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The availability and study of haplotype data is of considerable interest to a wide range of areas including general health care, personalized medicine, and pharmacogenetics. The inner workings of contemporary sequencing techniques however imply that genotype data is generated from a chromosome rather than haplotype data. The reconstruction of the latter from this kind of data lies at the heart of the well studied Pure Parsimony Haplotype Inference problem (PPHI). In this paper, we present a proof of concept that a GRASP-based approach for solving PPHI has the potential of yielding an attractive tool that complements existing approaches. The usage of this strategy for solving PPHI is novel. To assess its suitability, we have implemented it in basic form in the novel and freely available HAPLOGRASP approach which we assessed in terms of simulated and real data. Our findings are highly encouraging.