Fabian Becker
b1553f3088
Switched from Ant to Maven. Usage: - Install Maven 3.x - Enter directory with pom.xml - Type mvn compile - Enjoy!
56 lines
2.3 KiB
HTML
56 lines
2.3 KiB
HTML
<html>
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<head>
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<title>Generic Constraints</title>
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</head>
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<body>
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<h1 align="center">Generic Constraints</h1>
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<br>
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<p>To represent generic constraints on real-valued functions, this class can parse
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String expressions in prefix notation of the form:
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<blockquote>
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<expr> ::= <constant-operator> | <functional-operator> "(" <arguments> ")"<br>
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<arguments> ::= <expr> | <expr> "," <arguments>
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</blockquote>
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</p>
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Setting the <b>constraint string</b>:
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Constant operators have an arity of zero. Examples are:<br>
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(pi,0) (X,0) (1.0,0)<br>
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Functional operators have an arity greater zero. Examples are:<br>
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(sum,1) (prod,1) (abs,1) (sin,1) (pow2,1) (pow3,1) (sqrt,1) (neg,1) (cos,1) (exp,1)<br>
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(+,2) (-,2) (/,2) (*,2)<br>
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<p>
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Additionally, any numerical strings can also be used; they are parsed to numeric constants. The literal <i>n</i>
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is parsed to the current number of problem dimensions.<br>
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Notice that only the <i>sum</i> and <i>prod</i> operators may receive the literal X as input, standing
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for the full solution vector. Access to single solution components is possible by writing <i>x0...x9</i>
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for a problem with 10 dimensions.
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</p>
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<p>
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Thus you may write <font face="Courier">+(-(5,sum(X)),+sin(/(x0,pi)))</font>
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and select 'lessEqZero' as relation to require valid solutions to fulfill 5-sum(X)+sin(x0/pi)<=0.<br>
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</p>
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<p>
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Typical <b>relations</b> concerning constraints allow for g(x)<=0, g(x)==0, or g(x)>=0 for
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constraint g. Notice that equal-to-zero constraints are converted to g(x)==0 <=> |g(x)-epsilon|<=0 for
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customizable small values of epsilon.
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</p>
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<p>
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The <b>handling method</b> defines how EvA 2 copes with the constraint. Simplest variant is an
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additive penalty which is scaled by the penalty factor and then added directly to the fitness
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of an individual. This will work for any optimization strategy, but results will depend on
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the selection of penalty factors. Multiplicative penalty works analogously with the difference of
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being multiplied with the raw fitness.<br>
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In the variant called specific tag, the constraint violation is stored in an extra field of any
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individual and may be regarded by the optimization strategy. However, not all strategies provide
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simple mechanisms of incorporating this specific tag.
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</p>
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</body>
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</html> |