Handling Constraints

報告者 : 王敬育

Many researchers investigated Gas based on floating point representation but the optimization problems they considered were defined on a search space:

i.e., each variable Xk was restricted to a given interval

The domain D is defined by ranges of variables

for a given

• Example: p123

• We consider a particular class of optimization problems which are defined on a convex domain; these can be formulated as follows:

Optimize a function f(X1,X2…Xq), subject to the following sets of linear constraints:

The developed system (GENOCOP for GEenetic algorithm for Numerical Optimization for COnstrained Problems)

It combines some of the ideas seen in the previous approaches, but in a totally new context. The main idea behind this approach lies in:

(1) An elimination of the equalities present in the set of

constraints

(2) Careful design of special genetic operators, which guarantee to keep all chromosomes within the constrained solution space.

Operators

We describe six genetic operators based on floating point representation, which were used in modified version of the GENOCOP system. The first three are unary operators. The other three are binary.

•

• Boundary mutation

This operator requires also a single parent X and produces

a single offspring X’. The operator is a variation of the

uniform mutation with

where being either left(k) or right(k), each with equal

probability.

•

Non-uniform mutation

Arithmetical crossover

1

Testing GENOCOP • See p130 ~ p133

following parameters for all experiments:

pop_sizes = 70

k = 28(number of parents in each generation ; classification step)

b = 2(coefficient for non-uniform mutation)

Denote the GENOCOP II system as the method #4

GENOCOP III

This method incorporates the original GENOCOP system, but also extends it by maintaining two separate populations.

The first population Ps consists of so-called search points which satisfy linear constraints of the problem.

The second population Pr consists of so-called reference points; these points are fully feasible, they satisfy all constraints.