Adaptive fitness functions have led to very successful evolutionary algorithms (EA) for various types of constraint satisfaction problems (CSPs). In this paper we consider one particular fitness function adaptation mechanism, the so called Stepwise Adaption of Weights (SAW). We compare algorithm variants including two penalty systems and we experiment with extensions of the SAW mechanism utilizing a refinement function and a decay function. Experiments are executed on binary CSP instances generated by a recently proposed method (method E). This new method for generating problem instances allows one single hardness parameter and is well suited to study algorithmic behavior around the phase transition. The results show that the original version of the SAW mechanism is very robust and has a comparable or better performance than the extended SAW mechanisms.
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