Stepwise Adaption of Weights with Refinement and Decay on Constraint Satisfaction Problems

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ABSTRACT 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).

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    ABSTRACT: Evolutionary algorithms have employed the SAW (stepwise adaptation of weights) method in order to solve CSPs (constraint satisfaction problems). This method originated in hill-climbing algorithms used to solve instances of 3-SAT by adapting a weight for each clause. Originally, adaptation of weights for solving CSPs was done by assigning a weight for each variable or each constraint. Here we investigate a SAW method which assigns a weight for each conflict. Two simple stochastic CSP solvers are presented. For both we show that constraint based SAW and conflict based SAW perform equally on easy CSP samples, but the conflict based SAW outperforms the constraint based SAW when applied to hard CSPs. Moreover, the best of the two suggested algorithms in its conflict based SAW version performs better than the best known evolutionary algorithm for CSPs that uses weight adaptation, and even better than the best known evolutionary algorithm for CSPs in general.
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