HFSS15: Advanced Genetic Algorithm Optimizer Options

The Genetic Algorithm (GA) search for Optimization analysis is an iterative process that goes through a number of generations. In each generation some new individuals (Children / Number of Individuals) are created and the so grown population participates in a selection (natural-selection) process that in turn reduces the size of the population to a desired level (Next Generation / Number of Individuals).

If you select the Genetic Algorithm for an Optimization analysis, a Setup button is enabled on the Setup Optimization page.

1. Click the Setup button to open the Advanced Genetic Algorithm Optimizer Options dialog.

2. Select the Stopping Criteria. Any of the three following, or any combination of these can be selected.

• Maximum number of generations. If checked, this enables a value field.

• Elapsed time. If checked, this enables a drop down menu with times ranging from five minutes to two weeks.

• Slow convergence.

3. Specify the Parents.

The first step towards mating is a selection process that determines the participating individuals. Potential parents are selected from the Current Generation. This is a set of individuals that is always a subset of the current generation.

• Number of individuals value field -- specify the number of parents for the optimizer to use. You can set the Number of Individuals to less than or equal to the size of the "Current Generation". One reason to consider fewer parents than the possible maximum is to steer the GA towards improvement by selecting the better portion of the current generation to be able to mate.

• Roulette selection checkbox -- if checked, this enables the Selection pressure value field. This number defines how many times more probable is the selection of the best individual over the worst individual in an elementary spin of the roulette wheel.

4. Specify the Mating pool.

The Mating pool is created by selecting randomly from the parents, but with each selection, the parent gets "cloned" so it can be selected again and again.

• Number of individuals field -- specify the number individuals to include in the mating pool.

• Reproduction setup-- this button opens the Genetic Algorithm Optimizer Reproduction Setup dialog.

5. Click the Reproduction setup button for the dialog to specify the Crossover setup, and the Mutation setup.

The crossover and mutation operator have different roles: Crossover mixes "features" of the parents in a new combination, while mutation slightly alters the "features" of the individuals. Both need to be present in a GA. The crossover is a way to discover new combinations while the mutation acts as a local search or fine-tuning step. Mutation also keeps diversity in a population, which is a must for GA.

The crossover operator has two steps. It first alters the variable values of the parents according to a distribution. This tends to produce one child that looks a lot like one parent, and one child that looks a lot like the other parent. Next, some of the variable values of the two children can be exchanged in order to achieve more variation.

For crossover there are four possible parameters.

a. Individual Crossover Probability determines, for each pair in the mating pool, the probability that their features will be mixed. Usually, this probability should be close or equal to one. If you set it to less than one, some parents will produce two children which are exact clones of the parents. This means that some children inherit all the features of their parents unchanged.

b. Parents often have multiple variables. If the parent is a candidate for mixing, the Variable Crossover Probability determines, for each variable, the probability of mixing. This is usually set high to ensure that most or all variables mix.

c. Variable Exchange Probability: After the slight change in the variable values has been made, the crossover operation is also able to exchange the values of the variables between the two children that are being constructed. The Variable Exchange Probability governs the likelihood of exchange of any variable.

d. Mu is a general parameter defining the sharpness of the distribution that might be used for the Variable Crossover Probability. Mu should be greater than one. There is no theoretical upper limit, but we recommend not exceeding 30.

6. Select one of the four Crossover types from the drop-down menu.

The crossover type selected affects the options available.

7. Select the Mutation type--this can be one of three types, which you select from a drop-down menu.

• Uniform Distribution

• Gaussian Distribution

• Polynomial Mutation.

8. For the selected mutation type, set the following parameters:

• Uniform Mutation Probability: If this is more than zero (recommendation is to have still a small probability here), then there will be some children whose features are simply a completely random design (design variables randomly selected over the domain).

• Individual Mutation Probability controls, for each child, the likelihood of a mild mutation.

• Variable Mutation Probability. If the child will be mutated, this probability controls at the variable level the likelihood of a mutation of the variables.

• Standard Deviation is the standard deviation of the selected distribution that is being used for the mutation and it is measured relatively to the optimization-domain.

9. When you have completed the Reproduction setup in the Genetic Algorithm Optimizer Reproduction Setup dialog, click OK to close it and return to the Advanced Genetic Algorithm Optimizer Options dialog.

10. In the Advanced Genetic Algorithm Optimizer Options dialog, specify the children as a Number of Individuals.

11. Set the Pareto Front value.

This is the number of the very best individuals (identified relative to the cost function) to keep for future generations.

12. Set the Next Generation parameters. The Next Generation is selected from the Parents, the children, and the Pareto front.

• Number of individuals value field -- specify the number of individuals to survive to form the next generation for the optimizer to use.

• Roulette selection checkbox -- if checked, this enables the Selection pressure value field. This number defines how many times more probable is the selection of the best individual over the worst individual in an elementary spin of the roulette wheel.

13. Click OK to accept the settings for the Genetic Algorithm and to close the dialog.