Multi  Objective Genetic Algorithm (MOGA)
An extension of Genetic Algorithm that solves multiobjective 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 nondominated designs. Nondominated designs are better than other designs because at least one of the objective functions are considered.
Usability Characteristics
 Multi  Objective Genetic Algorithm uses a crowding distance metric to create a homogeneous distribution of the nondominated points on the Pareto front.
 Multi  Objective Genetic Algorithm terminates if one of the conditions below are
met:
 The convergence criteria is satisfied. This occurs when the minimum number of allowable iterations (Minimum Iterations) are run, feasible designs are found (Constraint Violation Tol. (%)), and the nondominated designs did not change in the last iteration.
 The maximum number of allowable iterations (Maximum Iterations) is reached.
 An analysis fails and the Terminate optimization option is the default (On Failed Evaluation).
 Supports input variable constraints.
 Although the number of evaluations per iteration is a combination of multiple settings, it is primarily affected by the Population Size setting. All evaluations within an iteration may be executed in parallel. If parallel computing is required, it is recommended to use the MetaModel or No Hybrid method.
Settings
Parameter  Default  Range  Description 

Maximum Iterations  50  >0  Maximum number of iterations allowed. 
Minimum Iterations  25 

Processes at least Minimum Iterations iteration steps. Use this setting to prevent premature convergence. By setting Minimum Iterations to be the same as Maximum Iterations, the defined number of iteration steps will be run. Multi  Objective Genetic Algorithm will be terminated if it has iterated the minimum iteration steps and feasible designs are found and the nondominated designs did not change in the last iteration. 
Population Size  0  Integer > 1 
If Population Size is 0, then
population size is calculated according to the following equation, where
N is the number of input variables.
$$Population\text{}Size=\left[3+37{e}^{{\left(\frac{N1}{5.806}\right)}^{0.5}}\right]N$$
If the allowable
computational effort is limited, set your own value.
Tip: In
general, it is better to process at least 25 iteration
steps.

On Failed Evaluation  Ignore failed evaluations 


Parameter  Default  Range  Description 

Crowding Distance  Design Space 

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

Discrete States  1024  Integer > 1 
Number of discrete values
uniformly covering the range of continuous variables including upper and
lower bound.
Tip: Select as a power of 2, for example 64 =
2^6, 1024 =2^10, and so on.
A larger value allows for higher
solution precision, but more computational effort is needed to find the
optima. 
Mutation Rate  0.01  0.0  1.0 
Mutation rate (probability).
Larger values introduce a more random effect. As a result, the algorithm
can explore more globally but the convergence could be slower.
Tip: Recommended range: 0.001 – 0.05

Elite Population (%)  10  1.0  50.0 
Percentage of population
that belongs to elite. The one with highest fitness value is directly
passed to the next generation. This is a very important strategy, as it
ensures the quality of solutions be nondecreasing. A larger value means
that more individuals will be directly passed to the next generation,
therefore new gene has less chance to be introduced. The convergence
speed could be increased. The drawback is that too large of values could
cause premature convergence.
Tip: Recommended range: 1.0 –
20.0.

Random Seed  0  Integer 0 to 10000 
Controlling repeatability of
runs depending on the way the sequence of random numbers is
generated.

Number of Contenders  2  Integer 2 to 5 
Number of contenders in a tournament selection. For larger values, individuals with lower fitness value have less chance to be selected. Thus, the good individuals have more chance to produce offspring. The bad effect is that, diversity of the population is reduced. The algorithm could converge prematurely. 
Penalty Power  1 

Penalty power in the
formulation of the fitness function as exterior penalty function.
Tip: Recommended range: 1.0 – 2.0.

Penalty Multiplier  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, larger values allow the solution to become
feasible with less iteration steps; but too large of a value could
result in a worse solution.
Tip: Recommended range: 1.0 –
5.0.

Distribution Index  5  Integer 1 to 100 
Distribution index used by real coded Multi  Objective Genetic Algorithm. Controls 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.
Tip: Recommended range: 3.0 –
10.0.

Type  Real  Real or Binary 

Max Failed Evaluations  20,000  >=0  When On Failed Evaluations is set to Ignore failed evaluations (1), the optimizer will tolerate failures until this threshold for Max Failed Evaluations. This option is intended to allow the optimizer to stop after an excessive amount of failures. 
Hybrid Algorithm  No hybrid 


Use Inclusion Matrix  With Initial 

