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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.



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


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


Name Description
- -


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



Source Code

ToDo:Link to SVN


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.