Configuring the Adaptive Simulated Annealing (ASA) Technique

Max Num of Generated Designs

This number does not account for the five initial designs used by the algorithm to determine the starting temperature of the cost function. The value type is integer. The default value is 10000. Other possible values are

\geq 1

.

Number of Designs for Convergence Check

A simple convergence check is implemented in the ASA algorithm. The cost value of each accepted design is compared to the cost value of the best design found so far. If the two values differ by less than Convergence Epsilon for N consecutive times (where N is the Number of Designs for Convergence Check), optimization terminates. The value type is integer. The default value is 5. Other possible values are

\geq 2

.

Convergence Epsilon

The Convergence Epsilon is the maximum difference of cost value between each accepted design and the best design found so far, to indicate that optimization is converged. The convergence criterion must be satisfied for N consecutive times (where N is the Number of Designs for Convergence Check). The value type is real. The default value is

1 \times 10^{- 8}

. Other possible values are

> 0

.

Relative Rate of Parameter Annealing

The relative rate of reduction of parameter temperatures during optimization. Reducing the value down from 1.0 allows the parameter temperatures to stay high for a longer time (more variation within generated designs). Increasing the value up from 1.0 reduces the parameter temperatures more quickly (less variation in the generated designs). The value type is real. The default value is 1.0. Other possible values are

> 0

.

Relative Rate of Cost Annealing

Control the relative rate of cost function reduction during optimization. Reducing the value down from 1.0 allows the cost temperature to stay high for a longer time (more generated designs are accepted by the algorithm). Increasing the value up from 1.0 reduces the cost temperature more quickly (more generated designs are rejected by the algorithm). The value type is real. The default value is 1.0. Other possible values are

> 0

.

Relative Rate of Parameter Quenching

Parameter quenching is a process of rapid reduction of the parameter temperatures and effectively overrides the slow annealing process and turns it into a fast quenching process. Using quenching considerably reduces the variability of the generated designs, which makes finding a global optimum less likely and greatly increasing chances of convergence to a local optimum. Increasing the value up from 1.0 activates the rapid parameter temperature reduction. Reducing the value down from 1.0 greatly extends the time required to reduce the parameter temperature for convergence. Use quenching only if you want to considerably accelerate or decelerate the convergence of the algorithm. The value type is real. The default value is 1.0. Other possible values are

> 0

.

Relative Rate of Cost Quenching

Cost quenching is a process of rapid reduction of the cost temperatures and effectively overrides the slow annealing process and turns it into a fast quenching process. Using quenching considerably reduces the acceptance probability, reducing the chances of finding a global optimum and greatly increasing the chances of convergence to a local optimum. Increasing the value up from 1.0 activates the rapid cost temperature reduction. Reducing the value down from 1.0 greatly extends the time required to reduce the cost temperature for convergence. Use quenching only if you want to considerably accelerate or decelerate the convergence of the algorithm. The value type is real. The default value is 1.0. Other possible values are

> 0

.

Maximum Number of Failed Designs

The maximum number of consecutive design analysis failures before the algorithm terminates. Because of the random nature of the algorithm, it is possible to generate designs that cannot be handled by the analysis codes. Such occasional failures are ignored by ASA. If the failures become persistent, the algorithm stops executing. The value type is integer. The default value is 5. Other possible values are

\geq 1

.

Init Param Temperature

Extend or reduce the execution time of the algorithm without changing the nature of the search. The value type is real. The default value is 1.0. Other possible values are

> 0

.

Reanneal Parameters

When the algorithm comes to a stagnation point, it may be beneficial to restart the annealing process again using the best design point found so far. If this option is set to yes, ASA employs several criteria to determine when a reannealing of parameters must be performed. One of the criteria is the Number of Generated Designs Before Reannealing. Another criterion is the Number of Accepted Designs Before Reannealing. The most effective criterion is the Minimum Ratio of Accepted Designs for Reannealing. The default setting is yes.

Reanneal Cost Function

When the algorithm comes to a stagnation point, it may be beneficial to restart the annealing process again using the best design point found so far. If this option is set to yes, ASA employs several criteria to determine when a reannealing of cost function must be performed (same criteria as for parameter reannealing). One of the criteria is the Number of Generated Designs Before Reannealing. Another criterion is the Number of Accepted Designs Before Reannealing. The most effective criterion is the Minimum Ratio of Accepted Designs for Reannealing. The default setting is yes.

Num of Des Before Reannealing

When the number of generated designs reaches this value, reannealing of parameter and/or cost function temperatures is performed, if allowed by the previous options. The value type is integer. The default value is 1000. Other possible values are

\geq 1

.

Num of Accept Des Before Reannealing

When the number of accepted designs reaches this value, reannealing of parameter and/or cost function temperatures is performed, if allowed by the previous options. The value type is integer. The default value is 100. Other possible values are

\geq 1

.

Min Ratio of Accept Des for Reannealing

When the ratio of the number of accepted designs to the number of generated designs reaches this value, reannealing of parameter and/or cost function temperatures will be performed, if allowed by the previous options. The value type is real. The default value is

1 \times 10^{- 6}

. Other possible values are

\geq 0

.

Rel Grad Step for Reannealing

During reannealing, parameter temperatures are increased in proportion to their effect on the cost function. To determine the effect of each parameter (design variable) on the cost function, gradients of the cost function are calculated using the finite differencing method. This parameter controls the value of the parameter step used for gradient calculation. The value type is real. The default value is 0.001 (0.1%). Other possible values are

\geq 0

.

Penalty Base

ASA evaluates the quality of a design point using the combined value of the objective function and penalty function. When calculating the penalty function of the design, the penalty base can be used for all designs that violate at least one constraint. This allows the technique to better differentiate feasible designs with a slightly higher objective function from infeasible designs with a slightly lower objective function.

The total penalty function is calculated as follows:

$P e n a l t y = P e n a l t y B a s e + P e n a l t y M u l t i p l i e r \times S u m ({V i o l a t i o n}_{i} \times W_{i} / S_{i}) \land P e n a l t y E x p o n e n t$

where ${V i o l a t i o n}_{i}$ is the $i - t h$ constraint violation value, $W_{i}$ is the corresponding weight factor, and $S_{i}$ is the corresponding scale factor. The penalty base is set to zero if no constraints are violated. The default value is 0.0.

Penalty Multiplier

Increase or decrease the effect of the total constraint violations on the measure of the design quality. The default value is 1000.0.

Penalty Exponent

Increase or decrease the nonlinearity of the effect of the total constraint violations on the penalty function value. The value type is integer. The default value is 2.

Max Failed Runs

Set the maximum number of failed subflow evaluations that can be tolerated by the optimization technique. If the number of failed runs exceeds this value, the optimization adapter will terminate execution. To disable this feature, set this option to any negative value (for example, –1). When this option is set to a negative value, the optimization will continue execution despite any number of failed subflow runs.

Failed Run Penalty Value

The value of the Penalty parameter that is used for all failed subflow runs. The default value is

1 \times 10^{30}

.

Failed Run Objective Value

The value of the Objective parameter that is used for all failed subflow runs. The default value is

1 \times 10^{30}

.

Use fixed random seed

If this option is selected, the random number generator used by the optimization algorithm is seeded using the Random seed value.

If this option is not selected, the random number generator is seeded by using the clock time at the moment of execution.

Random seed value

The random number generator used by the optimization algorithm is seeded using the value specified in the corresponding text box. All executions of the Optimization adapter will use the same sequence of random numbers and, therefore, will produce the same design points. This arrangement is useful for debugging the optimization process when it is necessary to reproduce the same sequence of design points.