Solving the all-interval series problem

Abstract

Although Boolean satisfiability (abbreviated as SAT) is a sub-field of constraint programming (CP), the former states and solves problems as a black-box approach, whereas the latter aims at being tunable and programmable. Although many researches bridging SAT and CP have been provided, surprisingly, only few researchers have compared the SAT and CP approaches on a particular problem. This paper studies how to solve the all-interval series problem through both approaches. We will show that by using a state-of-theart SAT solver and an appropriate SAT encoding the SAT approach obtains a significantly higher performance over the CP approach. Furthermore, we also provide the state-of-theart result for several all-interval series instances.

Constraint-directed search for all-interval series

“…In this approach, the 'first-fail' and 'indomain-min' strategies are used respectively as variable and value selection heuristics. As in [18], for experiments, we use the CP solver opturion CPX [2] although the ILog solver [1] was used in [12]. The CP approach could generate all RAIS of size up to 20.…”

“…SAT-Based Approach. Using AtMostOne and AtLeastOne constraints, the SATbased approach in [18], denoted by SAT here, provides an efficient SAT encoding of the RAIS problem. It then uses the SAT solver named Clasp [11].…”

“…TDLDSD, LDRDSD, TDRDSD, TDLDRD), all properties and no properties (no lemmas NL). The NL version is actually the one used in [18]. We use the CP solver opturion CPX [2] to run these versions of the CP approach.…”

“…In Table 1, we further compare the best results obtained by the versions listed above with that of the SAT approach [18]. Notice that the best results obtained from the CP versions with auxiliary constraints (denoted by aCP) overall are significantly worse than the SAT approach.…”

“…These include local search (LS) for satisfiability (SAT) [13,22,4] and constraint programming (CP) [23,20,12,7]. Using a reformulated definition [12], a very recent SAT-based approach in [18] can generate all solutions of size up to 24 given one week time. Since the search space to be explored for the AIS problem is of factorial size and the total number of solutions increases about 2 to 3 times with 1 increase in n [3], constraint-directed search algorithms developed on generic platforms do not scale well.…”