could be better.

Hybrid Algorithm

No hybrid

No hybrid, Meta-model based method

No hybrid

Meta-model based method

Constraint threshold

(EPSCON)

1.0e-4

> 0.0

This parameter is used for constraint value calculation. In general, constraint value is normalized to its bound value. One exception is that, constraint value is not normalized if its absolute bound value is less than this parameter. Recommended range is 1.0e-6 ~ 1.0.

Use Inclusion Matrix

(INCLUSI)

No

No, With Initial

No ignores the Inclusion matrix
With Initial combines Inclusion matrix with the initial population sample.