Optimization algorithms

The optimization of the solution process varies depending on the optimization algorithm that you select.

Least square algorithm

The least square algorithm minimizes the following modified objective function based on the square of the target errors and design variables changes:

At each optimization iteration, the least square algorithm performs the following steps:

1. It minimizes the objective function with no constraints on the design variables.

2. It fixes the design variables which have exceeded their limits at the respective lower or upper values, or it fixes the least sensitive design variables if you selected the Auto-filter Design Variables check box in the Optimize dialog box.

3. It minimizes the objective function with no constraints on the design variables on the reduced set of design variables.

4. It repeats steps 2 and 3 until no design variable exceeds their bounds.

5. It outputs the target errors and design variable values for the next optimization iteration.

The optimization with the least square algorithm stops when one of the following conditions is met:

• The maximum number of iterations is reached.

• The minimum improvement is reached.

• There is no improvement in the total error for five consecutive iterations.

• All design variables have reached either their lower or upper bounds.

• No more design variables can changed. This condition can be met only when you select the Auto-filter Design Variables check box in the Optimize dialog box.

Even though the minimum found might not be a global minimum, especially for a large number of targets, this algorithm converges extremely quickly in comparison to the two other algorithms.

Steepest descent algorithm

The steepest descent algorithm used by the Model Update solution process is a variation of the steepest descent algorithm as it is commonly defined in scientific literature. Instead of descending in the direction of the negative gradient, it descends in the negative direction of the largest component of the gradient.

At each optimization iteration, the steepest descent algorithm performs the following steps:

1. It determines the objective function variation caused by a change to each design variable using the design variable sensitivities.

2. It identifies the design variable that yields the largest improvement in the objective function when changed by the specified step size.

3. It changes the value of the identified design variable by the step size keeping the value inside the bounds.

4. It repeats steps 1 through 3 until one of the following conditions is met:It reaches the specified maximum number of steps.All design variables reach their limits.No further improvement is found for the specified step size.

5. It outputs the target errors and design variable values for the next optimization iteration.

The optimization with the steepest descent algorithm stops when one of the following conditions is met:

• The maximum number of iterations is reached.

• The minimum improvement is reached.

• There is no improvement in the total error for five consecutive iterations.

• All design variables have reached either their lower or upper bounds.

Genetic algorithm

The genetic algorithm minimizes the objective function based on techniques inspired by evolutionary biology. It represents a heuristic global search method. NOTE

The design variable linear range parameter also applies to each iteration performed with the genetic algorithm. Therefore, although the genetic algorithm performs a global search at each single iteration, this does not imply that the global optimum design point is found for the entire range of design variables after all iterations.

The implementation is based on the PIKAIA genetic algorithm engine. NOTE

At each optimization iteration, the genetic algorithm performs the following steps:

1. It generates the initial population. Each individual of this population is a random design point bounded by the design variable linear range and the lower and upper design variable bounds.

2. It calculates the fitness of each individual using the objective function.

3. It generates the population of the next generation by virtually mating the genes (numerical digits) of two individuals through mutation and cross-over. The probability of a specific individual to be chosen depends on its fitness. The fittest individuals are involved more often in breeding operations.

4. It repeats steps 2 and 3 for the total number of generations.

5. It outputs the best target errors and design variable values from all generations for the next optimization iteration.

Due to the intrinsic quasi-random nature of genetic algorithms, the total error is not guaranteed to decrease between two consecutive optimization iterations.

The optimization with the genetic algorithm stops when one of the following conditions is met:

• The maximum number of iterations is reached.

• There is no improvement in the total error for five consecutive iterations.

This algorithm always cycles over all iterations.

Look up more details

Model reduction in a SOL 200 Model Update solution

Reduced model sensitivities in SOL 200 Model Update solution

Computation of normal modes

Computation of frequency sensitivities

Computation of mode shape sensitivities

Optimization objective function

Model update references

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Optimization algorithms, Simcenter 3D 2021.1 Series

© 2020 Siemens

Goldberg, D.E., “Genetic Algorithms in Search, Optimization, & Machine Learning”, Addison-Wesley, 1989.

Davis, L., “Handbook of Genetic Algorithms”, Van Nostrand Reinhold, 1991.

Charbonneau, P., “An introduction to genetic algorithms for numerical optimization”, NCAR Technical Note TN-450+IA, April 2002.

Charbonneau, P., “A User's Guide to PIKAIA 1.0", NCAR Technical Note TN-418+IA, December 1995.

Charbonneau, P., “Release Notes for PIKAIA 1.2", NCAR Technical Note TN-451+STR, April 2002.

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });