coliny_ea

Evolutionary Algorithm

Topics

package_scolib, package_coliny, global_optimization_methods

Specification

• Alias: None

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		population_size	Set the population size
Optional		initialization_type	Specify how to initialize the population
Optional		fitness_type	Select fitness type
Optional		replacement_type	Select a replacement type for SCOLIB evolutionary algorithm ( coliny_ea)
Optional		crossover_rate	Specify the probability of a crossover event
Optional		crossover_type	Select a crossover type
Optional		mutation_rate	Set probability of a mutation
Optional		mutation_type	Select a mutation type
Optional		constraint_penalty	Multiplier for the penalty function
Optional		solution_target	Stopping criteria based on objective function value
Optional		seed	Seed of the random number generator
Optional		show_misc_options	Show algorithm parameters not exposed in Dakota input
Optional		misc_options	Set method options not available through Dakota spec
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods
Optional		convergence_tolerance	Stopping criterion based on objective function or statistics convergence
Optional		max_function_evaluations	Number of function evaluations allowed for optimizers
Optional		scaling	Turn on scaling for variables, responses, and constraints
Optional		model_pointer	Identifier for model block to be used by a method

Description

Evolutionary Algorithm

See the page :ref:`topic-package_scolib` for important information regarding all SCOLIB methods

coliny_pattern_search supports concurrency up to the size of the population

The random seed control provides a mechanism for making a stochastic optimization repeatable. That is, the use of the same random seed in identical studies will generate identical results. The population_size control specifies how many individuals will comprise the EA’s population.

The initialization_type defines the type of initialization for the population of the EA. There are three types: simple_random, unique_random, and flat_file. simple_random creates initial solutions with random variable values according to a uniform random number distribution. It gives no consideration to any previously generated designs. The number of designs is specified by the population_size. unique_random is the same as simple_random, except that when a new solution is generated, it is checked against the rest of the solutions. If it duplicates any of them, it is rejected. flat_file allows the initial population to be read from a flat file. If flat_file is specified, a file name must be given.

The fitness_type controls how strongly differences in “fitness” (i.e., the objective function) are weighted in the process of selecting “parents” for crossover:

• the linear_rank setting uses a linear scaling of probability of selection based on the rank order of each individual’s objective function within the population

• the merit_function setting uses a proportional scaling of probability of selection based on the relative value of each individual’s objective function within the population

The replacement_type controls how current populations and newly generated individuals are combined to create a new population. Each of the replacement_type selections accepts an integer value, which is referred to below as the replacement_size.

• The random setting creates a new population using (a) replacement_size randomly selected individuals from the current population, and (b) population_size - replacement_size individuals randomly selected from among the newly generated individuals (the number of which is optionally specified using new_solutions_generated) that are created for each generation (using the selection, crossover, and mutation procedures).

• The chc setting creates a new population using (a) the replacement_size best individuals from the combination of the current population and the newly generated individuals, and (b) population_size - replacement_size individuals randomly selected from among the remaining individuals in this combined pool. The chc setting is the preferred selection for many engineering problems.

• The elitist (default) setting creates a new population using (a) the replacement_size best individuals from the current population, (b) and population_size - replacement_size individuals randomly selected from the newly generated individuals. It is possible in this case to lose a good solution from the newly generated individuals if it is not randomly selected for replacement; however, the default new_solutions_generated value is set such that the entire set of newly generated individuals will be selected for replacement.

Note that new_solutions_generated is not recognized by Dakota as a valid keyword unless replacement_type has been specified.

Expected HDF5 Output

If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5:

• Best Parameters

• Best Objective Functions (when objective_functions) are specified)

• Best Nonlinear Constraints

• Calibration (when calibration_terms are specified)

Theory

The basic steps of an evolutionary algorithm are depicted in Figure 5.2.

image html ga.jpg “Figure 5.2 Depiction of evolutionary algorithm” image latex ga.eps “Depiction of evolutionary algorithm” width=10cm

They can be enumerated as follows:

1. Select an initial population randomly and perform function evaluations on these individuals

2. Perform selection for parents based on relative fitness

3. Apply crossover and mutation to generate new_solutions_generated new individuals from the selected parents

• Apply crossover with a fixed probability from two selected parents

• If crossover is applied, apply mutation to the newly generated individual with a fixed probability

• If crossover is not applied, apply mutation with a fixed probability to a single selected parent

4. Perform function evaluations on the new individuals

5. Perform replacement to determine the new population

6. Return to step 2 and continue the algorithm until convergence criteria are satisfied or iteration limits are exceeded