Large neighbourhood search algorithms for the founder sequence reconstruction problem

The reconstruction of founder genetic sequences of a population is a relevant issue in evolutionary biology research. The problem consists in finding a biologically plausible set of genetic sequences (founders), which can be recombined to obtain the genetic sequences of the individuals of a given population. The reconstruction of these sequences can be modelled as a combinatorial optimisation problem in which one has to find a set of genetic sequences such that the individuals of the population under study can be obtained by recombining founder sequences minimising the number of recombinations. This problem is called the Founder Sequence Reconstruction Problem. Solving this problem can contribute to research in understanding the origins of specific genotypic traits. In this paper, we present Large Neighbourhood Search algorithms to tackle this problem. The proposed algorithms combine a stochastic local search with a Branch-and-Bound algorithm devoted to neighbourhood exploration. The developed algorithms are thoroughly evaluated on three different benchmark sets and they establish the new state of the art for realistic problem instances.