Optimization techniques

You have the choice between two algorithms in order to solve the problem. The specific attributes you must set for these algorithms is described here.

NLPQL

NLPQL algorithm for optimization

When NLPQL algorithm is selected the properties shown below are displayed.

Figure 86: NLPQL properties

• Print mode

NLPQL algorithm Print mode

This property determines the level of output information displayed during execution. Three levels are available:

No print

Diagnostic

Verbose

• Relative gradient step

NLPQL algorithm Relative gradient step

The NLPQL algorithm needs Simcenter Amesim to compute the gradients of the objective function and constraints in all directions available in the design space. Each input involved in the optimization process is a direction. These gradients are computed using the finite difference method. To explain this, let us take an example. Imagine that the objective function is where x and y are the two input parameters. The gradient is

The above approximation is used to compute the gradients. The relative gradient step is the δ quantity. A run is performed with x = x0 and y = y0 to determine f(x0, y0). Then two further runs are needed to compute f(x0+δx0, y0) and f(x0, y0+δy0). This is called an iteration NLPQL algorithm iteration . Only the first run is stored in the log file. For other points, the computation of the gradient is not needed. In these cases, the iteration consists of one run only. Most of the problems you may encounter regarding algorithm convergence will be related to gradient computation accuracy.

• Desired final accuracy

NLPQL algorithm Desired final accuracy

This is the termination accuracy. It should not be much smaller than the accuracy by which gradients are computed.

Note

The messages that are added with Diagnostic and Verbose mode can only be useful if you have some knowledge about Sequential Quadratic programming (SQP).

Genetic algorithm

The following figure shows the area dedicated to Genetic algorithm settings.

Figure 87: Genetic algorithm properties

The basics of the Genetic algorithm are described in Genetic algorithm.

The properties you can set are explained below:

• Population size Genetic algorithm Population size

This is the number of individuals in the population.

• Reproduction ratio Genetic algorithm Reproduction ratio

This is the percentage of the population which is replaced by new individuals (children) at each iteration.

• Max. number of generation This is the number of reproduction cycles to perform.

• Mutation probability Genetic algorithm Mutation probability

The mutation probability is only used for discrete parameters. It represents the probability for each element of the population of having its discrete parameters mutated.

• Mutation amplitude This is a real number which must be between 0 and 1. Mutation consists in adding noise to parameters of a specific individual. The mean value of this noise is 0. This real value is used to compute the standard deviation of this noise. If this value is α, the noise standard deviation for a parameter is

In practice, if you set a value near 0, the speed of convergence is likely to increase. On the other hand if you set a value near 1, there is more design exploration and thus there is less chance that the algorithm will converge towards a local optimum.

• Seed Genetic algorithm Seed

Genetic algorithms are based on the use of random number generation. Simcenter Amesim implementation of this algorithm uses a pseudo-random number generator. This means that if you execute the algorithm twice without changing the settings, you will get exactly the same results. If you change only the seed values, then the starting points will be completely different as well as the randomly generated numbers.

Here are some rules to keep in mind when setting up Genetic algorithms:

• The number of runs that will be performed with your settings can be computed by applying the following formula:

where N is the population size, r is the reproduction ratio and G is the number of generations.

• The population size should be chosen according to the number of parameters. Experiments show that population size ≥ 4.5 x number of parameters often gives good results.

• A high reproduction ratio often leads to fast convergence but is also likely to lead to a local convergence. A reproduction ratio between 50% and 85% often gives good results.

• The number of generations to set depends on the number of runs you are ready to accept in term of calculation time but it must be greater than 10 to get relevant results