A Parthenogenetic Algorithm for the Founder Sequence Reconstruction Problem

The maximum fragment length (MFL) is an important computational model for solving the founder sequence reconstruction problem. Benedettini et al. presented a meta-heuristic algorithm BACKFORTH based on iterative greedy method. The BACKFORTH algorithm starts with a single initial solution, and iteratively alternates between a partial destruction and reconstruction in order to obtain a final solution. The kind of optimization mechanism, which is based on a single initial solution, may make the performance of the BACKFORTH algorithm sensitive to the quality of the initialization. In this paper, a practical parthenogenetic algorithm PGMFL, which is a populationbased meta-heuristic method, is proposed. The PGMFL algorithm can search multiple regions of a solution space simultaneously. A novel genetic operator is introduced based on the presented heuristic algorithm HF, which takes advantage of look-ahead mechanism and some potential information, i.e., the proportions of 0 and 1 entries in a column of recombinant matrix and those in the corresponding column of the founder matrix, and some other heuristic information, to compute the column values. The PGMFL algorithm can get fewer breakpoints and longer fragment average length than the BACKFORTH algorithm, which are proved by a number of experiments.