Documentation/Modules/ConstraintHandler

Summary

Some optimization problems define objectives as well as constraints.

For example, one can set for the optimization problem ProblemTruss the weight of the truss to be minimized, while a constraint is set on the maximum stress and displacement of the truss.

This module aggregates objectives and constraints into a single output.

Properties

General

Algorithm	deterministic (as no gradient handling is implemented)
Design Variables	continuous variables, discrete or mixed variables are possible.
Objectives	any number
Constraints	any number
Boundaries	not affected
Initial Search Region	not affected
Typical X	not affected
Initialization	not required

Connections

Starting at his module	One connection of type optimization
Ending at this module	One connection of type optimization

Actions

Name	Description
-	-

Options

The options are currently described as "pop-up help".

Module Description

The result of an evaluation of a solution may contain objective values f and constraint values g:

While bjectives are to be minimized (min(f)), constraints are to be fulfilled (g =< 0).

0. no constraint handling

This option turns off the constraint handling. Objective values and constraints are not changed.

1. delete constraints

Deletes all constraints. This can be used if the goal is to minimize the objective function(s) only. The objective functions are not changed.

2. Penalty method

All objective function values are summed. All violated constraints (i.e. the constraint value is >= 0) are summed and multiplied with a penalty factor p:

 output = sumi(fi) + sumj(max(gj,0))*p

Increasing the penalty factor p puts more weight on the constraints compared to the objectives.

3. Penalty method

This algorithm works only for population based search methods such as CMA-ES. There are 3 steps

 a. All objective function values are summed: sumi(fi)
 b. All violated constraints (i.e. the constraint value is >= 0) are summed: sumj(max(gj,0))
 c. Ranking of the solutions according to the Stochastic Ranking (1)

Usage

-

Source Code

ToDo:Link to SVN

References

(

1

) T. P. Runarsson and X. Yao, "Stochastic Ranking for Constrained Evolutionary Optimization", IEEE Transactions on Evolutionary Computation, Vol. 4, No. 3, pp. 284-294, Sep. 2000.