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This option use a proprietary version of the Fast Multi Objective Genetic Algorithm (FMOGA). FMOGA-II is an evolution of the traditional global search MOGA-II algorithm which uses internal adaptive Response Surfaces to speed up the search path. The Kriging response surface is used to evaluate a user specified percentage of individuals, reducing the overall number of real designs.
The algorithm will start evaluating the designs loaded in the initial Design of Experiment table and will proceed, by generations, evaluating a percentage of designs using the internal trained response surfaces and the remaining using the external user defined solver.
The system will always check if one real design evaluation has been already performed and will eventually skip the computation.
Several other parameters are internally settled in order to provide robustness and efficiency to the optimizer.
The user must specify:
Number of Generations: this value defines the maximum size of the run.
Probability of Directional Cross-Over: this is a proprietary operator that gives efficiency to the algorithm but decreases its robustness:
If this parameter is set to 1, only this operator is used. The search is efficient but in case of highly non linear problems the optimizer might stop at locally optimal solutions.
Nor 0 or 1 are recommended values. The default is set to 0.5.
The Probability of Directional Cross-Over should be increased in case of relatively smooth problems and decreased in other cases.
The default is recommended as a first trial if the problem is not known well.
The probability of the Classical Cross-Over is automatically set to:
Probability of Classical Cross-Over = 1 - (Probability of Directional Cross-Over + Probability of Selection + Probability of Mutation)
If the probability of the classical cross-over is high, the algorithm will jump more easily into different region of the design space but it will also be slower in convergence.
Probability of Selection: this value gives the probability that design configurations are not changed during the evolution.
This parameter should be kept small.
If the value is 1. no calculation will be performed apart the initial population.
The default value is 0.05 and should not be increased to values higher than 0.2.
Note:
If the Probability of Directional Cross-Over plus the Probability of Selection exceeds the value of 1.0 the following rule is applied:
Probability of Selection = 1 - (Probability of Directional Cross-Over)
Probability of Mutation: this value gives the probability that a design configuration is randomly changed:
If the value is 1, the algorithm becomes a pure random search.
The mutation probability should be kept at low values, usually smaller than 0.2.
A relatively high mutation rate (0.1) is the default value as in small population cases (typical of design optimization application) variability in the search process is recommended.
Note:
If the Probability of Directional Cross-Over plus the Probability of Selection plus the Probability of Mutation exceeds the value of 1.0 the following rule is applied:
Probability of Mutation = 1 - (Probability of Directional Cross-Over + Probability of Selection)
K-nearest designs: is the number of neighbor points that are going to be considered by the Kriging interpolation algorithm. The maximum number of neighbors is 30.
Semivariance Exponent: the exponent of the Kriging algorithm semivariance.
Probability of Virtual Design (PV): is the probability of a design being evaluated on the FMOGA internal response surfaces. The probability applies to the generations (e.g. PV=0.4 means that the 40% of the individuals in a given generation are going to be evaluated using the response surfaces).
PV Evolution Algorithm: The user can choose between Constant, Linear Annealing and Adaptive.
Constant works on a set of the Probability of Virtual Design (PV) is kept constant during the generational evolution, the overall percentage of virtual design is going to be equal to PV.
Linear Annealing the following linear annealing function is applied to the initial Probability of Virtual Design PV parameter:
PVi = PV*(1-Gi/NG)where PVi is the probability of virtual design at the i-th generation Gi and NG is the global number of generations. The overall percentage of virtual design is going to be equal to PV/2.
Adaptive the choice of the genetic algorithm operators is done dynamically during the search. The Probability of Directional Cross-Over and the Probability of Mutation are taken as initial conditions. During the search the adaptive algorithm changes their ratio according to the evaluation results. The adaptive evolution can be used when there is no clear idea about the probabilities of operators.
DNA String Mutation Ratio: this value gives the percentage of the individual DNA that is perturbed by the mutation operator. Each individual DNA is coded in a binary string, the mutation ratio defines the number of bits that mutate. If the mutation ratio is 0.0 none of the DNA bit are modified. A value of 1.0 will change all the DNA bits.
Example: DNA length = 10 DNA String Mutation Ratio = 0.5 (50% of the DNA string will be mutated) DNA = [ 1001001101 ] new DNA = [ 1101110100 ] x xxx x (x = bit changed)Five randomly chosen bits were changed out of 10.
Elitism: elitism can be enabled or disabled. This option (if enabled) will ensure that the best solutions (for each objective) are preserved during the evolution.
Random Generator Seed: the modification of this value allows the execution of different runs starting from the same initial population. The Seed is an integer number used for sequence repeatability. If two MOGA Sequences are evaluated with the same seed, they will generate and return identical sequences of numbers. If the seed value is 0, the sequence is automatically seeded to a value based on the machine clock.
Note:
The number of concurrent designs evaluation can be set in the Run Project Dialog.
The number of initial designs in the DOE table should be greater (or at least equal) than the number of concurrent designs.
