Distances using Domain-Independent Planning

The use of planning for computing genome edit distances was suggested by Erdem and Tillier in 2005, but to date there has been no study of how well domain-independent planners are able to solve this problem. This paper reports on experiments with several PDDL formulations of the problem, using several state-of-the-art planners. The main observations are, first, that the problem formulation that is easiest for planners to deal with is not the obvious one, and, second, that plan quality – in particular consistent and assured plan quality – remains the biggest challenge. Introduction For several decades now, the comparative study of biologica l sequence data (i.e., DNA or protein amino acid sequences) has played an increaing role in determining the evolutionary history of life on Earth (e.g., Page and Holmes 1998). While early studies examined differences in the nucleotide sequences of individual genes, more recent work has also examined differences in the arrangement of genes across a whole genome (Sankoff et al. 1992; Boore and Brown 1998; Snel, Huynen, and Dutilh 2005). A computational problem that arises in this context is the calculation of edit distances between sequences: that is, t he number of “mutation events” required to transform one sequence into another. The edit operations considered depends on the type of sequence. For DNA sequences, they are typically insertion, deletion or substitution of indiv i ual nucleotides. Minimising this edit distance is the famou s sequence alignment problem. For genome rearrangement, the edit operations usually assumed are inversions and tran spositions (and combined transposition and inversion, call ed transversions) of subsequences within the genome, plus insertion/duplication and deletion if needed to account for d ifferences in gene content. Erdem and Tillier (2005) suggested that the calculation of genome edit distance under these operations can be considered as a planning problem: The arrangement of genes is the state, and each edit operation is an action that modifies it. These actions may furthermore be assigned different costs, to account for different relative frequencies with which th ey are assumed to occur in the organisms studied. They developed a solution to the problem based on TLPlan, which was later refined by Uras and Erdem (2010). However, the system developed by Erdem and colleagues is a plain depth-first state-space search guided by entirely domain-specific heuristics. Although the problem is formulated in a planning language, the solver makes essentially n o use of this. Consequently, there has been no comprehensive study of how well state-of-the-art domain-independent pla nners are able to solve the genome edit distance problem. 1 In this paper, I discuss alternative encodings of the genome edit distance problem in PDDL, and evaluate the ability of some current domain-independent planners to solve the resulting formulations. My aim is not to show that domain-independent planners are better than Erdem et al.’s system (quite unlikely, given the extent to which it is tailored to the domain), but to find out exactly how well – or badly – such planners perform on this problem, and what shortcommings of these planners may need to be addressed to improve their usefulness. Phylogenetic Reconstruction and Genome Edit Distance A phylogeny (evolutionary tree) is a tree where the leaf nodes represent living taxa (species or species groups) and interior nodes the ancestral organisms from which they have evolved. Typically, these ancestors are long extinct. The problem of phylogenetic reconstruction is to find the best, i.e., most plausible, such tree, based on observed characte rs of the living taxa. In a genome-based phylogenetic analysis , these characters are the content and arrangement of genes in the organisms genomes. What constitutes a “most plausible” phylogeny depends on what criteria are assumed. A common criterion is parismony, i.e., preferring trees with the smallest total amount of change. Criteria such as maximum likelihood can also be used, but depend on additional assumptions about the evolutionary process. Finding a maximum parsimony phylogeny based on genome rearrangement events is computationally hard. Distance-based methods simplify the problem by divding it into two steps: The first is to compute a matrix of pair-wise distances between the taxa, and the second to construct a tree with minimum total distance. Optimal tree constructio n Erdem and Tillier report that they formulated a highly simplified version of the problem in PDDL, and had little success solving it using HSP and SATPLAN.